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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] 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 [2] 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, [3] [4] 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, 10 is divided by the sum of 30 and 10, giving 0.25, or 25%.
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.
It is important to note that using pot odds makes assumptions of your opponent's hand. When calculating the odds of Alice drawing her flush, it was assumed that her opponent did not hold any of the remaining clubs. It was also assumed that her opponent did not have two-pair or a set. In these cases, her opponent could have been drawing on a higher flush, a full house, or four of a kind, all of which would win even if Alice made her flush. This is where considering the range of an opponent's hands becomes important. If, for example, Alice's opponent raised multiple times preflop, it would be more likely that they have a stronger drawing hand, such as Ace-King of clubs, by the time the turn came.
Pot odds are just one aspect of a sound strategy for poker based on game theory. The purpose of using game theory in poker is to make a player indifferent to how their opponent plays. It should not matter if the opponent is passive or aggressive, tight or loose. Pot odds can help the player make more mathematically based decisions, as opposed to playing exploitatively where the player guesses their opponent's decisions based on certain behaviors.
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.
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, 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).
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.
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.
With one card to come, Bob has a made hand, but the board shows a potential flush draw. According to the Fundamental theorem of poker, Bob wants to bet enough for an opponent with a flush draw to incorrectly 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).
Slanksy notes that 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. His strategy is an equilibrium strategy in the sense that it is optimal against someone playing an optimal strategy against it, though no lesser strategy can beat it (another strategy may beat the lesser strategy by more).
Five-card draw is a poker variant that is considered the simplest variant of poker, and is the basis for video poker. As a result, it is often the first variant learned by new players. It is commonly played in home games but rarely played in casino and tournament play. The variant is also offered by some online venues, although it is not as popular as other variants such as seven-card stud and Texas hold 'em.
Poker is a family of comparing card games in which players wager over which hand is best according to that specific game's rules. It is played worldwide, but in some places the rules may vary. While the earliest known form of the game was played with just 20 cards, today it is usually played with a standard deck, although in countries where short packs are common, it may be played with 32, 40 or 48 cards. Thus poker games vary in deck configuration, the number of cards in play, the number dealt face up or face down, and the number shared by all players, but all have rules that involve one or more rounds of betting.
In poker, the strength of a hand is often called its value; however, in the context of poker strategy the term is more often used to describe a betting tactic, a bet for value. This bet is intended to increase the size of the pot, by inducing opponents to call. A bet for value is in contrast to a bluff or a protection bet.
Protection in poker is a bet made with a strong but vulnerable hand, such as top pair when straight or flush draws are possible. The bet forces opponents with draws to either call with insufficient pot odds, or to fold, both of which are profitable for the betting player. By contrast, if he failed to protect his hand, another player could draw out on him at no cost, meaning he gets no value from his made hand.
A poker player is drawing if they have a hand that is incomplete and needs further cards to become valuable. The hand itself is called a draw or drawing hand. For example, in seven-card stud, if four of a player's first five cards are all spades, but the hand is otherwise weak, they are drawing to a flush. In contrast, a made hand already has value and does not necessarily need to draw to win. A made starting hand with no help can lose to an inferior starting hand with a favorable draw. If an opponent has a made hand that will beat the player's draw, then the player is drawing dead; even if they make their desired hand, they will lose. Not only draws benefit from additional cards; many made hands can be improved by catching an out – and may have to in order to win.
In a poker game with more than one betting round, an out is any unseen card that, if drawn, will improve a player's hand to one that is likely to win. Knowing the number of outs a player has is an important part of poker strategy. For example, in draw poker, a hand with four diamonds has nine outs to make a flush: there are 13 diamonds in the deck, and four of them have been seen. If a player has two small pairs, and he believes that it will be necessary for him to make a full house to win, then he has four outs: the two remaining cards of each rank that he holds.
Omaha hold 'em is a community card poker game similar to Texas hold 'em, where each player is dealt four cards and must make their best hand using exactly two of them, plus exactly three of the five community cards. The exact origin of the game is unknown, but casino executive Robert Turner first brought Omaha into a casino setting when he introduced the game to Bill Boyd, who offered it as a game at the Las Vegas Golden Nugget Casino. Omaha uses a 52-card French deck. Omaha hold 'em 8-or-better is the "O" game featured in H.O.R.S.E.
In the card game of poker, a bluff is a bet or raise made with a hand which is not thought to be the best hand. To bluff is to make such a bet. The objective of a bluff is to induce a fold by at least one opponent who holds a better hand. The size and frequency of a bluff determines its profitability to the bluffer. By extension, the phrase "calling somebody's bluff" is often used outside the context of poker to describe situations where one person demands that another proves a claim, or proves that they are not being deceptive.
Texas hold 'em is one of the most popular variants of the card game of poker. Two cards, known as hole cards, are dealt face down to each player, and then five community cards are dealt face up in three stages. The stages consist of a series of three cards, later an additional single card, and a final card. Each player seeks the best five-card poker hand from any combination of the seven cards: the five community cards and their two hole cards. Players have betting options to check, call, raise, or fold. Rounds of betting take place before the flop is dealt and after each subsequent deal. The player who has the best hand and has not folded by the end of all betting rounds wins all of the money bet for the hand, known as the pot. In certain situations, a "split pot" or "tie" can occur when two players have hands of equivalent value. This is also called "chop the pot". Texas hold 'em is also the H game featured in HORSE and HOSE.
Slow playing is a deceptive play in poker where a player bets weakly or passively with a strong holding. It is the opposite of fast playing. A flat call can be a form of slow playing. The objective of slow playing is to lure opponents into a pot who might fold to a raise, or to cause them to bet more strongly than they would if the player had played aggressively. Slow playing sacrifices protection against hands that may improve and risks losing the pot-building value of a bet if the opponent also checks.
David Sklansky is an American professional poker player and author. An early writer on poker strategy, he is known for his mathematical approach to the game. His key work The Theory of Poker presents fundamental principles on which much later analysis is based.
The fundamental theorem of poker is a principle first articulated by David Sklansky that he believes expresses the essential nature of poker as a game of decision-making in the face of incomplete information.
Every time you play a hand differently from the way you would have played it if you could see all your opponents' cards, they gain; and every time you play your hand the same way you would have played it if you could see all their cards, they lose. Conversely, every time opponents play their hands differently from the way they would have if they could see all your cards, you gain; and every time they play their hands the same way they would have played if they could see all your cards, you lose.
Jack "Treetop" Straus was an American professional poker player.
Morton's theorem is a poker principle articulated by Andy Morton in a Usenet poker newsgroup. It states that in multi-way pots, a player's expectation may be maximized by an opponent making a correct decision.
Badugi is a draw poker variant similar to triple draw, with hand-values similar to lowball. The betting structure and overall play of the game is identical to a standard poker game using blinds, but, unlike traditional poker which involves a minimum of five cards, players' hands contain only four cards at any one time. During each of three drawing rounds, players can trade zero to four cards from their hands for new ones from the deck, in an attempt to form the best badugi hand and win the pot. Badugi is often a gambling game, with the object being to win money in the form of pots. The winner of the pot is the person with the best badugi hand at the conclusion of play. Badugi is played in cardrooms around the world, as well as online, in rooms such as PokerStars. Although it hasn’t had its own tournament per se at the WSOP, it is featured in the Dealers Choice events as well as in the Triple Draw Mix. The 2023 WSOP event does have a Badugi tournament scheduled.
In no-limit or pot-limit poker, a post-oak bluff is a very small bet relative to the size of the already-existing pot. This type of bluff may be employed as an attempt at using reverse psychology to steal the pot. It holds comparatively little risk for the player making the bet. The term was popularized by Doyle Brunson in his 1979 book Super System.
Fold equity is a concept in poker strategy that is especially important when a player becomes short-stacked in a no limit tournament. It is the equity a player can expect to gain due to the opponent folding to his or her bets. It equates to:
The following is a glossary of poker terms used in the card game of poker. It supplements the glossary of card game terms. Besides the terms listed here, there are thousands of common and uncommon poker slang terms. This is not intended to be a formal dictionary; precise usage details and multiple closely related senses are omitted here in favor of concise treatment of the basics.
Poker is a popular card game that combines elements of chance and strategy. There are various styles of poker, all of which share an objective of presenting the least probable or highest-scoring hand. A poker hand is usually a configuration of five cards depending on the variant, either held entirely by a player or drawn partly from a number of shared, community cards. Players bet on their hands in a number of rounds as cards are drawn, employing various mathematical and intuitive strategies in an attempt to better opponents.
Draw poker is any poker variant in which each player is dealt a complete hand before the first betting round, and then develops the hand for later rounds by replacing, or "drawing", cards.