This is a discussion on The science of winning poker within the online poker forums, in the Poker News section; Bluffing still matters, but the best players now depend on math theory http://s.wsj.net/public/resources/images/RVAL163_POKER_G_20130726185305.jpg The World Series of Poker, 2010. Associated Press More than 6,300 players, each paying an 


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The science of winning poker
Bluffing still matters, but the best players now depend on math theory
The World Series of Poker, 2010. Associated Press More than 6,300 players, each paying an entry fee of $10,000, gathered in Las Vegas early this month for the championship event of the 44th annual World Series of Poker. The tournament ran for 10 days, and just nine players now remain. They will reunite in November for a twoday live telecast to determine who wins the first prize: $8.3 million. Poker didn’t get this big overnight. In 2003, a thenrecord 839 players entered the championship for a shot at $2.5 million. The winner was an amateur with the improbable name of Chris Moneymaker. After ESPN devoted seven primetime hours to his triumph, online poker took off and tournament participation ballooned, as did prize pools. The U.S. government’s ban on the major online poker sites in 2011 reined in enthusiasm, but the game has continued to grow in Europe, Asia and Latin America. This growth over the past decade has been accompanied by a profound change in how the game is played. Concepts from the branch of mathematics known as game theory have inspired new ideas in poker strategy and new advice for ordinary players. Poker is still a game of reading people, but grasping the significance of their tics and twitches isn’t nearly as important as being able to profile their playing styles and understand what their bets mean. In nolimit hold’em poker, the game used for the World Series championship, each player is dealt two private cards and attempts to make the best fivecard hand that he can by combining his own cards with five cards that are shown faceup and shared by all players. Those cards are revealed in stages: The first three are the “flop,” the fourth is the “turn,” and the fifth is the “river.” Players can bet any amount they like at each stage. Suppose you hold a pair of sevens, and before the flop is dealt you go allin (bet all of your chips). One player calls your bet, and everyone else folds their hands. You both turn your cards face up, and you are happy to see your opponent show a pair of sixes. You are in great shape, since you have the better hand. But when the flop arrives, it contains a six, giving your opponent three sixes, and your own hand doesn’t improve, so you lose. Was your allin play correct? In terms of results, it wasn’t, because you lost all your chips. But according to the math of hold’em, a pair of sevens is favored to beat a pair of sixes 81% of the time. So if you can go allin with sevens and get your bet called by players holding sixes over and over again, luck should even out, and eventually you will be a big winner. Poker theorist David Sklansky once wrote that you should consider yourself a winner as long as you had the higher probability of winning the hand when all the money went into the pot. This attitude is consistent with the underlying mathematical reality of poker, and it can smooth out your emotional reactions to losses and wins. What matters is the quality of your decisions, not the results that come from them. A few years ago, a young pro named Phil Galfond published a crucial refinement to Mr. Sklansky’s point. He showed that the right way to analyze a poker decision is to consider your opponent’s “range”—that is, the full set of different hands that he could plausibly have, given all the actions that he has thus far taken. So if, for example, you believed that your opponent would only call your bet if he held sixes or a better pair, then at the moment he calls—before he turns up his cards—you should be unhappy. You want to see the sixes and be an 81% favorite, but you are much more likely to see a hand like eights, nines or higher, and against any of these your likelihood of winning is only about 19%. In fact, against this range of pairs from sixes up to aces, your “equity”—your winning chances averaged over all of those possible hands—would be just 27%. Of course, in poker, you rarely know your opponent’s range precisely, nor does he know yours. In our example, if your opponent thinks you would never go allin without at least a pair of tens, he probably won’t call you with anything worse than that. So his calling range depends on what he thinks your range could be. In practice, this means that you should not make a particular play (such as an allin bet) only when you have a superstrong hand, because this makes it easy for an observant opponent to deduce your range and fold with all but his own superstrong hands. If you sometimes make a strong play with weak hands—the ancient practice of bluffing—your opponent has a harder time narrowing your range down. This concept, known as “balancing” one’s range, supplements an expert’s intuition about when to bluff with logical explanations of why and how often it is the right play. Calculating equities for ranges is too complicated to do while you are playing. Today’s top tournament players advise upandcomers not to memorize formulas but to improve their feeling for ranges by playing with poker calculation apps that rapidly estimate odds by simulating thousands of hands. Why this sudden leap forward in the strategy of a game that has existed for over a century? Computer analysis has contributed, just as it has wrought changes in backgammon and chess theory. But the real cause of the advances that have accompanied the poker boom has been the boom itself. With 10 times more people seriously playing the game, the collective creativity and thinking power of the poker world has grown by at least an order of magnitude. The growth of poker theory is a perfect example of how innovation accelerates in interacting communities. Today’s poker players are in a worldwide arms race to discover new ideas and refine their playing styles, led by the younger generation of more mathematically minded pros. And collective progress comes from the application of collective intelligence: Putting more minds to work on a problem makes the discovery of new and better solutions much more likely. Jason Lee 1. Each player is dealt two private cards. The goal: to make the best fivecard hand using the five faceup cards shared by all players. 2. Player A gets two sevens; Player B gets two sixes. Neither player knows what the other has yet, but a pair of sevens is favored to beatapair of sixes 81% of the time. 3. After the shared cards are dealt and the players reveal their hands, Player B wins with three sixes, beating the odds. —Mr. Chabris is a psychology professor at Union College, the coauthor of “The Invisible Gorilla: How Our Intuitions Deceive Us” and a chess master. He played in his first World Series of Poker this year 
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I believe that now in this day and age of super sick players,
the most important thing is being able to apply your image to your game with the understanding of using it deceptively against top thinking players. Also having the observation to be able to pin point their game and how many layers they have to their deceptive strategy as and how they use this and how and when betting patterns are in sync with the board textures. This for me is by far the hardest part of my game to master, since its constantly changing and becoming more evolved/advanced it has to come down to individual expert observation skills if you want to succeed at the highest level over a long period this is clinical to a players game 
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I believe the science in winning poker lies in your emotions. Many players go on tilt and they mess up their bankrolls. I really feel that handling your emotions is a very important part of poker that is usually overlooked. If more people would know the scinece of emotions and tilting they would be better players.

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re: Poker & The science of winning poker
Great article....much informed. It was a great read.
Question though...since i'm not too good at Maths...since the chances of 77 vs 66 is 81%......would the percentage be the same with AA vs KK, QQ vs JJ, TT vs 99 ect etc? ...whats formula is used to attain this,,,nothing major just curious 
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"Poker theorist David Sklansky once wrote that you should consider yourself a winner as long as you had the higher probability of winning the hand when all the money went into the pot''.
I think like this too.....just a short while ago I was in the bankroll mob freeroll with 39 players left and i was 3rd place in the chip lead when i was dealt an AQ...after deliberating for a long while I decide to go all in and after deliberation for a long while some guy called me with AK suite...we both hit an ace and he won...but i was so bummed because the guy hand the better pre flop hand....It would have been a different story had he won me with Ace rag lol 
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AA to KK is favored 81%. KK to QQ is favored 81%. These numbers are accurate in heads up play. If more people are in the pot, they change. The point is, the bigger pair will always be favored to win. 
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Points taken. I think ranging and range calculations are my biggest weakness. 
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re: Poker & The science of winning poker
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The rule of 2 is: For every out you have to make a (probable) winning hand you multiply this by 2 times the number of cards to come down on the board. You can check this as follows  say you have AK before the flop. The chances of an Ace or a King coming down on the flop is 6 (3 aces and 3 Kings left in the pack) times 3 cards to come on the flop times 2 = 6x6 = 36%. This is approximate but good enough for quick calculations. Assuming one does not drop, the chance of one coming on the turn alone is 6 times 1 times 2 = 6x2 = 12%. And so on. To get the chances of 77 against 66 the formula is: The 66 hand needs another 6 to drop (forget the straights etc for the moment). There are two left and five cards to drop in total so the chances are 2 x 5 x 2 = 20%. Actually you should then add: But if a 6 does drop there is still a 20% chance that a 7 will drop as well. So the 20% chance of a 6 dropping and winning is reduced by 20% (a fifth) which leaves you with a very approximate 16% chance of the 66 winning. The rule of 2 assumes there are 50 cards in the pack and that there are always same number of cards left to be dealt after the flop, turn, river etc when of course this is not so. So the actual percentages are always different but near enough for our purposes. 
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re: Poker & The science of winning poker
For me the way I feel and focus is a huge part of the success I have or do not, catching things that do not make since during the hand and check raising does help win allot of pots that otherwise would have been folded by me

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Curious though, could you please list some of the great 'poker' players (not tennis) who actually believe this? It'd seem odd for the great ones to believe something like this 
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Figuring the odds when too players are all in is just a matter of feeling good about your chances or feeling lousy. Both hands are exposed and whatever will happen happens. Determining odds on any other two hands presupposes that a player is good enough to have a "read" on someone else's covered cards. The best most players can manage is a read on a range of hands  he might have this or he might have that or he might have something else. The earlier it is in the hand the more difficult this is. The math part is important when it has to do with your hand and your hand only  what are the odds of making my flush compared to how much money I have to invest and how much I can expect to win. Knowing these "odds" is essential. Otherwise, I believe that your biggest asset in a poker game is not knowing the numbers but knowing the people. Psychology will serve you better in most instances than math.
I recently read a quote which I hope I have right that wasn't attributed to anyone in particular but it makes sense to me. It went " Poker is not a game that people play with cards but a game of people played with cards." If that's not exact it's close. 