Reducing Your Pot Odds With More than One Card to Come

Let's say you are playing hold 'em, and after the flop you have a four-flush that you are sure will win if you hit it. There are two cards to come, which improves your odds of making the flush to approximately 13/4-to-l. It is a $10-$20 game with $20 in the pot, and your single opponent has bet $10. You may say, "I'm getting 3-to-1 odds and my chances are 13/4-to-l. So I should call"
However, the 13/4-to-l odds of making the flush apply only if you intend to see not just the next card, but the last card as well, and to see the last card you will probably have to call not just $10 now but also $20 on the next round of betting. Therefore, when you decide you're going to see a hand that needs improvement all the way through to the end, you can't say you are getting, as in this case, 30-to-10 odds. You have to say, "Well, if I miss my hand, I lose $ 10 on this round of betting and $20 on the next round. In all, I lose $30. If I make my hand, I will win the $30 in there now plus $20 on the next round for a total of $50." All of a sudden, instead of 30-to-10, you're getting only 50-to-30 odds, which reduces to 12/3-to-l.
These are your effective odds - the real odds you are getting from the pot when you call a bet with more than one card to come. Since you are getting only 12/3-to-l by calling a $10 bet after the flop, and your chances of making the flush are 13/4-to-1, you would have to throw away the hand, because it has turned into a losing play - that is, a play with negative expectations. The only time it would be correct to play the hand in this situation is if you could count on your opponent to call a bet at the end, after your flush card hits. Then your potential $50 win increases to $70, giving you 70-to-30 odds and justifying a call.2
It should be clear from this example that when you compute odds on a hand you intend to play to the end, you must think not in terms of the immediate pot odds but in terms of the total amount you might lose versus the total amount you might win. You have to ask, "What do I lose if I miss my hand, and what will I gain if I make it?" The answer to this question tells you your real or effective odds.

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2 While a call on the flop might be a bad play, a semi-bluff raise could be a good play. Sometimes folding is a better alternative to calling, but raising is the best alternative of all. (See Chapters Eleven and Thirteen.)


Let's look at an interesting, more complex application of effective odds. Suppose there is $250 in the pot, you have a back-door flush draw in hold 'em, and an opponent bets $10. With a back-door flush you need two in a row of a suit. To make things simple, we'll assume the chances of catching two consecutive of a particular suit are 1/5 X 1/5. That's not quite right, but it's close enough.3 It means you'll hit a flush once in 25 tries on average, making you a 24-to-l underdog. By calling your opponent's $10 bet, you would appear to be getting 26-to-1. So you might say, "OK, I'm getting 26-to-1, and it's only 24-to-l against me. Therefore, I should call to try to make my flush."
Your calculations are incorrect because they do not take into account your effective odds. One out of 25 times you will win the $260 in there, plus probably another $40 on the last two rounds of betting. Twenty times you will lose only $10 when your first card does not hit, and you need not call another bet. But the remaining four times you will lose a total of $30 each time when your first card hits, you call your opponent's $20 bet, and your second card does not hit. Thus, after 25 such hands, you figure to lose $320 (S200 + $120) while winning $300 for a net loss of $20. Your effective odds reveal a call on the flop to be a play with negative expectation and hence incorrect.