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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 compared to the odds of winning a hand with a future card in order to estimate the call's expected value. The purpose of this is to statistically guide a player's decision between the options of call or fold. Raising is an alternative to place this decision on the opponent.
Pot odds are only useful if a player has enough equity. Equity is the chance a player has to win the hand at showdown. It is calculated as the fraction of remaining cards in the deck for each remaining street (sequential card being dealt, e.g. turn, river) that can give a player the winning hand. For example, in Texas hold'em, if a player has an inside straight draw on the flop, there are four remaining cards in the deck, or outs, that can give them a straight on the turn or the river. The addition law of probability combines the chances of making the straight on the turn (4/47 = 8.5%) and on the river (4/46 = 8.7%) to give the player an equity of 17.2%, assuming no other cards will give them a winning hand. Calculating equity makes an assumption of the opponents hand. If the opponent holds blockers (outs that the player needs to make their hand), then the player's equity is lower than what is calculated from assuming all outs remain in the deck. While this may be a lot for a player to consider in the moment, calculating equity can be simplified with the rule of two and four.
When playing against a clock, calculating odds and percentages under pressure can be challenging. To facilitate this, the rule of two and four can be used. It is an estimate of equity. The player's number of outs are multiplied with double the amount of remaining streets. Using the example from before, the player had 4 outs with two streets to come. 4 outs multiplied by 4 (double the amount of remaining streets) gives an estimated equity of 16%. Compared to the actual equity of 17.2%, this estimation is close enough for games such as Texas hold'em where bet sizes are usually kept to less than or equal to 100% of the pot, where the relative pot odds have a large enough margin of error for the player to meet with their calculated equity.
Odds are most commonly expressed as ratios, but they are not useful when comparing to equity percentages for poker. The ratio has two numbers: the size of the pot and the cost of the call. To convert this ratio to the equivalent percentage, the cost of the call is divided by the sum of these two numbers. 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, 1 is divided by the sum of 3 and 1, giving 0.25, or 25% or 1/(3+1).
To convert any percentage or fraction to the equivalent odds, the numerator is subtracted from the denominator. The difference is compared to the numerator as a ratio. For example, to convert 25%, or 1/4, 1 is subtracted from 4 to get 3. The resulting ratio is 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 hand that wins at showdown. If the odds of drawing a desired hand are better than the pot odds (e.g. 3:1 drawing odds against 4:1 pot odds), the call has a positive expected value. The law of large numbers predicts the player will profit in the long run if they continue to call with advantageous pot odds. The opposite is true if the player continues to call with disadvantageous pot odds.
Alice holds 5-4 of clubs. The board on the turn is Queen of clubs, Jack of clubs, 9 of diamonds, and 7 of hearts. Her hand will almost certainly not win at showdown unless one of the 9 remaining clubs comes on the river to give her a flush. Excluding her two hole cards and the four community cards, there are 46 remaining cards to draw from. This gives a probability of 9/46 (19.6%). The rule of 2 and 4 estimates Alice's equity at 18%. The approximate equivalent odds of hitting her flush are 4:1. Her opponent bets $10, so that the total pot now becomes, say, $50. This gives Alice pot odds of 5:1. The odds of her hitting her flush are better than her pot odds, so she should call.
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Pot odds AI simulator
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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 compared to the odds of winning a hand with a future card in order to estimate the call's expected value. The purpose of this is to statistically guide a player's decision between the options of call or fold. Raising is an alternative to place this decision on the opponent.
Pot odds are only useful if a player has enough equity. Equity is the chance a player has to win the hand at showdown. It is calculated as the fraction of remaining cards in the deck for each remaining street (sequential card being dealt, e.g. turn, river) that can give a player the winning hand. For example, in Texas hold'em, if a player has an inside straight draw on the flop, there are four remaining cards in the deck, or outs, that can give them a straight on the turn or the river. The addition law of probability combines the chances of making the straight on the turn (4/47 = 8.5%) and on the river (4/46 = 8.7%) to give the player an equity of 17.2%, assuming no other cards will give them a winning hand. Calculating equity makes an assumption of the opponents hand. If the opponent holds blockers (outs that the player needs to make their hand), then the player's equity is lower than what is calculated from assuming all outs remain in the deck. While this may be a lot for a player to consider in the moment, calculating equity can be simplified with the rule of two and four.
When playing against a clock, calculating odds and percentages under pressure can be challenging. To facilitate this, the rule of two and four can be used. It is an estimate of equity. The player's number of outs are multiplied with double the amount of remaining streets. Using the example from before, the player had 4 outs with two streets to come. 4 outs multiplied by 4 (double the amount of remaining streets) gives an estimated equity of 16%. Compared to the actual equity of 17.2%, this estimation is close enough for games such as Texas hold'em where bet sizes are usually kept to less than or equal to 100% of the pot, where the relative pot odds have a large enough margin of error for the player to meet with their calculated equity.
Odds are most commonly expressed as ratios, but they are not useful when comparing to equity percentages for poker. The ratio has two numbers: the size of the pot and the cost of the call. To convert this ratio to the equivalent percentage, the cost of the call is divided by the sum of these two numbers. 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, 1 is divided by the sum of 3 and 1, giving 0.25, or 25% or 1/(3+1).
To convert any percentage or fraction to the equivalent odds, the numerator is subtracted from the denominator. The difference is compared to the numerator as a ratio. For example, to convert 25%, or 1/4, 1 is subtracted from 4 to get 3. The resulting ratio is 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 hand that wins at showdown. If the odds of drawing a desired hand are better than the pot odds (e.g. 3:1 drawing odds against 4:1 pot odds), the call has a positive expected value. The law of large numbers predicts the player will profit in the long run if they continue to call with advantageous pot odds. The opposite is true if the player continues to call with disadvantageous pot odds.
Alice holds 5-4 of clubs. The board on the turn is Queen of clubs, Jack of clubs, 9 of diamonds, and 7 of hearts. Her hand will almost certainly not win at showdown unless one of the 9 remaining clubs comes on the river to give her a flush. Excluding her two hole cards and the four community cards, there are 46 remaining cards to draw from. This gives a probability of 9/46 (19.6%). The rule of 2 and 4 estimates Alice's equity at 18%. The approximate equivalent odds of hitting her flush are 4:1. Her opponent bets $10, so that the total pot now becomes, say, $50. This gives Alice pot odds of 5:1. The odds of her hitting her flush are better than her pot odds, so she should call.