3.4.1 Pot Odds

Also called immediate odds, pot odds are the ratio of money in the pot against the cost to call. For example, if there are $12 in the pot and it costs $4 to call then you are getting 3-to-1 odds ( winnings-to- ``cost to stay in"). This can be translated to a percentage, representing the size of your contribution in the new pot, by using the following formula:

$$\lq\lq winnings-to-cost'' \: \sim \: \frac{cost}{(pot\_size + cost )}.$$ (3.1)

This percentage is the required probability of winning. If you are on the final round of betting then these are the odds you should have of winning the hand.

Continuing the example, the required probability is 4/(12+4) = 0.25. Hence, you need at least a 25% chance of winning to warrant a call. For example, if your hand was 4$\diamondsuit$-8$\diamondsuit$ and the board was 7$\diamondsuit$-A$\diamondsuit$-6$\clubsuit$-K$\heartsuit$ you would have a four-card diamond flush on the turn. You would estimate having 9 outs of the remaining 46 cards to make a winning diamond flush. This translates to a hand potential of 9/46 = 0.196 so it would be incorrect to call. On the other hand, you also have an inside straight draw (any 5 would give you a straight) and this is an additional 3 outs (the 5$\diamondsuit$ has already been counted). Now your potential is 12/46=0.261 so it is correct to call.

However, there are several caveats. Simply making the call does not necessarily end the round in a multi-player scenario; if there is a player behind you who has yet to see the bet, they may raise. In the above example, if you were expecting the player behind you to raise another $4 and the original bettor to call, then your pot odds are now 5-to-2 (pay $8 to win $20), elevating the threshold for staying in the hand to 8/(20+8) = .286. Also, knowledge of your opponents is not only required for an accurate estimate of hand strength or potential, but also to determine if you can expect to have to pay more. When considering potential this also assumes that the cards you are hoping for will make your hand the winner and not the second best. Further complications arise when there is more than one card left to be dealt.