Introduction to pot odds

Imagine there is $10,000 in the pot. You are heads-up, and your opponent goes all-in for his remaining $10. You don't even have a pair, but you do have an open-ended straight draw. Hopefully, this is a no-brainer decision — even though you are probably not winning at the moment, the pot is extremely big compared with the size of the bet you are facing, and you have a fair chance of hitting your hand. So the correct decision is to call the $10.

Now, imagine another situation, but this time there is only $5 in the pot. The flop is Th Jh Qh. Your opponent goes all-in for $2,500, and you are holding two black deuces. Now, only the craziest player would consider calling in this situation. Even in the very unlikely situation that you are currently winning, you will probably be outdrawn by the river (for example, if your opponent had Ah9d, even though at present you have the winning hand, he can hit any heart, any Ace, any King, any Nine, any Eight, or the board can double pair, and he will win). Of course, your opponent probably already has you beat, and you have at most one out (2d). The important point here is that the size of your opponent's bet is so large ($2,500) relative to the size of the pot ($5) that it is best to fold and wait for a better opportunity to get your money in. It is just not worth getting involved.

Of course, in real life everything is less clear-cut. A typical example might be that there is $140 in the pot and your opponent bets $45 on the turn. You have the flush draw. Should you call? Fortunately, a few simple calculations can help you make the correct decision when the situation is marginal.

Forget the cards for a moment, and imagine we are rolling a die — the game is that you win if a six comes; otherwise, I win. So the chances of you winning are 5-to-1 (normally written 5/1), because on average you will get five losses for every one win. Pot odds basically means that the price you are getting for staying in the pot should be longer (better) than the chance that you actually win.

So, suppose we are playing the die game, there is $4 in the pot, and I bet $1. Now there is $5 in the pot and you are faced with a decision of whether to call the $1 or fold. Here, every time you risk $1, you could potentially win $5, or, in other words, the pot is offering you 5/1 on your money — which is exactly the same as your chances of winning the game. This means that you are in a break-even situation: it doesn't matter whether you call or fold. On average, for every six times you play this game, fives times you will lose $1, and one time you will win $5, so you will be even.

Now suppose there is only $3 in the pot, and again I bet $1. Now the pot has $4 in it, and you are facing a bet of $1. The pot is offering you 4/1, but of course the chance of you winning the game is still 5/1. So, as the pot odds are too short, and you will lose money if you call in this situation. On average, for every six times you play this game, five times you will lose $1, but now the one time you win, you only get $4, which does not make up for the amount you have lost.

Similarly, if there was $5 in the pot and I bet $1, making a total pot of $6, you would be getting 6/1 on a call; and as the chance of you winning the game is still 5/1, this is a winning proposition for you to take.

Getting back to poker, suppose you have a flush draw on the turn — so you reckon that there are nine cards out of the 46 left unseen in the deck that will give you the winning hand. This means that there are 37 cards left in the deck that will not give you the winning hand, so the odds of you making your draw are 37/9, which is better expressed as 4.1/1. So, in exactly the same way as for the die game, the break-even point (where it doesn't matter if you call or fold) is when the pot is 4.1 times larger than the bet you are facing. For example, suppose there is $140 in the pot, and I bet $45. So the pot stands at $185 and you are facing a bet of $45: the pot is offering you 185/45, which is 4.1/1. So, since this is the same as your actual chance of winning the hand, this is the break-even point. Knowing this, you can see that if the pot is $140 and I bet less than $45, you should call; and if I bet more than $45, you should fold.

In general, if you are facing a bet of $X, and the chance of you winning is W/1, then the break-even point occurs when the current pot size is the product of $X and W. So, for example, when facing a bet of $25 with your chance of winning being 5/1, the break-even point is when the pot is $25 x 5 = $125. So you should call if the pot is larger than $125, and fold if it is less than $125.

Pot odds can be used the other way round as well. Suppose you have TPTK ('top pair, top kicker') and you are sure your opponent is on the flush draw. If you bet an amount such that your opponent gets at least 4.1/1 from the pot, you are giving him a good price and he should call you. This isn't good poker for you, as you want to make your opponent pay over the odds. Whether or not the flush actually comes, you want to make him pay for the privilege of drawing against you. To offer your opponent odds of W/1 when the pot is currently $X, divide $X by W-1 and bet that amount. For example, if the pot is $95 and you want to offer odds of 4.1/1, bet $95 / (4.1 - 1) = $95 / 3.1 = $30. This would be the break-even point; betting less than $30 gives your opponent a favourable proposition (which is bad for you!); and betting more than $30 gives your opponent a losing proposition (which is good for you!). Remember that every time you make your opponent accept a losing proposition, you are playing winning poker, regardless of whether the flush actually comes in.

We have seen that when we have nine outs on the turn, we are 4.1/1. However, what if you have four outs on the turn? Or 15 outs on the flop? Here is a handy table that shows what your odds are. For example, with 11 outs on the flop, you are 1.4/1.

outs turn flop
20 1.30 0.48
19 1.42 0.54
18 1.56 0.60
17 1.71 0.67
16 1.88 0.75
15 2.07 0.85 [flush and straight draw]
14 2.29 0.95
13 2.54 1.08
12 2.83 1.22
11 3.18 1.40
10 3.60 1.60
9 4.11 1.86 [flush draw]
8 4.75 2.18 [straight draw]
7 5.57 2.59
6 6.67 3.14
5 8.20 3.91
4 10.50 5.07 [gutshot/two-pair]
3 14.33 7.01
2 22.00 10.88
1 45.00 22.50