woensdag 12 september 2007

(dutch article`s) Equity en het belang om verder te leren!

2 Artikelen die perfect op elkaar aansluiten over Equity en het belang om verder te leren in poker.

volg de reacties op het forum voor nog meer interesante stof.
Het artikel van Leroy:
http://www.pokerinfo.nl/Topic709007-617-1.aspx
Ik heb mezelf in het verleden vaak afgevraagd wat ik beter moest doen om hogerop te komen in poker. Ik keek dikwijls omhoog naar de betere spelers in de hoop iets te leren waardoor ik antwoord kon krijgen op die vraag. Nu ik een aantal jaren verder ben en een stuk beter ben gaan spelen, lijkt het me niet meer dan eerlijk dat ik die vraag eens beantwoordt. Niet zozeer voor de Leroy van een paar jaar geleden, die zo graag antwoord had gewild op die vraag. Maar voor de mensen die nu in zijn schoenen staan en net zoals hem hoopvol omhoog kijken voor een antwoord.

In twee artikelen bespreek ik vijf lessen die ik gaandeweg heb geleerd en beschouw als mijlpalen in mijn pokerontwikkeling. Hoewel het onwaarschijnlijk is dat ik met het delen van deze lessen anderen in één keer op een hoger niveau zal tillen, is het wel mijn intentie om beginnende spelers te laten zien in welke richting ze zich moeten proberen te ontwikkelen.


Breek los van de vuist regels
Vuistregels zijn waarschijnlijk even gevaarlijk in poker als ze nuttig zijn. Aan de ene kant kunnen ze een verdwaalde speler houvast bieden in complexe situaties. Aan de andere kant kunnen ze een mentale luiheid tot gevolg hebben die veel geld kan kosten. Het grootste probleem met vuistregels doet zich voor als mensen situationele factoren niet meer meenemen en prat gaan op vuistregels.

Op pokerfora vind je dagelijks een grote hoeveelheid voorbeelden van verkeerd gebruik van vuistregels. Zoals spelers die altijd continuation-betten (i.e., de flop betten als je preflop de agressor bent geweest). Of spelers die bepaalde handen altijd spelen ongeacht de situatie. Daarvoor hebben ze vaak verschillende redenen. Soms vinde ze dat hun hand sterk genoeg is voor een raise, omdat het te weak is om te folden of omdat je toch wel implied odds hebt.

Van Seven Card Stud heb ik de situationaliteit van Poker Situaties leren waarderen. Beslissingen op de eerste inzet ronde van Seven Card Stud (3rd street) waren daarvoor een geweldig inzicht. Expert beslissingen op 3rd street zijn namelijk zo afhankelijk van situatie dat het bijna niet meer nodig is om je spel te variëren.

Onlangs nog postte er iemand een TT hand die hij three-handed speelde. De button raisete en de SB re-raisete. De poster wist dat de Button en SB met een groot scala van handen zouden raisen in deze situatie. TT was een te sterke hand om preflop weg te leggen opperden sommigen.

Als we de vuistregel echter loslaten zien we dat callen ervoor zorgt dat de TT hand nogal transparant wordt, waardoor de tegenstander in de hand in een erg voordelige situatie zou komen in een erg grote pot. Tevens mogen we er rekening mee houden dat post flop beslissingen vaak lastig worden, als we veel actie krijgen op lage flops of op flops met kaarten hoger dan een T. Misschien dat een fold dan toch niet zo slecht is, ook al is het slechts 3 handed.

Een ander voorbeeld is als spelers met suited connectors uit positie een preflop raise callen. Vaak redeneren ze als volgt: De agressor raisete minder dan 10% van zijn stack, dus als ik hit, dan kan ik genoeg winnen om deze hand winstgevend te spelen.
Maar als we de vuistregel loslaten, dan zien we dat we ons misschien vergissen.

Ten eerste hitten we maar zelden een made-hand. En als we die hitten is dat vaak een zwak paar of een monster op een gevaarlijk board (zoals een 3 flush board of straight board). Dus we zullen erg vaak als we spelen met een draw of zwak paar komen te zitten.

Ten tweede zitten we uit positie post flop. Zeker voor het spelen van en value halen met draws is dat erg lastig. Je moet al snel een semi-bluffen en op die manier een grote pot bouwen. En dat met het nadeel dat je elke straat als eerste moet handelen. Daarbij komt kijken dat je niet per se afbetaald krijgt als je jouw draw of monster hit. Die kaarten kunnen nogal de actie doden. Misschien dat die implied odds toch niet zo goed zijn als ze lijken.


Poker draait om Equity
Veel mensen zijn bezig met allerlei zaken in poker, behalve de zaken waar het echt om draait, en waar het echt om draait is equity (i.e., het percentage van de pot wat jouw hand gemiddeld waard is).

Veel mensen raisen bijvoorbeeld om ‘te weten waar ze staan’, of om ‘hun hand te beschermen’. Maar ze houden geen rekening met hun equity tegen de hand ranges van hun tegenstanders wanneer deze bijvoorbeeld gebet hebben of gecalled hebben. Het kan namelijk prima zou zijn dat je na gebet of geraised te hebben, helemaal geen equity in de pot overhoudt omdat jouw tegenstander al zijn zwakkere handen heeft gefold.

Het belang van equity leerde ik indirect in Sit and Go’s (een-tafel tournooien). Als de blinds in tournooien hoog worden ten opzichte van jouw stack, dan heb je eigenlijk geen keus meer dan all-in te gaan of te folden. Callen of normaal raisen zit er niet meer bij. Wanneer je dan all-in moet gaan kan je aardig benaderen door equity berekeningen uit te voeren. Door een tijd lang op een droge en puur wiskundige manier te spelen heb ik het belang van equity in poker geleerd. En die kennis heb ik overgedragen naar No Limit Cash games.

Het resultaat was tweevoudig. Enerzijds leerde ik om een minder emotionele, maar meer analytische benadering voor poker. Het ging immers niet meer om outplayen of als beste de tafels breken. Het ging om equity, en equity was niet romantisch of emotioneel. Nee, equity was saai en rekenkundig.

Anderzijds ging ik inzien dat ik altijd moest letten op handranges, en hoeveel kans mijn hand had om te winnen tegen de hand ranges van mijn tegenstander. Ik zag opeens in dat sommige raises die ik maakte niet goed waren, omdat mijn tegenstanders die raises nog met te weinig handjes callden. Tevens zag ik in dat ik op dezelfde manier verkeerde bets of calls maakte.

Een voorbeeld van zo’n situatie is wanneer je KK preflop reraiset en jouw tegenstander je callt met JJ+, AQs+ en AK. Op een QJT flop heb je dan opeens minder dan 30% equity in de pot. Waar ik voorheen nog wel eens wou vuren hier, check en fold ik nu.

Een ander voorbeeld was dat ik leerde hoe onwaarschijnlijk monster handen vaak zijn ten opzichte van andere mogelijke holdings. Op een board als Ad Qs 6s is een set zo onwaarschijnlijk als je preflop niet gere-raised bent, dat de equity van jouw handen enorm omhoog gaat. Met een hand als AhQh bijvoorbeeld lig je achter tegen AA, QQ, en 66.

Omdat de pot niet gere-raised was en jij een A en Q in je hand hebt, is de kans op AA of QQ verwaarloosbaar klein bijna en 66 kan jouw tegenstander nog maar op 3 manieren hebben (6c6d, 6c6h of 6d6h). Als je hier bet en geraised wordt, moet je je bedenken dat maar 3 waarschijnlijke handen jou beaten en je moet je eens voorstellen hoe makkelijk dat de hand speelbaar maakt. Nu is dit voorbeeld natuurlijk erg duidelijk. Maar het gaat op in bijna alle situaties.



Toch kom je er niet met equity alleen, ondanks het feit dat het erg belangrijk is. Je hebt meer middelen nodig om poker te verslaan. In het volgende artikel zal ik het hebben over de andere 3 lessen die ik heb geleerd. Het zal gaan over het onderscheiden van relevante en irrelevante informatie, creatief zijn en toegeven dat je het niet snapt.



Het artikel van stoep:
http://www.pokerinfo.nl/Topic710670-617-1.aspx

Pokeren leer je zo!

“It takes a minute to learn and a lifetime to master”, is een beroemde uitspraak in de pokerwereld. En het klopt als een bus. De regels van poker zijn betrekkelijk simpel en iedereen kan het spelletje binnen een minuut meespelen. Maar om het spelletje echt te beheersen, dienen er bergen verzet te worden. In dit artikel zal ik enkele leertheorieën uit de psychologie in relatie brengen tot het poker en daarbij valkuilen en aandachtspunten in kaart brengen. Daaruit zal naar voren komen dat écht leren pokeren nog niet zo eenvoudig is en dat men tevens nooit uitgeleerd raakt.



Hoe leren we?

De manier waarop mensen leren of nieuwe informatie tot zich nemen krijgt al enkele tientallen jaren de aandacht van de psychologie. In eerste instantie waren psychologen wantrouwig ten opzichte van processen die zich in het brein afspelen en richtten hun aandacht alleen op waarneembaar gedrag. Wat psychologen opmerkten was dat mensen heel goed konden leren op basis van het directe resultaat van gedrag. (operant conditioneren). Het idee hierachter was dat correct gedrag door de resultaten werd beloond en daardoor vaker zou voorkomen. Tegelijk zou incorrect gedrag door de resultaten worden bestraft en daardoor minder vaak voorkomen. Denk hierbij aan het leren selecteren van starthanden. Je zal snel ondervinden dat AA goeie resultaten oplevert en deze hand vaker gaan spelen. Tegelijkertijd zal je 72o vaker in de muck gaan gooien, omdat je er maar zelden mee wint.

Een andere invalshoek is het leren door observatie. Mensen kunnen nieuwe kennis en vaardigheden aanleren door het gedrag van anderen te kopiëren. Denk bijvoorbeeld aan het leren van een dans of het leren van piano spelen. Het dagelijkse pokerleven is vervult van kopieergedrag. Kijk maar eens hoeveel mensen hun tafelhouding hebben geleerd van de professionals.

Later richtte men zich in de psychologie meer op de processen die zich “in” het brein afspeelden. Dit gaf onder meer het belangrijke inzicht dat men kan leren door inzicht. Dat wil zeggen dat de mens een situatie kan bekijken, beoordelen en overdenken, om vervolgens de juiste handelingen toe te passen.

Valkuilen bij het leren van Poker

Als men deze leermethoden loslaat op het pokeren, dan zien wij gelijk enkele valkuilen. In het poker is het immers mogelijk dat verkeerd gedrag wordt beloond en dat goed gedrag wordt afgestraft. Het directe resultaat is dus geen goede aanwijzing voor het leren pokeren op een winnende manier.

Daarnaast schuilt er ook in het leren door observatie een valkuil. Wie Jamie Gold in High Stakes Poker ziet limpen met J6o, kan op verkeerde ideeën gebracht worden. Of nog erger, er zijn genoeg spelers die mensen zien winnen door 72o hard te raisen en daarom maar besluiten om die ook te gaan raisen. Of spelers die AA gaan limpen omdat ze anderen hard met AA zien verliezen als het geld erin gaat.

Men dient dus niet klakkeloos gedrag van professionals of anderen te kopiëren, maar men dient zelf de theorieën en ideeën achter het poker te begrijpen en toe te passen.

Om dezelfde reden is het ook niet slim om zonder nadenken rijtjes starthanden uit je hoofd te leren. Poker is een spel van situaties. En elke situatie kan om een andere benadering vragen.

Hoe te leren in Poker

Voordat mensen alle vertrouwen in de psychologie opzeggen, moet ik zeggen dat er oplossingen zijn. De problemen met het leren in poker onstaan doordat mensen zich richten op de verkeerde informatie. Ze kijken naar de hoeveelheid geld die iemand op een avond wint of uitsluitend naar de keren waarop een ander succes had. Maar in het poker kan je dus blijkbaar niet uitgaan van het directe resultaat van jouw beslissingen of van die van anderen.

In plaats daarvan moet je jezelf richten op de informatie die er echt toe doet. Je moet je richten op de winstgevendheid van beslissingen. En om die informatie te vinden moet je voorbij de oppervlakte van poker zoeken.

Goed winnend leren pokeren doe je door op de juiste manier de handrange van je tegenstander in te schatten. Je gebruikt daarbij alle informatie die voor handen is. Vervolgens bepaal je jouw equity, door jouw hand af te zetten tegen de handrange van je tegenstander. Op basis van die informatie kies je de actie die jouw winst op de lange termijn maximaliseert (ref. REM-strategie van Flynn en Mehta in Professional No Limit Hold ‘Em, twoplustwo publishing).

Als je goed wilt leren pokeren dien je deze vaardigheden te optimaliseren. Dat kan je doen door boeken te lezen, die je nieuwe inzichten kunnen geven. Daarnaast dien je veel na te denken over je spel en moet je je eigen spel blijven analyseren en verbeteren. Maar bovenal leer je goed pokeren door vooral heel, heel, héél veel te spelen. Door veel te spelen ga je situaties herkennen en is het tevens mogelijk om bepaalde handelingen automatisch te laten verlopen (waardoor je je aandacht op andere informatie kan richten). Al die extra moeite kan er toe leiden dat jij op een betere manier handranges kan inschatten, op een betere manier jouw equity kan bepalen en op een betere manier de juiste actie kan kiezen. En uiteindelijk zal je dan vanzelf een betere speler worden.

Maar dit is geen gemakkelijk proces. Het duiken onder de oppervlakte van poker en uitzoeken naar relevante informatie is een ingewikkeld proces, een proces wat maar weinigen aankunnen. Het is daarom dat er zoveel fishes in poker zijn, de meesten leren nooit hoe ze goed moet leren!

Conclusie

Concluderend kan men stellen dat leren pokeren nog niet zo eenvoudig is. Men kan niet uitgaan van het directe resultaat en men dient zich te richten op de zaken die er echt toe doen; handranges, equity en het maximaliseren van de winst. Daarnaast zien we dat ervaring erg belangrijk is. Leren pokeren is een continu proces, waarin je je hele leven kan blijven verbeteren. Kortom:”Poker, it takes a lifetime to master”.

Stoep

PS Grote dank gaat uit naar Leroy Soesman voor zijn deskundige feedback!



PPS Een bekend post op 2+2 van Zeejustin sluit mooi aan bij dit onderwerp en is zeker de moeite om te lezen. http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=7339473&page=0&fpart=1&

maandag 9 juli 2007

Advanced Thinking and Hand Ranges

By Nick Eisel
Any good poker player knows that there is no such thing as "always" in our game.

One of the many reasons the game is so strategically lucrative is that every hand is unique and every decision has to be weighed against a wide array of factors. This month I want to take a very advanced look at putting a strong opponent on a range of hands and then see how this range of hands changes the "standard" play of a hand into a play that certainly has negative expectation. So, consider yourself warned this article is not for the beginning poker player or even for someone who has just recently switched over to No-Limit Hold'em cash games.

The hand in question happened the other day during one of my usual 12 tabling sessions on PokerStars. The game is $1/$2 No Limit Holdem (9 players) with everyone at the table having around $200 in front of them. Everyone folded to me in the small blind and I was holding 4c 4d. My opponent in the big blind is a very solid thinking player.

I decided to make my usual play in this spot and raise to $6. Whether or not this is the best play against a strong opponent is the topic of another article, but suffice to say that this guy is smart enough that I'm not going to win a big pot off of him if we don't start building it early. There is also a large likelihood of him either folding pre-flop, or calling and folding to the continuation bet I will make on most boards. Since pocket fours doesn't rate to improve that often, the best way to make money with the hand is to be aggressive in a heads up situation.

My opponent surprised me by re-raising to $21 rather quickly and now it's $15 for me to call. Normally I avoid situations like this with a small pair heads-up and out of position, but in this case I decided that it would be hard for my opponent to give up AA, KK, or QQ if he had one of those hands and flopped an over-pair and I flopped a set. I guess the point I'm getting at here is that I felt there was enough implied value in calling here even against a tough opponent and while out of position. Over-pairs or top pair good kicker hold more weight in a blind battle than they would normally.

The flop came Ac Tc Ts and there was $42 in the pot.

Nothing special here, if he had AK or AQ he just got there and I have absolutely no way to ever know where I'm at in this hand without first investing a lot of money. I check with the intention of folding and my opponent checks it back.

The turn came the beautiful 4h giving me a full house.

What to do?

There are a number of lines I can take here to make some money on the hand, but I chose to check and let my opponent bet a weaker hand and then confront him with a raise. After all, he could've checked something like AK on the flop trying to trap me or maybe he'd decide I was bluffing and pay me off. Another option was to check call the turn and then bet out on the river which may induce a call from something like KK, QQ, or JJ that wants to get a showdown on this board.

I checked and my opponent bet $20. I decided to check-raise to $56 and hopefully keep him in the hand. He called relatively quickly.

The river was an interesting card, the Qc. There was $154 in the pot so I decided to bet $72 which I felt he would probably call with AK or AQ.

Before I knew it, my opponent had pushed all in, I had called, and my hand had gone to the muck as I saw the bad news that he was holding AA and had flopped the top full house. Bad beat, right? Hang on a second.

The tendency of most players at this point would be to curse their bad luck or possibly go on tilt. I try to be more rational about things and something bothered me right away after that hand that I couldn't explain. The rest of the session ended without incident, and I couldn't stop thinking that maybe I'd done something wrong in this hand and could've saved some money. I showed a few friends the hand history and both of them asked me what my problem was as it's not like I can ever get away from that big of a hand. After spending some more time thinking about the hand, I believe I could've played it much better than I did and I'm going to explain why. Let's take it one street at a time.

Pre-flop

Okay, so I raise in and my opponent re-raises. If he had just flat called preflop he could literally have anything and I wouldn't really be able to narrow his range any just yet. Since he re-raised however, I know he has a pretty strong hand since I also know that this opponent respects my play and plays against me on a pretty regular basis. I'd say loosely that his range here is pairs from AA down to 99, AK, and AQ and sometimes complete air, but rarely.

Flop

Since I was playing 11 other tables at the same time I was involved in this hand, the flop action didn't mean as much to me as it should have if this hand occurred in a casino or if I just hadn't opened up any other games yet.

The fact that my opponent checked behind me on the flop is a huge deal in terms of narrowing his range down. The more I thought about this hand afterwards, the more I realized that this opponent would only rarely check behind on the flop with AK or AQ in this spot. He knows that I'm going to fold to a lot of continuation bets here and he is smart enough to mix in actual hands for value along with his bluffs. I'm also pretty sure that he wouldn't consider top pair a slow-playing hand on this board with Broadway possibilities and a flush draw. So since he checked I think we can eliminate a large percentage of AK and AQ type hands. Obviously you can't entirely remove them from your analysis since he could be varying his game or check it back for any other number of reasons, but I'd say it's very unlikely he has just AK or AQ after the flop check.

The hands that fit this flop action would be KK-JJ since he'd be looking to get to a cheap showdown and wouldn't want to expose himself to a check-raise bluff here in a big re-raised pot where he couldn't possibly call. By checking with those hands he can then call the turn and make a decision on the river if I bet again.

Other hands that would check the flop are AA and TT since they would be plenty strong enough to slow-play.

As I said in my preflop analysis, I don't think he would re-raise me with KQs, KJs, or QJs (again I could be wrong), so we don't have to worry too much about him taking a free card here with a club draw.

Also; 99 is a hand I'm pretty sure he bets the flop with as he doesn't want to get to a showdown and his hand has literally no value if I bet on a future street so he would want to take a stab here and give up if he got any heat.

Getting inside of your opponent's head and figuring out how he would play each of these hands is really what separates the good players from the great ones and I clearly was not on top of my game during this hand.

Turn

Okay, so now I've got my full house and have to figure out what to do with it. If I'd been doing the full hand analysis all along this would be an easy decision for me but I wasn't in the zone on this particular day and was almost on auto pilot and probably shouldn't have been 12 tabling. There are a few courses of action that can be okay considering his potential range here. If I check now he will check back with KK-JJ and probably bet AA and TT trying to get value. He may also bet KK trying to get me to check the end as well. I could also lead out here but then I'd be in a real conundrum when he raised me as he couldn't really have a hand that I could beat if I was totally in sync with his range like I am now looking at the hand in retrospect.

At any rate, I like a check and call here with the intention of probably leading out on the river and folding to a big raise. Kinda crazy, I know, but if you think about the big picture it's almost impossible for him to take this type of a line as a bluff.

This was probably the most important street in the hand and I played it terribly because I didn't fully understand what his flop check meant in the heat of battle. A check-raise really doesn't do anything for me except fold out worse hands and make me pay the maximum when I'm beaten.

River

Since I check-raised the turn it's pretty hard to not get all in here on the river. Taking an alternate line like check calling the turn clearly would've been a better option. Since I did check-raise the turn, I should probably check this river and call a moderate bet and fold to an all in.

Summary

As you can see, it's easy to become blinded at the table and look at your hand simply based on what it is instead of looking at it in terms of how it fares against your opponent's potential range in a given situation. Being on auto-pilot caused me to overplay my full house here to the tune of probably $80-$100 depending on what my opponent did. Most of the time when you have a full house you should be looking to get all of the money in the middle but there are always exceptions like this hand. If you can consistently identify these and take your foot off of the gas pedal when they arise, it will benefit you quite a bit in the long run.

Remember, I'm not advising that you start laying down monsters like this or becoming passive with them, but knowing your opponent and what hands he is likely to hold in a given spot should give you enough of an edge to take the proper action with your hand.

Good luck at the tables.

zaterdag 9 juni 2007

Ace Speaks: About Bluffing

By Rolf Slotboom

People who don't know much about poker often think it's a bluffing game. They have seen some Hollywood-movies or heard stories about players winning huge pots with nothing and bluffing out the best hand. The fact of the matter is that bluffing can sometimes be an important factor in poker (especially in pot- and no-limit poker), but that most of the time solid play gets rewarded and the best hand will win the pot.

Bluffing is often referred to as "the act of the desperate". When you have nothing to show in the end, you'll have to bet to have at least some chance to get the money. On the other hand, not many things give greater pleasure to poker players than making your opponent fold the better hand. If you are able to win pots because of the way you play, rather than the cards you hold, the skill factor in poker gets rewarded, rather than the ability to wait patiently for the best hand (which, as you should all know, is very important in just about every poker game).

There are some people who hardly ever bluff; there are people who bluff all the time. The first group of players can't expect to be paid off on their good hands (and thus make less money than they potentially could), the second group loses money because people will just check to them and let them bluff off their money. Somewhere in between, there must be some kind of "optimum bluffing point". What's more, the importance of bluffing is not equal in all poker games. Let's take a look at two of the most popular (and, in fact, my favorite) poker games: limit hold'em and pot-limit Omaha. Bluffing in limit hold'em.
People often say that there is no bluffing in limit hold'em, that it's a showdown game where the best hand wins, that bluffing here equals throwing away your money. There may be some truth in this, especially for the low limit hold'em games. In the higher-limit games ($10-20 and up) the bluff is an important factor however. A large percentage of the pots at the higher limits is won without a showdown, thus giving the bluff a better chance to succeed.

In limit hold'em, a large percentage of the pots can be called the "default pots", when no one has a real hand. The first one to become aggressive can expect to pick up the pot and this might just as well be you. Excellent candidates for steals are ill-coordinated flops like K83 or flops with a pair and no draws possible (for example 833 rainbow). You might be able to steal a few pots per session, and knowing that there is hardly a player at the higher limits who figures to make more than one big bet per hour, this adds up to a lot.

Still, it's important not to overdo these kinds of steals and to sometimes bet your good hands on flops like these as well (for example, your AJ on a JJ6 rainbow flop). If people catch up on what you're doing, they will start re-stealing or calling you down (setting you up to bluff off your money), thus making your attempts unsuccessful. Against coordinated boards (two of a suit or straight draws possible) you never bluff, period. You might decide to semi-bluff or bet a rather weak hand to try to get heads up against a probable draw, but you never bet to pick up the pot when you can expect your opponents to like the flop. Bluffing on the river is hardly ever successful in hold'em, unless you can convince your opponent the river has made the hand you had been drawing for (for example, you have T9, the flop comes J83 with two hearts and on the river comes a third heart; by betting here you might make your opponent fold a winner), or if you think your opponent has a weak (or busted) hand himself.

Most of the time, bluffing on the river in hold'em only works if you can make your opponent think you've got a made hand (rather than a draw) by betting all the way. Let's take the same flop, Jh 8d 3h, and once again you're in there with T9 (I don't recommend you're in there with this hand too often, but that's not the point here). If you come out betting with this hand on the flop and the turn as well and you've got only one opponent left, he might be in there with a hand like QT or the nut-flush draw for example and fold without much thought if the river hasn't helped him and you keep betting. That is: by semi-bluffing early in the hand you have paved the way for a bluff on the end. If you just call all the way with your draw and then suddenly bet on the river when the board doesn't seem to have changed that much, your more skilled opponents will become deeply suspicious and call you with hands as weak as one pair or even ace high. Conclusion: bluffing in limit hold'em can be done occasionally, but the situation has to be right and also your image has to be right. If people tend to see you as the famous Rock of Gibraltar who wouldn't dare steal a pot, your bet is more likely to win the pot than if people suspect you might be in there with nothing.

Bluffing in pot-limit Omaha.
In pot-limit Omaha a lot more bluffing is possible, still it's more of a semi-bluffing than a bluffing game. In this game it's often the big draw that becomes aggressive on the flop, rather than the made hand (in fact, if the flop comes Jh 9d 3h and the J9 faces a bet by Kh Qd Td 8h and the bettor shows his hand to him, the J9 is going to fold without a shred of doubt even though he has got top two pair and the bettor only has king-high). Because draws can be so powerful in this game, playing like this is hardly ever considered semi-bluffing anymore, let alone bluffing. Bluffing on the river is possible every now and then, although in the big pots one or all players involved will be all-in on the flop or turn most of the time, and decisions are therefore made early in the hand rather than at the river.

If the money is deep, a big bluff on the river is possible, even if you suspect your opponent has a very good hand. Example: flop Kh Tc 3h, your opponent bets the pot, you (in early position) call with Ah Jh xx. Turn: Jd. You figure your opponent for a very good hand (top set, three kings) but decide to represent the nut straight you might very well have (after all, you must be in there with something to call a pot-sized bet on the flop, right?) and bet the pot. After some hesitation, your opponent calls. If the board rags on the river, a good-sized bet might very well win the pot for you, even though you're up against a very good hand. Every time you think the nuts might not be out there, your bluff has a good chance of success. Another example of a bluff that might very well work in pot-limit Omaha is the "bare-ace play". The flop comes three of a suit (or even better, two of a suit, you bet, get called and on the turn comes the third card of that suit); if you have the lone ace of that suit you might be able to win the pot because in this game people know better than to call with a non-nut flush (you, of course, should know which players are and which players aren't capable of folding the king-high flush).

Don't overdo this play, however, better that you don't make people even think you know about its existence. This play works best when you've also got a set in addition to your lone ace: if someone decides to call you down with a flush, you might be able to win the pot by improving to a full (in fact, you would be semi-bluffing here, rather than bluffing). Some words of caution: always be aware of your and your opponents' stack size. If some of them (or you yourself) are close to all-in, no one is going to fold a made hand and you're basically giving away your money. Also, you've got to be a hell of a guy, a real strong character, to pull off a big bluff on the river. It can be tough for you when you try to bet your opponent off his great-but-non-nut hand, and he starts staring you down for a long time, trying to figure out if you are strong or are in fact only representing strength. Take care, guys, and good luck.

Ace Speaks: About Position

By Rolf Slotboom

Position is one of the most important, yet one of the least understood aspects in poker. A lot of players don't ever think about their position relative to the button; they think about their cards only and don't adjust their decisions (whether / how to play) to their position in the betting.

Another group of players talk about position all the time; they play hands "because they are on the button", they bet "because they always bet when they are last to act" or make remarks like: "I don't play cards. I play position." The first group of players doesn't make the adjustments necessary to become a winning player and is often easy to play against. The second group seems to focus on one aspect of the game only and tends to forget that (especially in limit poker) card selection might be even more important; that most of the time you're going to have to show the best hand to win the pot.

Nevertheless, position is a very important factor in poker. Hold'em and Omaha are positional games: the closer you are to the button, the better. You might occasionally play hands that are slightly below your usual standards. You might decide to become a little bit more aggressive with your hand because you're last to act or try to steal a pot because of the weakness the other players have shown by checking, but if you overdo this you'll find your edge might decrease instead of increase. People might start check-raising you because they know you are going to bet whenever it's been checked to you; in fact, even tight, solid players like myself are going to (semi-) bluff check-raise you (and the other opponents) out of the pot.

Position in limit hold'em.
Position in limit hold'em is important, although not as important as many players seem to think. In loose / passive games your position often enables you to win more on your good hands (especially your good drawing hands) and lose less with them than you would otherwise. In tight / aggressive games (the usual standard for the limits $10-20 and up), you might be able to pick up some small pots because of your position.

However, in games like these the opposition is more knowledgeable than in the lower-limit games. People expect the button to bet when there hasn't been any action yet; they expect someone in late position to raise before the flop to try to steal the blinds. They will play back with nothing, expecting you to have nothing. This also means that if you do have the goods in late position, you might be able to win a huge pot because your late-position aggressiveness isn't necessarily the sign of a great hand to them. In loose / passive games, the free card play is profitable and will often work. Let's say you're playing a suited ace on the button, you flop a four-flush, there's an early-position bettor, three callers and you raise; they all call your raise. In games like these the check-to-the-raiser attitude still exists. People might very well check to you on the turn.

When you have improved you bet and when you haven't you check, getting more money in the money when you make your hand and losing less when you don't. In the higher limit games, the free card play will rarely succeed. People know what you're doing so they will either reraise on the flop or (better) call your raise and then bet into you when it seems like you haven't improved. I they do check to you on the turn, you might decide to bet rather than check because of the weakness they have shown.

If for example the board is Jh 8d 2h and you've got Ah 9h you would most of the time bet your four-flush, even if the turn hasn't helped you: someone with a jack or eight might fold, leaving you heads up against some kind of (straight) draw, that is your ace-high might win the pot. When the river is a blank and your opponent checks, you check it back (never bet your ace-high in cases like this, just show the hand down) and if he bets, you're going to have to grit your teeth and pay off (a bet by a busted hand is too likely in cases like this to fold).

Another play a lot of (semi-) knowledgeable players like to make is reraising a late-position raiser with a small wired pair. They expect the raiser to be on a steal and figure their hand is a small favorite hot-and-cold against two random cards; they want to play the hand heads up in position. I don't like this play however and use it only sparingly, only when I think somebody is out of line or tries to run over the game. The fact is: the raiser might have a good hand (he doesn't always need to be in there with nothing), one of the blinds may wake up with a real hand (forcing you to pay four bets for a hand that may barely be worth one), or the raiser may in fact be playing two random cards but receive help from the board.

In limit hold'em, you should be able to save money or make money because of the information you get by the players acting before you in the betting process. Therefore you might start betting second pair in late position because you think your hand is best; you might pick up an occasional pot if you think there are no great hands out there but don't overdo it. If people start passing their hands to you, fully expecting you to bet, to put the check-raise in and they do this habitually, then you might have gone a little too far with your late-position play and you should start tightening up a little (betting when you have the goods, checking when you don't).

Position in pot-limit Omaha.
In pot-limit Omaha, compared to limit hold'em, position is of paramount importance. Because in this game so many turn- or river cards may cripple your hand, people are reluctant to give free cards. Therefore, if it's been checked to you, the odds are against anybody being in there with a real hand, and a good-sized bet has a good chance of winning the pot right away. Even if people suspect you are stealing, they still tend to give up the hand. Pot-limit players don't like to battle for small pots with less than premium hands, even if they think the bettor doesn't need to have a premium hand either.

Often the person who makes the first bet is able to pick up the pot, and therefore it might just as well be you who does the grabbing here. But once again, don't overdo it. Just like in limit hold'em, people might start check-raising you with hands they will fold against others. If you bet a marginal hand that you will have to give up against a check-raise (for example, an open-ended straight draw when there's a two-flush on the board) it might be better not to bet at all, since you can make your hand for free; in fact, if you get check-raised here, you are losing money on a hand you actually could have made some money with. In general, I like to play for the big pots in Omaha.

If there has been no raise before the flop and the hand gets checked to me, I often check my marginal hands back. I don't want people to think I'm trying to pick up pots all the time. If on the other hand the pot has been raised before the flop and the money is deep, I might become very aggressive when I'm in position and I suspect there are no great hands like top set or some kind of monster draw out there. I try to use my tight image to represent the temporary nuts (most often top set) and if someone decides to play back at me, all the money is going to be in the middle. If I get called, I will have a lot of outs no matter what (in Omaha, you hardly ever bet or raise without having outs because people may be in there with all kinds of hands, and therefore the likelihood of getting called is high).

If you bet or raise on the flop with a fine draw (wraparound straight- and flush draw) and get called, it's up to you whether or not to bet the turn as well. Against most players I have the tendency to keep putting as much pressure on them as possible if I think they're in there with something like top two pair or a small set, to try to make them fold their hand. If the player is unlikely to fold even after a second pot-sized bet (either because he's a really bad player or simply because he doesn't respect your play), you should just check it back and try to make your hand for free. One more thing: while in general you can become more aggressive with your hand the closer you are to the button, sometimes the opposite is also true.

If you flop a very good draw in early position, you might decide to go all-in on the flop by check-raising or betting out yourself, whereas you would have just called a bet (rather than go all-in) in late position. By going all-in, you try to get maximum value out of your hand. If you just call a bet when you're out of position and then you make your hand, the original bettor might fold if you come out betting and if you check, he might check it back. If you are last to act, the original bettor will most of the time be forced to pay you off, since he may feel his check might have induced some kind of bluff; if the board pairs on the turn or river you just fold your hand and save money you wouldn't have saved in early position.

Some final words.
Your position in the betting is always an important consideration in poker. Still, you shouldn't make decisions based on position only but use your position in combination with all other important factors: is the opposition likely to be weak, what do I think I'll have to beat, if I bet will they suspect me of stealing, does the board make it likely for someone to be checking a monster, are there any habitual check-raisers anyway etc. If you are able to combine all those factors with your position in the betting process*, then you should be able to make (or save) a lot of money, just because you're last to act.

* In pot-limit poker, there is also another important positional consideration besides position in the betting process and that is position on the preflop raiser. If there has been a late- position raise and you are on the button, your position is in fact rather vulnerable. People might check their good hands to the raiser on the flop, expecting him to bet (which, even in Omaha, will happen quite often) and thereby bagging you as well. If the preflop raiser doesn't bet, it is by no means certain that a bet by you will win the pot because someone might be lurking in the woods. On the other hand, if you're the big blind and there has been an under-the-gun raise, your position may not be as bad as it seems. When the flop is favorable, you just check and if the preflop raiser bets, you might be able to bag the entire field, or induce some kind of (semi-) bluff by someone who tries to pick up the pot because there has been no action yet.

Ace Speaks: About Draws

By Rolf Slotboom

Most of the time, if you've got a made hand in poker (for example, JT in hold'em and the flop comes JT3), you will bet your hand. If you're drawing (let's say you have Q9 against the same board), you may very well decide to check. In fact, checking and calling is the natural thing to do when you have a drawing hand. However, this isn't always automatic. In limit poker, you're going to have to bet your draws as well as your made hands sometimes to avoid becoming too predictable. Betting a draw on the flop (or even the turn) is sometimes referred to as semi-bluffing. That is: you would like everybody to fold since you don't have anything yet, but if you get called you might win the pot anyway by making your hand.

Some people (especially rocks or weak-tight players) don't like it when players bet their draws aggressively. They will make remarks like: "Why did you bet? You had nothing yet". In the game I like best (pot-limit Omaha) you will never hear comments like this. In this game, the big draw is often king; draws are often favorite over made hands on the flop. Drawing hands can and should therefore often be played aggressively. Now, let's take a look at how to play drawing hands in three of the most popular poker games: limit hold'em, limit stud and pot-limit Omaha.

Draws in limit hold'em.
You may have heard limit hold'em is no drawing game. This is true to a large degree, because it's harder to draw out in hold'em than in any other game. Most of all, this means hold'em is a kicker game: if you've got AK, there's an ace on the board and your opponent is playing a bad ace, you figure to make a lot of money (he has to hit his kicker to win). It doesn't mean straight or flush draws shouldn't be played.

In fact, drawing hands can be very profitable in hold'em, especially if the game is loose (lots of preflop callers) and passive (not a lot of raising). Your implied odds in games like this can be very good, since it doesn't cost you much to draw to your hand and if you make it, you will probably get paid off. In games like this volume hands like small suited connectors and suited aces can be played for profit, sometimes even from early position.

However, in position these hands do better: you will make more money if you make your hand, and lose less if you don't. If the game is tighter and more aggressive (like most hold'em games at the levels $10-20 and up) you're not going to play these hands, and if you do you're going to raise with them (rather than call) from late position to try to win the blinds. If you flop a good draw at the higher limits, how you play your hand depends upon the opposition. How many players are in, what kind of hands do you think they hold, do they respect your play, can you win the pot against them by semi-bluffing etc.

Let's say you're in the big blind with 98 and the flop comes 652. If you're up against one or two tight players who figure to hold big cards only, you might become aggressive with this hand from the flop on, even though all you have is a gutshot and two overcards. If, on the other hand, you're in the big blind with Q9 against the same players and the flop comes JT2, don't be too thrilled about your hand; in fact, I would recommend checking and folding here. If they hold AK, AQ or KQ, it's hard to get them out of the pot (if they have flopped top pair it's going to be even harder), and the only card that gives you a sure winner is an eight. Drawing hands in position can sometimes be profitable hands in hold'em, especially in loose / passive games where the free card play might work. Against tougher opposition, the made hands are king. If there are only two players left on the flop in hold'em, it's hard for the draw to be the favorite over the made hand, even if the hand to beat is just top pair / top kicker.

Draws in 7 Card Stud.
In seven stud you're not going to start with hands like 987 or J98 to try to make a straight. You do play suited cards (if none or only one of your suit are out). If you get another suited card on fourth street, you have a powerful hand (depending of course on what the opposition has). On fourth or fifth street you might become aggressive with your four-flush in one of the following situations: a) you're in the hand with three or four opponents who won't bet but will call with their hands and don't figure to hold super-hands. In this case you are betting for value (that is, a bet here has positive expectation even though you don't have anything yet) or b) you're in the hand on against a single opponent who you figure to be rather weak, yet has a stronger hand than you at the moment.

In this case, you are semi-bluffing to try to make him lay down his hand on fifth street (in stud, whenever someone calls your bet on fifth street, he will most likely go all the way to seventh street). Most of the time, things are rather clear-cut in seven stud: the big pair (or the most dangerous-looking board) bets and the draw calls. Still, in stud it's a lot harder to protect your one- or two-pair hands than in hold'em and playing (quality) draws can be very profitable here. Just remember you're going to have to make your hand. It's almost impossible to bluff your opponent out on the end (like you can occasionally do in hold'em, by representing something you don't have). Since the pots are so big and the last card is dealt face down, the one- or two-pair hand will just grit his teeth and pay off your bet.

Draws in pot-limit Omaha.
Pot-limit Omaha is the ultimate drawing game. If the flop is Kh 9h 2d, you have Ah Qd Jd Th and your opponent, holding K9, knows you've got this hand, he is going to fold his hand without a shred of doubt. That's right: he has got top two pair, you have ace-high only and still he's going to pass. In Omaha, the draw is king. On the flop, the drawing hand can be the favorite over the temporary nuts, even when the nuts is as strong as top set or a made straight. Draws can and should often be played aggressively, especially if you suspect there is no set out there.

Still, don't over-estimate the power of the straight draw, because they sometimes look better than they really are: someone may have the same straight draw you have (so you might make your hand and have to split the pot) or a flush may be completed on the turn or river (so you make your hand but still lose). Pot-limit Omaha is a game of implied odds. You've got to know exactly where you're at in the hand, you've got to know exactly what you have to beat since this will decide which strategy is best (push or pull).

If you're relatively new to the game, be very careful about drawing hands that may be second best if you make them. The king-high flush is a hand that can in fact be very profitable, if you know how to play it; if the novice player gets any action when holding this hand, he will most likely lose his entire stack.

Two more things. First, in Omaha it's important to know exactly how many outs you have (for example, if your opponent has a set and you've got the nut-flush draw, you've got seven outs, not nine). Only if you are able to calculate your outs quickly and without mistakes, and of course if you are able to read your opponent's hand well, is it possible to know for sure if you belong in the pot or not. Second, make sure you've got good computer software available to you, so you can simulate interesting hands that have occurred, are able to calculate your drawing odds in Omaha better, and in time will play a better game overall. Take care, guys, and good luck playing your draws.

How Poker Players Suffer Big Losses By "Reverse Manufacturing"

By Mike Caro

Most players, even serious one, suffer much greater poker losses than they should. That makes me sad, so I'll try to fix it. One reason is that their losses are "reversed manufactured." Now there's a fancy term. What does it mean? Reverse manufactured means that those losses are the necessary byproduct of trying to manufacture a winning streak.

Oh, fine, but what does "manufacture a winning streak" mean. Ah, now we're getting right to the heart of it. You might have manufactured some yourself and not realized it. You're probably manufacturing a winning streak (and, in fact, manufacturing wins) if you like to brag about the number of times you've won in a row. If you go around telling anyone who will listen, "I'm on an 18 day win streak," more likely than not, you're manufacturing wins.

How can you manufacture a win? It's amazingly easy. All you have to do is refuse to settle for a loss and accept small wins whenever you need to. The only requirement is that you fight back when you're behind, hoping to break into the plus column, then quit happy if you succeed, rejoicing in the notion that you overcame adversity, struggled to restack your chips, and are now going home to rest victorious. It will feel like a proud accomplishment to you, but it shouldn't.

How you won

Let's look at how it might have just happened. You're a medium-limit player, not competing quite large enough to make a good living, but large enough to supplement your income or to barely get by without a job when required. In this way, you're like the majority of winning poker players - somewhere between just eking out a profit and professional wage-earner status.

Anyway, today you sit down in a $10/$20 hold 'em game, supposedly hoping to make a profit by showing off your Sunday-best poker skills. Sad stuff happens right away, though. Down goes a king-high heart flush, which you flopped, when a player holding the ace of hearts and deuce of diamonds sees a fourth heart come on the river. Next you flop three jacks, but they finish third when two opponents hit straights. Then there's that devastating hand where you got bluffed out of your birdcage by Bruno, who never, ever did that before. And it gets worse. The little medium hands that can go either North or South, all go South. Losses pile up. Misery surrounds you.

But somewhere deep, deep inside, you maintain your faith and conviction, and the spirit strikes you. You fight back. Hours pass. You grow weary. Hours pass. You fight to stay alert and wait for your luck to change. Hours pass.

It's now 3:40 in the morning and you need to be up at 8:30. Suddenly several pots are pushed to you. Then a small setback. Then you win more pots. After a string of pots go your way, you win a really big one. Is your recovery complete? You don't know, because you haven't had time to count your chips.

"Deal me out one hand," you tell the table. You need to stack these newly won chips, count them, find out where you stand. Down $135, put 10 of these $5 chips here, down $85 now, put these two $25 chips off to the side, down $35, oops, three more $5 chips under a $20 bill, exactly even, and that leaves these three $1 chips, change from the rake, so up $3! You did it! Your winning streak continues!

Time to go

"Deal me out!" you announce. "It's getting later than I thought." "Don't you wanna play till your blind?" someone asks. "You've got another hand coming." You're tempted, after all, you can just fold everything except aces - even aces if you really want to. But you just wave away the suggestion. "Nah, deal around me." And within minutes you're cashed out and on your way home. As you're leaving, a friend asks you how you did tonight. Your chest puffs out proudly and you say, "I won a tiny bit. Nothing that matters, but that's 19 winning days in a row."

Signs of trouble, my friends. Bad signs of trouble. You're manufacturing that win streak just so you can make yourself feel good about it. But you're not manufacturing profit. Sure, you think you're making profit, but really you're putting your bankroll at risk. You have tallied a lot of wins - a couple when you got off to a fast start and kept on winning, a few short ones when you started fast, but faltered and quit before you found yourself in the negative column, some where you'd come from behind and quit when you got ahead. And, of course, tonight when you'd stuck it out and turned a major loss into a tiny win.

Speaking of tiny wins, that's exactly the kind you're likely to have when you strive to extend a winning streak. That's simply because you're willing to settle for them. You'll quit with small wins when you've been winning more to keep from dropping below break even. And you'll gladly cash out with a small win if you've been losing and get ahead. However, there is no such thing as a small loss. You won't accept one. It's either a win or a big loss. You need to keep that winning streak alive if you can, right?

The wrong time to play

But, all together, this strategy means you're playing more hours than you should when you were losing, because you're trying to catch up. And it means you're playing fewer hours when you're winning, because you're eager to cash out and add to your win streak. By manufacturing a win streak, by forcing small wins, you're also putting yourself in grave danger of manufacturing huge losses - you simply won't experience them as long as your luck holds and your winning streak is extended.

You see, when you try hard as you can to dig yourself out, you risk digging yourself deeper. It's like that popular advice, "When you find yourself in a hole, stop digging." I think those words were tailored for poker. Beware! On the few occasions that you won't be able to experience the glory of cashing out with that $3 profit and puffing up proudly, you're likely to suffer painful losses and depart pitifully from the poker table, all chance of recovery now hopeless. Maybe chance of recovery tomorrow will be hopeless, too. You will have lost way more than you should have. And I'm not talking about a magic stop-loss or predetermined limit on how much you should risk in a game.

Listen closely. I'm saying something different. I'm saying you lost much more than you should because you played poker in the worst of circumstances. When you're winning, opponents are usually intimidated by you. They're less likely to play their best games, less likely to make daring bets and raises with winning hands and extract every penny of profit from you. This means you can make value bets that can push your profits to the limit. Opponents who are intimidated usually keep calling in frustration, but seldom raise with anything but obviously strong hands. In doing so, they neglect to take advantage of all their edges, so you rule the table, and your profit soars.

Conversely, when you're losing, opponents are inspired. They play better against you specifically. They think, "Hey, there's someone I can beat. There's someone who's unluckier than I am." And they single you out for money extraction.

So, I don't like to hear about long manufactured winning streaks, because I know that those invite huge manufactured losses, too. And, in the long run, long winning streaks usually mean that you've played most of your time under bad circumstances and limited the time you've played under good circumstances. And that isn't a smooth path to poker profit.

zondag 3 juni 2007

Choosing the best seat versus a maniac

By Rolf Slotboom

A lot has been written about some of the difficult situations you will encounter when there's an extremely aggressive player, a maniac, at your table. Most poker writers have claimed you should try to sit to his immediate left, so you will be in position to isolate him. That is: when he raises before the flop, you can re-raise with your good hands to shut out the entire field and play heads up, in position with a hand that figures to be best. In my opinion, choosing this seat is not necessarily the best way to neutralize the maniac's power. In fact, I think that for quite a few games the advice given might even be dead wrong. I would contend that in some cases the seat to the maniac's immediate left might be the absolute worst seat at the table. (Note that I said in some cases, not in all cases). In this article, I will take a closer look at some of the problems you will face, sitting on the maniac's immediate left.

The best seat in pot-limit Omaha.
In pot-limit poker, one of the most important considerations in choosing your seat is the size of your, and your opponents', stack. If you are playing a small stack, then the best seat is almost always the one on the maniac's immediate RIGHT. You will be able to create some monster pots by either limp/re-raising before the flop or by check-raising after the flop. Because you can almost always count on him to do the betting for you, you have basically given yourself last position. You can let the actions from not just the maniac, but from the other players in the middle as well, dictate your best course of action (fold / call / raise). Had you been sitting on the seat that is recommended by a lot of writers (on his immediate left), you would indeed have been able to isolate him on a few occasions. By re-raising pot you would have been able to shut out the others and have the maniac all to yourself, while having position on him. There are a few problems with this strategy, however:

* By re-raising, you will usually be able to get only 20 to 40 percent of your stack in before the flop (depending on the size of the blinds and your exact stack size). Therefore, the maniac can put a lot of pressure on you later in the hand; when it looks like the flop hasn't helped you, but might have helped him. He may semi-bluff you out of the pot or make you pay off when he does have the goods.
* The advantage of a good hand over an average hand is not as big in Omaha as in hold'em, for example. It's pretty easy for someone to beat aces or kings when holding a random hand, especially a no-pair random hand, and this is exactly the type of hand the maniac might be holding.
* If you re-raise the maniac with an excellent hand like KKQJ (you would definitely re-raise with this hand, wouldn't you?) and someone behind you comes over the top, you are almost certainly facing aces. If the maniac chooses to fold, you will have to call an extra 60 to 80 percent of your stack with a hand that is very good, but a big dog heads up against aces. (For the exact match-ups of aces vs. either kings, high cards or medium rundowns, see my article "Defending against aces"). Had you been on the maniac's right, you would have been able to let go off your kings without it costing you too much, or you would have been able to see the flop rather cheaply in a multiway pot (which is desirable in the situation described here, because if you hit the flop you figure to have a nut hand, and you don't mind being up against a lot of opponents).
* The hands you do win by isolating the maniac will not be that big- you will either double up your small stack or lose. In pot-limit Omaha, it is possible to do a lot better than that. You can easily turn your $200 minimum buy-in into $700 or $800 if you try to maximize your winnings by sitting on the maniac's immediate RIGHT. (For more on the exact strategies required when playing a short or medium stack, see my article "Pot-limit game conditions"). Of course, after you have tripled your initial buy-in you have to change seats immediately- you don't want to play a medium or big stack with the maniac having position on you. But if you are playing a small stack sitting to his left and your strategy works (i.e. you isolate the maniac and double up through him) then your stack is still relatively small- and you still face the same problems you had before you doubled up.

The best seat in limit hold'em.
Of course I know that most poker literature is aimed at limit hold'em, and that the advice given (sitting on the maniac's immediate left) is meant for that game and not necessarily for pot-limit Omaha as well. However, even in limit hold'em I usually try to avoid the seat to the maniac's immediate left, for the following reasons:

* In the games I play in, most of my opponents tend to adjust their play to special circumstances fairly quickly. If they see me sitting to the maniac's immediate left, they know I will try to isolate him with any decent-looking hand; they know I won't need aces or kings to three-bet before the flop in this situation. If someone is sitting behind me with a relatively marginal hand like AQ (which he would fold for three bets under normal circumstances), he will probably not fold now- in fact, he might even cap it at four bets (and if he doesn't, the maniac might). What happens now, is you are sandwiched between a highly aggressive player who will bet after the flop with anything, and a serious player behind you who has shown strength- now, this is not an enviable situation to be in.
* Most players know that if there's a maniac in your game, you should tighten up considerably, simply because it will be more expensive than usual to see a flop. (This is common knowledge, and I generally agree with this reasoning). Now, if you are sitting on his immediate left, you will be seeing even less flops than that, exactly because of the seat you have chosen. When you have a hand that looks good enough to play, you will usually three-bet to shut the others out and to give your hand the best chance to hold up unimproved (hands like AQ or 88 come to mind). However, if you get any action behind you after you have three-bet with hands like these, you are in deep trouble. In fact, you will have paid three or four bets with a hand that clearly has negative EV for this situation: the player behind you almost certainly holds a better hand than you do. This doesn't mean that your three-bet was wrong; based on the information you had, it seemed like a reasonable play (your hand was quite likely to be best on this given deal). However, this does not change the fact that you have now paid three or four small bets for a hand that may barely be worth one, and in the long run your hourly rate will suffer. But flat-calling with the hands I mentioned is no option, either. If you get any callers behind you, you are in the same (bad) situation as described above: sandwiched between a highly aggressive player who will bet with anything, and players behind you who may or may not have received help from the flop.
* In limit hold'em, the expert player is able to make or save money because of the information he gets from his opponents' betting actions. If serious players have raised or re-raised when the action gets to him, he will almost certainly pass a hand like AQ, while this same AQ might have been a calling or raising hand for him under different circumstances. When sitting on the maniac's immediate left, you will not have a lot of information to rely on. Had you taken the seat I usually recommend for limit hold'em (three or four seats to the maniac's left, preferably with some weak callers in the middle), you would have had more information available to you in making your decisions. Also, you will have this information on exactly the type of hands where you need it most (pocket pairs, suited connectors), in the position where you are most likely to play them (the last four positions). By choosing the seat I recommend, you will have neutralized the maniac's power to a large degree, while still having position on him on the hands that count most (on or near the button). Now, because of the actions of the players in the middle, you will know whether you have the right odds to play your ten-nine suited, and if your pair of sixes might be profitable or not. Sitting on the maniac's immediate left, you would have had no other choice but to fold these, potentially profitable, hands.
* The other people in the game will certainly adjust their play because of the maniac's presence. Almost all players, even the ones that aren't usually very imaginative, will try to check-raise the maniac on the regular basis, and by doing this they will be bagging you as well. Therefore, isolating the maniac after the flop will not be easy either. If everybody checks to the maniac who bets, you are once again in the middle. You will have to fold a lot of your marginal hands that may in fact be good, simply because you don't know if the checks by the other players mean "I have nothing" or "I am waiting to trap the bully".
* Not only will you play very few hands, the pots you win will also be relatively small. On top of that, you are risking three or four bets instead of the usual one or two. Unless you are fortunate enough to pick up kings or aces, you will also lose a rather high percentage of the hands you three-bet against the maniac, simply because he receives help from the flop and you don't (or when he does have a better hand than you. The fact that he raises so often, doesn't mean he cannot hold aces or kings now- even a maniac is entitled to his fair share of premium hands, just like any other player). There's a lot of luck involved in hold'em once the flop comes and while it's not easy for him to outdraw aces, it is not that difficult with some of the other hands you might three-bet with (AK, AQ, AJs, KQs for example). Also, if the maniac raises and you three-bet, he knows the type of hand you are holding, but you know nothing about his hand. If the flop comes AKQ, he will definitely fold to your bet if he has nothing, but what do you do, having three-bet with AK, when three small cards flop and he comes out betting? Remember, there is hardly a maniac who is highly aggressive before the flop, but timid after. Most likely the maniac will put a lot of pressure on you when the flop is unlikely to have helped you. By playing like this, you will of course make money when you have him beat, but he will also force you to lay down the best hand every now and then, and he will often get paid off generously when he has a real hand.

Some final words.
What all these points illustrate, is that the seat to the maniac's immediate left isn't necessarily the best or most profitable one. I know that equally valid points can be made in favor of this seat, and I think that in some cases (especially when your opponents respect your re-raises and fold all but the very best hands) choosing this seat will be profitable for you. However, in quite a few of the games I have played in, the problems associated with this specific seat outweigh its benefits by far, and I guess that in your game they might too. Therefore, I suggest you take a closer look at the exact type of game you're in, at the tendencies of your opponents, the atmosphere at the table, and in pot-limit games at the amount of money at the table as well. You should take all these factors into consideration when choosing your seat and then use this seat as a starting point to a) neutralize the power of the maniac and b) to exploit his weaknesses.
Take care, you guys, and good luck.

The Truth About Tells

By Daniel Negreanu.

I’m going to let you in on a little secret here. If you believe that watching for a twitchy eye or a flared nostril is what poker is all about — you’re quite wrong. Many poker players (mainly those who are new to the game) are preoccupied with the notion that bluffing and the ability to discover tells are what it’s all about.

I often hear someone say something like, “Oh, I could never be a good poker player. I have a terrible poker face.” Or, “I wouldn’t be very good at poker. I just can’t tell a lie, so I wouldn’t be able to bluff with a straight face.”

Well, if you believe that, this column should be a pleasant awakening. While it is important to avoid giving away too much information with your body language, it’s nowhere near as important as learning the fundamentals of the game. In fact, I would bet that a world-class player could beat a low-limit game even if he told his opponents what he had on the turn every single time! Of course, that would work only if his opponents didn’t always believe him, but I think you get the idea.

So, what is it, then? What is it that separates average and good players from the great ones? Well, obviously, tell recognition would be one factor, but it’s simply not the most significant. The answer is: hand-reading ability; the ability to process information that you’ve gathered from your opponent in the current hand and in past hands, and to use that information to narrow down your opponent’s holdings. Picking up on your opponents’ betting patterns and understanding what they are and aren’t capable of doing, makes this much easier. So, when you hear people talk about “reading people,” what it really comes down to is reading into your opponent’s mind what he is thinking at the moment, and trying to figure out how he would play various situations. It’s not about noticing that when Al has a flush draw, he eats an Oreo cookie without opening it up first, but when he has top pair, he licks out all the cream first. That would be one heck of a tell, but obvious tells like that are pretty much reserved for the movies. However, some pros would like you to believe that their biggest strength is their ability to “see through your soul”; that is, knowing what your holecards are just by looking at you. This might be true in cases in which players have exaggerated tells, but for the most part, a great player makes his read based on the actual betting that took place, not the facial tics.

Now, I shouldn’t be telling you this, but I will anyway. It’s simply a scare tactic used by many pros to make you feel uncomfortable. Think about it: When you make a bet (whether it’s a bluff or not) and your opponent throws his hand in immediately, or even calls immediately, is it intimidating? No, not really. Well, what if he takes extra time? He stares you down. He cuts his chips out to make it look like he wants to raise, and so on. Now, that might make you sweat a little bit, especially if you are indeed bluffing! If it doesn’t make you sweat, it at least might make you uncomfortable having a guy stare at you for so long. It’s all a ploy, as simple as that.

Most often, a player knows exactly what he’s going to do within five seconds. You’ll see it on the World Poker Tour telecasts quite often, thanks to the hidden cameras. There was a hand at the World Poker Open tournament in which Dave “Devilfish” Ulliot made a play with the 5diamonds 2diamonds. The player he had raised moved all in, and David went into the tank (meaning he took a substantial amount of time pondering whether or not to call the bet)! Why did he do this? After all, he is an experienced pro, and knew full well that he wasn’t going to call the all-in raise, so why waste all that time?

Well, there are a couple of possible answers to that question. He may have just wanted to save face in order to conceal the fact that he was raising with a trash hand, or, more likely, he was trying to make his opponent sweat a little bit. He wanted to make him nervous, and put him through three minutes of torment before finally releasing his hand. Many players in this situation would be so relieved that it’s finally over that they subconsciously might think to themselves, “Hmm, I better think twice about making any moves against that guy in the future.”

Well, that’s just what the Devilfish wanted from him. He wanted to scare him. He wanted him to think that if he ever tried to bluff him, he would have to deal with a full five-minute stare-down. That’s more than the average guy wants to deal with at the table, so many of them will begin playing in a straightforward manner from that point on — thus making it even easier on our pro to control the table.

Don’t be paranoid of or obsessed with tells. That’s not where your focus should lie. I remember a few years ago something that I thought was rather cute. There were a few aspiring pros in a $10-$20 game at the Mirage one night. They looked fresh and ready to play. For several hours I watched them. Their eyes were constantly fixated on the player who was next to act. They gave each and every player the stare-down — on every street, whether they were in the hand or not! I thought it was quite funny, actually. They were so obsessed with trying to figure out what people’s tells were that they completely neglected what was actually going on in the hands — who bet, who raised, and so on. Instead of watching the action of the game and studying betting patterns, they spent all of their time trying to figure out if Grandma Betty actually had a nervous twitch, and whether or not her twitch revealed something about her holecards! They clearly had a lot of passion and energy for the game, but they were wasting all of that energy exercising the wrong muscles.

When To Call And When To Bet - Finally, Some Powerful Answers

By Mike Caro

"Somebody's got to keep him honest," Tom said, calling the bet. The next player to act raised. The original bettor reraised. And poor Tom folded.

"Betting is more a matter of feel than science," Dick explained to me years ago in Gardena. I had folded before the draw. He had drawn two cards to queens with an ace kicker and made aces up. I knew this for a fact, because he showed me. Because he didn't want other players around us to hear, his voice was low and conspiratorial. He immediately was raised by a pleasant 97-year-old woman in a frayed pantsuit - well, maybe not 97, but close enough. He called reluctantly, and lost. Poor Dick.

We were playing hold'em and young Harry said, "I'm going to fold. You've been bluffing too many times. I think this time you've got it." He threw his cards away proudly. The man he was addressing then said, "You shoulda called me, son," turning over a jack high with a smirk. He had missed a straight. Poor Harry.

I'm not singling those three players out for ridicule. Sometimes it seems as though these same mistakes are made by practically every Tom, Dick, and Harry you meet at the poker table. And because these mistakes are so common, I think we should examine them today.

Tom's Mistake
How many times have you heard that "Gotta keep 'em honest" line? Well, there's a bit of truth in it, because if you never call with questionably strong hands, your opponent can bluff whenever he chooses and will beat your brains out. Now, I tend to be a guy who thinks getting your brains beat out is bad poker, so I advocate calling sometimes to "keep 'em honest." But when?

The simple answer is that you should call whenever you calculate that if you made the same call in the same situation a million times, you would show an overall profit. That sounds obvious to experienced players, but it's important that beginners grasp the concept. You don't much care about whether you're going to make money by calling right now. In fact, most of the time, you'll lose money by calling. And that's how it should be, because - at least in limit poker - the rewards of winning the pot are always much greater than the cost of the call. Therefore, you're risking much less by calling than the reward you'll receive if you win. That means you can call and lose lots of times for every rare time you call and win - and you'll still make money.

Catch a Bluff and Lose
So, sure, keep 'em honest at the river. You don't want to be bluffed very often in limit poker. But the weaker your hand, the less likely you should be to try to catch a bluff. There comes a point where your hand is so weak that you can catch an opponent bluffing and lose. And, of course, if your hand is relatively strong, but not strong enough to catch most "legitimate" bets, you might unexpectedly beat opponents who are too exuberant in their value betting. So, even when you think you're trying to catch a bluff, the stronger your hand is, the more likely you are to win.

This is even more important when you're in a situation like Tom's. Tom made the mistake of trying to catch a bluff without considering how many players remained to act behind him. One of the simple techniques I teach is to decide in advance when you're the cop and when you're not the cop. You're the cop - and in a position to keep opponents "honest" - when you're heads up or when you're last to act and nobody has called. Hey, when nobody else calls, we're all counting on you! Otherwise, we don't get to see if the bettor is bluffing, and that can drive us crazy, right? But even if you're in the last position and everyone else has passed, you still shouldn't call all the time, and the stronger your hand is, the more likely you should be to call. Everyone knows that, but did you know that you often need a stronger hand to call in the last position after everyone has passed than you would if you were heads up?

How come? It's because most opponents are less likely to bluff into many opponents than they are just one opponent. Not only is this how most opponents play, they are correct in playing this way. Yes, the pot is usually bigger when there are more players. That means there's more to win by bluffing and more to win by calling. But the success rate for a bluff is greatly reduced against many opponents. What happens in practice is that potential callers at the river, when there are many of them, do not adequately take into account how significantly overcalls diminish the value of a call. This lack of correct handicapping is true whether it applies to the original call or the overcall.

You Must Call Most of the Time
As I've explained before, if a single player would call only 50 percent of the time, it's always a good idea to bluff. The pot is likely to be five times the size of the bet. So, if you lose your bet half the time and win the pot half the time, your profit is enormous. You lose $100 on one failed bluff; you win $500 on another bluff that works. That's $400 profit on two attempts, or an average gain of $200 on a $100 bet - a 300 percent return on investment or a 200 percent gain. It's what skilled players live for.

But what if there are two opponents who can call? What if they are oblivious to the fact that they should be more careful with their calls when there are several opponents in the pot? What if they continue to call half the time? Now, half the time that the bluffer survives the first opponent, he loses because the second opponent calls. That comes out to only a 25 percent chance of success - still enough to merit a bet, especially since the pot he's shooting at is likely to be larger with more players. What if there are four potential callers? Then, there's only a 6.25 percent chance (50 percent times 50 percent times 50 percent times 50 percent) that the bluff will succeed against opponents who won't adapt. The odds are then 15-to-1 against success, and the bluff is unprofitable unless the pot is at least 15 times as large as the wager. And it gets worse if there are more players.

Also, it gets worse because most opponents call more than half the time. When heads up, they better, otherwise they're likely to get bluffed out of their bankrolls. Another important point about overcalling is that it takes a much stronger hand to justify an overcall than a call itself. Suppose the pot is $100. If you're the last caller and it costs $10, you're getting 10-to-1 odds, and you'll break even by winning just one out of 11 times. But if there's already been a call and you're the overcaller, you're facing a $110 pot while getting 11-to-1 odds. Unfortunately, if you think you have only the same chance of winning as the first caller, you're going to win the pot only half the time that you beat the original bettor. That means the pot that you're going after is theoretically only half as large - $55. So, you're investing $10 to win $55. You need to have a hand that's strong enough to beat the bettor one out of 6.5 times to break even.

Trust me, there's a lot of difference between a hand that will win once in 11 times and one that will win once in 6.5 times. The lesson learned: You need a hand that is much stronger to overcall than to call, even though the pot is bigger when you overcall

Here's another factor: Players don't correctly adjust to the additional strength that's required to overcall. Therefore, you need to be more cautious than you theoretically should be when you make that first call with players waiting to act behind you. This was Tom's mistake. It might have been better had he raised with his medium-strong hand to prevent calls behind him. This is a powerful tactic that you should occasionally choose when you think there's a reasonable chance that you're facing a bluff and several opponents could overcall with mediocre hands if you merely call.

Dick's Mistake
Dick's mistake was thinking that you should just bet at whim - whenever you feel like it. In fact, there is great science that governs when you should bet and when you shouldn't. Here are just four of dozens of major factors that guide you wisely toward the right decision:

* Oftentimes you shouldn't bet a strong hand if your opponent bluffs too much. You'll sometimes make more money by checking and letting him try to bluff when he holds a weak hand.
* The more liberally your opponent calls, the more medium-strong hands you should bet for value.
* If a player is threatening to call, you should bet all medium-strong hands. When you see this, the player is trying to prevent your bet. That means he's weak and looking for a cheap showdown, but will often call reluctantly if you bet.
* You should not bet medium-strong hands into very tight players. You won't get called by weak hands that you can beat, and are only likely to lose when you get called.

Harry's Mistake
Harry's mistake is very common. He thinks opponents randomize correctly, and that if they've been bluffing a lot, you can "time" them and figure they're not bluffing this time. Sure, there's a good chance that the player will have a strong hand this time, but that's usually so regardless of previous actions. Players who bluff too much are always profitable to call unless you have a specific reason, usually a tell, to believe they almost certainly aren't bluffing right now.

My advice: When you hold questionable hands against opponents who have bet and who bluff too much historically, keep calling. When you hold questionable hands against opponents who have bet and who don't bluff often enough historically, keep folding. Don't try to time your opponents

So, we've learned:
1. An overcall must be done with a much stronger hand than a call.
2. A first call must be done with a stronger hand than you'd theoretically consider calling with if opponents waiting to act behind you are oblivious of point No. 1 above.
3. A first call should indicate more strength than a call with nobody to act behind you, assuming the pots are the same size.
4. In practice, it's less profitable to bluff two players than one player, and even less profitable to bluff three or more players. All attempts to bluff four or more players, throughout the history of poker, have been massively unprofitable, on average.
5. Sometimes it's better to raise than call with a medium-strong hand with players yet to act behind you.

zaterdag 2 juni 2007

Are You Sage? Getting an Edge in Heads-Up No-Limit Hold'em

A poker tournament is often as much about mental endurance and discipline as it is about the cards and strategy. After all, particularly in no-limit hold'em, a single error can put you on the sidelines, even after playing flawlessly - or brilliantly - up to that point.

But let's assume that you've made it past all but one opponent; you're heads up at the end of a no-limit hold'em tournament. All of your work (and, let's be honest, luck) has paid off; you and your opponent are contesting for the top prize. The cruel irony, of course, is that both of you are mentally (and perhaps physically) exhausted, but you're about to play for the largest single increase in prize money, and this is the portion of the event that scares people the most. Many folks are so delighted to make it down to heads-up play (and are exhausted from the event) that they lower their focus. And, regrettably, lots of players feel completely lost playing heads-up no-limit hold'em. They either guess their way through it or seek a deal with their opponent; they're willing to give up some equity just to be done with the confusing and sometimes terrifying two-player battle. The poker player who can wade into this battle with courage and knowledge stands to win the largest prize in the entire event, not to mention the glory of finishing first.

The good news is that mathematics and game theory can often provide a clear and well-lit path through the foreboding forest of the heads-up portion of a no-limit hold'em tournament.

In this feature, we describe a simple technique that you can use in many heads-up no-limit situations; we call it the SAGE™ System. It is so straightforward that you can write it down on a 3"-by-5" card. With a few minutes' study, you can memorize it and use it anytime you find yourself heads up.

Why do I need the SAGE System?
Some players have said to us, "Well, I think I'm already playing pretty well heads-up." Frankly, this is unlikely, because: Most players play far too tightly in heads-up jam-or-fold situations.

This is not our opinion - it is a mathematical fact. And don't believe for a moment that tournament pros such as Chris Ferguson are not aware of this.

With that said, please understand that this system will not make you invincible in the heads-up portion of a no-limit hold'em tournament. However, against most opponents, who don't correctly adjust for the large blinds and weaker hand values of heads-up play, you should have a 5 percent-40 percent advantage; 5 percent is good, 40 percent is crushing.

You might ask, "Hasn't this material already been published?" Well, yes, but not widely. There are a few places in the online forum world where this information is shared (most notably in the "Two Plus Two" forums - http://www.twoplustwo.com/). But we are not aware of any book or magazine that contains this information, and we believe our presentation is easier to use in practice than anything that has been published in any medium. Dan Harrington has produced a stunning pair of books (Harrington on Hold'em, two volumes) that give a lot of information about playing heads-up. However, the main thrust of his discussion is major tournaments, where the stack-to-blinds ratios are often 100-1 or more (so our system does not apply). And in fact, we believe Harrington gives incorrect advice in one of his smaller-stack examples (more about that in a bit).

When does the SAGE System apply?
Let's be sure that you understand exactly when you can apply SAGE:
1. You are heads up with a single opponent at the end of a no-limit hold'em tournament. The important point is that there is just a single prize left. Note that a one-table satellite into a larger event also has this feature (the single prize is a seat in the larger event).

2. The blinds are large compared to the stack sizes. To put a value on this, if the ratio of the smallest stack to the big blind is greater than about 10-1, our system is of no use to you. However, this small-stack-to-blind ratio is extremely common in online sit-and-go tournaments, and even more so in brick-and-mortar casino sit-and-go tournaments and one-table satellites (thus the acronym SAGE: Sit And Go Endgame System). Please note that our system doesn't worry about the size difference between the stacks. Only the size of the shorter stack matters.

3. The small blind (who is on the button, and acts first) chooses to either move all in ("jam") or fold. As the blinds grow large compared to the stacks, this is a winning strategy for the small blind (SB). Of course, once the SB jams, the big blind (BB) can choose only between calling or folding; our system will tell the BB how to defend optimally.

When does the SAGE System not apply?
1. When there are more than two players left. For example, you may ask: "Suppose that we're threehanded, the button folds, and I'm the small blind. What should I do?" The system we present here cannot answer that question. Here is why: When you are threehanded, there are two more prizes to be contested (second and first; everybody is already guaranteed third-place money). In this situation, the value of the chips is not fixed; that is, the value of a single chip in your stack may be different than the value of that same single chip in an opponent's stack. An exception to this would be a one-table satellite with a single prize: a seat in the target event. In this case, all that matters is the stack sizes.

2. When the stacks are still large compared to the blinds. This is an important point. For instance, if you are in the final event of the World Series of Poker, the stack to blind ratios will be so large that SAGE does you no good. You will just have to (as the pundits are fond of saying) "play good poker."

3. When the small blind limps or makes only a small raise. In these cases, our system provides no guidance to the big blind (BB) player (at least not yet; this is obviously an interesting area for further research).

Now that you understand when the SAGE System does and does not apply, we're finally ready to tell you about the system!

So, what is this SAGE System?
The SAGE System is based on what mathematicians call an "equilibrium strategy," which is a strategy that cannot be "beaten" in the following sense: If either player deviates from the equilibrium, his expectation will go down (and thus, in a two-player game, his opponent's expectation must go up). Studies have shown that for short-stacked, heads-up no-limit hold'em, using an equilibrium strategy makes the outcome of the tournament nearly a coin toss (weighted by the players' relative stack sizes, of course). To put it another way, if you find yourself facing Chris Ferguson heads up, this system will prevent him from using his (presumably) greater poker expertise to get an advantage over you.

There are many ways to find the equilibrium strategy; we started by ranking the 169 possible hold'em starting hands according to their overall "power" in heads-up play (unsurprisingly, A-A is first and 3-2 offsuit is last). Starting with this list enabled us to devise the SAGE System so that it is easy to use in practice (it also results in a slight deviation from the "true" equilibrium strategy, but it gives up virtually zero edge). We then modeled the expected winnings of each player mathematically and used a procedure called "minimax" to find the equilibrium strategy. The following table summarizes the results:

Optimal Top Percentage and Cutoff Hands


Here's how to interpret the above table:


• The "R" column is the ratio of the shorter stack to the big blind, after the blinds have been taken. For instance, if the shorter stack is $17,000 and the big blind is $3,000, R = $17,000 ÷ $3,000, or about 6.

• The "SB Top %" is the percentage of your hands that you should jam with in the small blind, given that value of R.


• "SB Cutoff Hand" is the worst hand that meets that criterion. Of course, for this to be any good to you, you have to know the ranking of all 169 starting hands. SAGE makes it unnecessary to know this list.

• "BB Top %" is the percentage of your hands that you should call with, if the SB jams.


• "BB Cutoff Hand" is, again, the worst hand that you should call with, if the SB jams.

• "SB Edge" is the amount that the SB can expect to win, in "big blind" units, for that value of R, if both players follow this system. Note that when R is 7 or greater, the SB has a slight negative expectation if he employs only the jam-or-fold strategy. If R is this high and you're the SB, you should "play good poker" (that is, mix up limping, minimum raising, and jamming). However, if you think your opponent is substantially better than you, you can simply play the equilibrium strategy, secure in the knowledge that you're giving up only a microscopic edge.


Now, if you had a list of all 169 starting hands, you could just find your hand in that list and see if it's above or below the threshold in the table above. While this is straightforward for a computer to do, it's not the sort of thing that most of us could do in a live tournament. The SAGE System simplifies the entire process into two easy steps. As promised, you can keep it on a 3"- by- 5" card with you if you're playing online, and can quickly memorize it for brick-and-mortar casino use.

1. Compute a Power Index (PI)
1. The "power number" of each card is its rank: J=11, Q=12, K=13, A=15 (don't forget that the ace is 15!)


2. Take the power number for your higher card and double it.

3. Add the power number of your lower card.

4. If it's a pocket pair, add 22.


5. If they're suited, add 2.

6. The sum is the Power Index (PI) of your hand.


2. Use the PI

1. Compute the ratio (R) of the shortest stack to the big blind.


2. Look up the necessary PI for that value of R.

3. If the PI of your hand is greater than or equal to that value, jam (if you're the button/SB) or call (if you're the BB).

3. The SAGE Table

SAGE Examples

Example No. 1

The blinds are $500-$1,000. After the blinds are taken, the SB has $5,635 in chips and the BB has $2,865 in chips. The SB has pocket threes. So, what's his power index (PI)?

PI = (2 x 3) + 3 + 22 = 31

The BB has J-4 suited. His PI = (2 x 11) + 4 + 2 = 28. The value of R is the smaller stack ($2,865) divided by $1,000, which is close enough to 3 for our purposes.

Looking at the table, the SB should jam. His PI of 31 is much greater than the necessary value of 22. The BB should call; his PI of 28 is greater than the necessary value of 24.

Example No. 2:

The stack sizes and starting hands are the same, but the blinds are $200-$400. Is anything different? The SB's PI is still 31, but R is now $2,865 divided by $400, which is about 7. Looking at the entry for R=7, the SB number is 26, so he should still jam. But the BB, whose PI is 28, doesn't have the value of 30 necessary to call. He should fold if the SB jams.

Conclusions

There's one important thing to learn from this: Heads-up no-limit hold'em is not rocket science when the blinds are high compared to one of the stacks. Note that suitedness counts for almost nothing, and connectedness counts for less. We suspect that you will now agree with us that most players grossly underestimate the need to jam early and often. For that reason, you will often have a dramatic advantage over your opponents when using this system.

This information is correct, and provably so. Yet, even Dan Harrington got one of his examples wrong. On Page 409 of Harrington on Hold'em, Volume II, he describes a scenario in which you are in the big blind with Q-7 offsuit. The blinds are $3,000-$6,000 with a $300 ante, and this is the second hand of the heads-up finale of a tournament. Your opponent has $35,400 and you have $144,600. Your opponent, on the button, jams; what should you do? Dan goes into quite a bit of discussion about why this is a close decision. With SAGE, you simply compute the power index for your hand and the current value of R:

PI = (12 x 2) + 7 = 31.

R = $35,400 ÷ $6,000 6.

You look in the table and see that the value for calling is 29. You have 31. It's an easy call, and you hope that the flop is Q-Q-7.

Last question: Why are we giving this away? First, because it advances the game of poker. No discipline (including a game) can grow and thrive unless its disciples discuss, argue, prove, and disprove. Second, we don't see why just a select few people should have this information. You can bet your entire bankroll that Chris Ferguson and many others have it. Now, you do, too. *

We are indebted to Mike Maurer for his review and critique of this system.Please note that the SAGE System is Copyright © 2005 by James Kittock and Lee Jones, and the terms SAGE System and "Are you SAGE?" are trademarks. You have our permission (indeed, our encouragement) to use it. But you can't take credit for it and you can't sell it.Lee Jones is the author of the best-selling book Winning Low Limit Hold'em, and is the cardroom manager for PokerStars.com. James Kittock is a math teacher at Mission College in Santa Clara, California, and a serious low-limit hold'em player

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