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Home arrow The Mathematics of Poker arrow The Odds of a Pot
The Odds of a Pot


Pot odds are the odds the pot is giving you for calling a bet. If there is $50 in the pot and the final bet was $10, you are getting 5-to-1 odds for your call. It is essential to know pot odds to figure out expectation. In the example just given, if you figure your chances of winning are better than 5-to-1, then it is correct to call. If you think your chances are worse than 5-to-1, you should fold.

Calling on the Basis of Pot Odds When All the Cards are Out

When all the cards are out, you must decide whether your hand is worth a call, and that depends upon the odds you are getting from the pot and what you think of your chances of having the best hand. It is a judgment problem more than a math problem because there is no way to calculate your chances of winning precisely. If you can beat only a bluff, you have to evaluate the chances that your opponent is bluffing. When you have a decent hand, you must evaluate the chances that your opponent is betting a worse hand than yours. Making these evaluations is often not easy, especially when you have a marginal hand like two pair in seven-card stud. Your ability to do so depends upon your experience, especially your ability to read hands and players. Some things can be learned only through trials by fire at the poker table.

Calling on the Basis of Pot Odds with More Cards to Come

What about deciding whether to call before the draw in draw poker and in stud games when there is one card to come? Now the math becomes important. If you know you have to improve your hand to win, you have to determine your chances of improving in comparison to your pot odds. With a flush draw or an open-ended straight draw-we'll assume the games is five-card draw poker you would be correct to call a $10 bet when the pot is $50 since your chance of making the flush or the straight is better than 5-to1. Specifically, the odds of making the flush are 4.22-to-1 against and the odds of making the straight, 4.88-to-1 against.

Figuring the odds for making a hand is done on the basis of the number of unseen cards and the number among them that will make the hand. In five-card draw there are 47 unseen cards- the 52 in the deck minus the five cards in your hand. If you are holding four of a suit, nine of the 47 unseen cards will give you a flush and 38 won't. Thus, the odds against making the flush are 38-to-9, which reduces to 4.22-to-1. If you are holding, say any 6, 7, jack, or queen makes the straight, reducing the odds to exactly 2-to-1 against. Sixteen cards make the hand, and 32 don't. The smaller the pot odds vis-a-vis the chances of making your hand, the more reason you have to fold. With only $30 in the pot instead of $50, calling a $10 bet for a flush draw or a straight draw (assuming you do not have a joker in your hand) becomes incorrect- that is, it becomes a wager with negative expectation - unless the implied odds are very large, as they might be in a no-limit or pot-limit games.

It is because of the pot odds that people say you need at least three other players in the pot to make it worth paying to draw to a flush in draw poker. With the antes in there, the pot odds are about 4-to-1, and when the bug is used, your chances of making the flush are 3.8-to-1. Notice, incidentally the effect of the antes, the higher they are, the better the pot odds, and the easier it is to call with a flush draw. On the other hand, with no ante and three other players in the pot, you'd be getting only 3-to-1 if you called a bet before the draw, and so you'd have to fold a four-flush then eight of the 47 unseen cards will make the straight --- four 8s and four kings -while 39 of the cards won't help, which reduces to 4.88-to-l.

When a joker or bug is used, as in public card rooms in California, you have an additional card to use to make flushes and straights, which improves the chances of making the flush to 3.8-to-1 and of making the straight to 4.33-to-1. With a joker in your hand, the chances of making a straight improve dramatically; instead of having eight or nine cards to help your hand, you might have 12 or even 16. For example, if you are holding.

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