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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. 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.
Converting odds ratios to and from percentages
Odds are most commonly expressed as ratios, but converting them to percentages 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, these two numbers are added together and the cost of the call is divided 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, 30 and 10 are added to get a sum of 40 and then 10 is divided by 40, giving 0.25, or 25%.
To convert any percentage or fraction to the equivalent odds, the numerator is subtracted from the denominator and then this difference is divided by the numerator. For example, to convert 25%, or 1/4, 1 is subtracted from 4 to get 3 (or 25 from 100 to get 75) and then 3 is divided by 1 (or 75 by 25), giving 3, or 3:1.
Using pot odds to determine expected value
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, a portion of the pot that is greater than the cost of the call is won. Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and the expectation is to win less money on average than it costs to call the bet.
Implied pot odds
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.
Example (Texas hold'em)
On the turn, Alice's hand is certainly behind, and she faces a $1 call to win a $10 pot against a single opponent. There are four cards remaining in the deck that make her hand a certain winner. Her probability of drawing one of those cards is therefore 4/47 (8.5%), which when converted to odds is 10.75:1. Since the pot lays 10:1 (9.1%), Alice will on average lose money by calling if there is no future betting. However, Alice expects her opponent to call her additional $1 bet on the final betting round if she makes her draw. Alice will fold if she misses her draw and thus lose no additional bets. Alice's implied pot is therefore $11 ($10 plus the expected $1 call to her additional $1 bet), so her implied pot odds are 11:1 (8.3%). Her call now has a positive expectation.
Reverse implied pot odds
Reverse implied pot odds, or simply reverse implied odds, apply to situations where a player will win the minimum if holding the best hand but lose the maximum if not having the best hand. Aggressive actions (bets and raises) are subject to reverse implied odds, because they win the minimum if they win immediately (the current pot), but may lose the maximum if called (the current pot plus the called bet or raise). These situations may also occur when a player has a made hand with little chance of improving what is believed to be currently the best hand, but an opponent continues to bet. An opponent with a weak hand will be likely to give up after the player calls and not call any bets the player makes. An opponent with a superior hand, will, on the other hand, continue, (extracting additional bets or calls from the player).
Limit Texas hold'em example
With one card to come, Alice holds a made hand with little chance of improving and faces a $10 call to win a $30 pot. If her opponent has a weak hand or is bluffing, Alice expects no further bets or calls from her opponent. If her opponent has a superior hand, Alice expects the opponent to bet another $10 on the end. Therefore, if Alice wins, she only expects to win the $30 currently in the pot, but if she loses, she expects to lose $20 ($10 call on the turn plus $10 call on the river). Because she is risking $20 to win $30, Alice's reverse implied pot odds are 1.5-to-1 ($30/$20) or 40 percent (1/(1.5+1)). For calling to have a positive expectation, Alice must believe the probability of her opponent having a weak hand is over 40 percent.
Manipulating pot odds
Often a player will bet to manipulate the pot odds offered to other players. A common example of manipulating pot odds is to make a bet to protect a made hand that discourages opponents from chasing a drawing hand.
No-limit Texas hold 'em example
With one card to come, Bob has a made hand, but the board shows a potential flush draw. Bob wants to bet enough to make it wrong for an opponent with a flush draw to call, but Bob does not want to bet more than he has to in the event the opponent already has him beat.
Assuming a $20 pot and one opponent, if Bob bets $10 (half the pot), when his opponent acts, the pot will be $30 and it will cost $10 to call. The opponent's pot odds will be 3-to-1, or 25 percent. If the opponent is on a flush draw (9/46, approximately 19.565 percent or 4.11-to-1 odds against with one card to come), the pot is not offering adequate pot odds for the opponent to call unless the opponent thinks they can induce additional final round betting from Bob if the opponent completes their flush draw (see implied pot odds).
A bet of $6.43, resulting in pot odds of 4.11-to-1, would make his opponent mathematically indifferent to calling if implied odds are disregarded.
According to David Sklansky, game theory shows that a player should bluff a percentage of the time equal to his opponent's pot odds to call the bluff. For example, in the final betting round, if the pot is $30 and a player is contemplating a $30 bet (which will give his opponent 2-to-1 pot odds for the call), the player should bluff half as often as he would bet for value (one out of three times).
However, this conclusion does not take into account some of the context of specific situations. A player's bluffing frequency often accounts for many different factors, particularly the tightness or looseness of their opponents. Bluffing against a tight player is more likely to induce a fold than bluffing against a loose player, who is more likely to call the bluff. Sklansky's strategy is an equilibrium strategy in the sense that it is optimal against someone playing an optimal strategy against it.
- List of poker terms
- Poker strategy
- Poker probability
- Poker probability (Texas hold 'em)
- Poker probability (Omaha)
- Sklansky, 1987, Glossary
- David Sklansky (1987). The Theory of Poker. Two Plus Two Publications. ISBN 1-880685-00-0.
- David Sklansky (2001). Tournament Poker for Advanced Players. Two Plus Two Publications. ISBN 1-880685-28-0.
- David Sklansky and Mason Malmuth (1988). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN 1-880685-22-1.
- Dan Harrington and Bill Robertie (2004). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume I: Strategic Play. Two Plus Two Publications. ISBN 1-880685-33-7.
- Dan Harrington and Bill Robertie (2005). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume II: The Endgame. Two Plus Two Publications. ISBN 1-880685-35-3.
- David Sklansky and Ed Miller (2006). No Limit Hold 'Em Theory and Practice. Two Plus Two Publications. ISBN 1-880685-37-X.