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 game 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-to-1. Specifically, the odds of making the flush are 4.22-to-l against and the odds of making the straight, 4.88-to-l 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-l. If you are holding, say

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-l and of making the straight to 4.33-to-l. 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

any 6, 7, jack, or queen makes the straight, reducing the odds to exactly 2-to-l 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 game.

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-l, and when the bug is used, your chances of making the flush are 3.8-to-l. 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-l if you called a bet before the draw, and so you'd have to fold a four-flush.

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