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‘Easy’ Things to Do to Win at Poker — Part VIII

Compute the odds

by Barry Tanenbaum |  Published: Jan 08, 2010

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This series of columns focuses on things that you can do at the table to improve your decision-making. I have been discussing each item on the list below, extracted from my book Advanced Limit Hold’em Strategy.

• Pay more attention
• Select the best games
• Learn how your opponents play
• Study betting patterns
• Analyze every situation
• Plan in advance
• Play focused on the game
• Count the pot
• Compute the odds
• Figure out how the play might go
• Estimate what your opponents think you hold and how you should respond
• Then, make a decision

In my last column, I explored playing focused on the game and counting the pot (all of the columns in this series are available at www.CardPlayer.com). This column will discuss computing the odds.

Computing the Odds: First, here’s a commercial in favor of computing the odds. At its core, poker requires evaluating your risks and rewards. How many chips do you have to put at risk, and how big a pot will you drag if you succeed? The problem is that poker is also a game of incomplete information, so while you may know how big the pot is (having read my last column), figuring out what to put in the numerator can sometimes be tough.

For example, you have a hand on the river that can beat only a bluff. Your lone opponent bets, making the pot 10 big bets. If you win 10 percent of the times that you call, you’ll be a winner (lose nine times and collect 10 bets when you win). So, if your opponent bluffs 15 percent of the time in this situation, you must call. If he bluffs 5 percent of the time, you should fold. Unfortunately, your opponent does not have a sign that tells you how often he bluffs (even online, you can tell how often he loses showdowns, but not how often his losses were bluffs).

Even worse, if you call and lose, you still have no idea whether your call was good or bad. Given all of that, how is this a commercial in favor of computing odds? Well, through close observation of each opponent’s style, you can get a feel for what each person’s number might be. Many people bluff with great frequency, and others bluff roughly never. Few bluff with the exactly correct game-theoretical frequency to render your decision irrelevant. Knowing the odds, even in uncertain situations, still gives you a better guideline than simply calling every time or folding in disgust when your opponent bets the river.

Even when you know the exact odds, you still have a lot of thinking to do. You not only need to compute the chances that you will make your hand, but you also must understand the chances that your hand will win if you make it. I want to spend some time explaining this, because this concept escapes many players. The example I’ll use is open-end straight draws.

Most poker books and several websites will tell you the chances of completing a flopped open-end straight draw. They are 17 percent on the turn, 17.4 percent on the river if you miss the turn, and 31.4 percent if you wait for two cards.

But, not all open-end straight draws are alike. Holding K-Q on a J-10-6 board is completely different from holding A-8 on a J-10-9 board. Yes, the chances of making your hand are the same, but your chances of making the winning hand are very different. In the first case, any straight that you make will be the nuts. In the second, you may be drawing dead already if your opponent has K-Q, but even if he doesn’t and a queen comes, you still will be beat if he has a king in his hand.

OK, that was pretty obvious. Let’s now look at these three situations, with you holding the hand in parentheses:

(1) K (Q-J) 10
(2) 9 (8-7) 6
(3) 6 (5-4) 3

All of these situations look pretty much alike. You have an open-end straight draw, and will have the nuts if you make it. But what happens if you pair your top card on the turn? In case (1), you now may be drawing for a tie with an opponent who has A-J. In case (2), with an 8 on the turn, you are drawing for a tie only if your opponent is playing 10-7, while in case (3), with a 5 on the turn, he has to hold 7-4.

In addition, hitting a queen in case (1) will dry up your action if an ace or 9 comes on the river, making the board A-K-Q-10 or K-Q-10-9. The same may not happen in case (3) if the board is 7-6-5-3. Opponents may be wary, but it will be harder to put you on a 4.

In many games, hitting your 5 on the turn in hand (3) gives you several extra outs (for trips and two pair, depending on the size of the field and the likelihood that one of your opponents is playing a hand with a 7 or deuce in it). In hand (1), almost the last hand that you want to make is two pair. Hand (2) falls somewhere in the middle.
Thus, in close cases, situation (3) offers several possible extra outs that do not exist in situation (1). Take this sort of thing into account when you compute your chances of winning.

Important note: The foregoing does not mean that you should play 5-4 and toss Q-J. It does mean that you need to account for the potential of each hand when computing how much money it may take to pursue your draw. Your 5-4 in certain situations may be worth an additional fraction of a bet in some open-end straight draw cases if you do get lucky, but more frequent cases, such as flopping a pair, substantially favor the high cards.]

One factor slightly favoring case (1) is that your opponents are more likely to hit two pair when you do make your straight, and therefore may give you more action.

Final thoughts: Many other factors will influence your computations, including whether or not the board has a flush draw, how many opponents there are, and how likely your opponents are to pay you off if you bet or check-raise the turn or river.

Many years ago, an opponent who typically played a much higher limit was in my game, having temporarily experienced a shortage of funds. After I won a pot, he explained that he would have won if he had stayed in, but since he figured (correctly) that one of his opponents was on a flush draw, he counted only six outs and the pot was not quite big enough for him to call the turn. The river was in fact one of his six outs, but he had the poker knowledge and discipline to make the right decision. Needless to say, he was quickly back playing the high-limit game, as he did very well in our game. It was a great lesson for me, and I have been computing odds ever since.

Next issue, we will look at figuring out how the play might go. Spade Suit

Barry Tanenbaum is the author of Advanced Limit Hold’em Strategy, and collaborator on Limit Hold’em: Winning Short-Handed Strategies. Barry offers private lessons tailored to the individual student. Please see his website, www.barrytanenbaum.com, or write to him at pokerbear@cox.net.