Pot odds

In poker, pot odds are the ratio of the current size of the pot to the cost of a contemplated call. 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.

Odds are most commonly expressed as ratios, but converting them to percentages 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 percentage, 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 percentage, we add 30 and 10 to get a sum of 40 and then divide 10 by 40, giving us 0.25, or 25%.

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

When a player holds a drawing hand (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.

Implied pot odds, or simply implied odds, are calculated the same way as pot odds, but take into consideration estimated future betting. Implied odds are calculated in situations where the player expects to fold in the following round if the draw is missed, thereby losing no additional bets, but expects to gain additional bets when the draw is made. Since the player expects to always gain additional bets in later rounds when the draw is made, and never lose any additional bets when the draw is missed, the extra bets that the player expects to gain, excluding his own, can fairly be added to the current size of the pot. This adjusted pot value is known as the implied pot.

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