Pot odds

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In poker, pot odds are the ratio of the current size of the pot to the cost of a contemplated call[1]. In other words, if the pot contains $100, and a player must call $10 to stay in the hand, then the player has 100-to-10, or 10-to-1 (commonly expressed as 10:1), pot odds. Pot odds are often compared to the probability of winning a hand with a future card in order to estimate the call's expected value. Indeed, a common usage of the term is to say that one "has pot odds", meaning that the present pot odds, compared to one's estimated chance of winning, make it profitable to call.

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Converting odds to and from probabilities

Odds are ratios, but converting them to probabilities will often make them easier to work with. The ratio has two numbers: the size of the pot and the cost of the call. To convert this ratio to the equivalent probability, we add these two numbers together and then divide the cost of the call by this sum. For example, the pot is $30, and the cost of the call is $10. The pot odds in this situation are 30:10, or 3:1 when simplified. To get the probability, we add $30 and $10 to get a sum of $40 and then divide $10 by $40, giving us 1/4, or 25%.

To convert any probability to the equivalent odds, we subtract the numerator from the denominator and then divide this remainder by the numerator. For example, to convert 1/4 (or 25%), we subtract 1 from 4 to get a remainder of 3 (or 25 from 100 to get a remainder of 75) and then divide 3 by 1 (or 75 by 25), giving us 3, or exactly 3:1.

Using pot odds to determine expected value

When a player holds a drawing hand, or a hand that is behind now but is likely to win if a certain card is drawn, pot odds are used to determine the expected value of that hand when the player is faced with a bet.

The expected value of a call is determined by comparing the pot odds to the odds of drawing a card that wins the pot. When the odds of drawing a card that wins the pot are numerically higher than the pot odds, the call has a positive expectation; on average, you win a portion of the pot that is greater than the cost of the call. Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and you can expect to win less money on average than it costs to call the bet.

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