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The fundamental theorem of poker

Main articles: Fundamental theorem of poker and Morton's theorem

The fundamental theorem of poker, introduced by David Sklansky, states that every time you play your hand the way you would if you could see your opponent's cards, you gain, and every time your opponent plays his cards differently from the way he would play them if he could see your cards, you gain.[1] This theorem is the foundation for many poker strategy topics. For example, bluffing and slow-playing (explained below) are examples of using deception to induce your opponents to play differently than they would if they could see your cards. There are some exceptions to the fundamental theorem in certain multi-way pot situations, as described in Morton's theorem.

Pot odds, implied odds and poker probabilities

Main articles: Pot odds and poker probability

The relationship between pot odds and odds of winning is one of the most important concepts in poker strategy. Pot odds are the ratio of the size of the pot to the size of the bet required to stay in the pot.[1] For example, if a player must call $10 for a chance to win a $40 pot (not including his $10 call), his pot odds are 4-to-1. To have a positive expectation, a player's odds of winning must be better than his pot odds. If the player's odds of winning are also 4-to-1 (20% chance of winning), and if he plays the pot five times, his expected return is to break even (losing four times and winning once).

Implied odds is a more complicated concept, though related to pot odds. The implied odds on a hand are based not on the money currently in the pot, but on the expected size of the pot at the end of the hand. When facing an even money situation (like described in the previous paragraph) and holding a strong drawing hand (say a four-flush) a skilled player will consider calling a bet or even opening based on their implied odds. This is particularly true in multi-way pots, where it is likely that one or more opponents will call all the way to showdown.

Deception

By employing deception, a poker player hopes to induce his opponent(s) to act differently than they would if they could see his cards. Bluffing is a form of deception to induce opponents to fold superior hands. If opponents observe that a player never bluffs, they won't call his bets unless they have very good hands. Slow-playing is deceptive play in poker that is roughly the opposite of bluffing: betting weakly with a strong holding rather than betting strongly with a weak one. If opponents observe that a player never slow plays, they can pounce at any sign of weakness.

Position

Position refers to the order in which players are seated around the table and the strategic consequences of this. Generally, players in earlier position (who have to act first) need stronger hands to bet or raise than players in later position. For example, if there are five opponents yet to act behind a player, there is a greater chance one of the opponents will have a better hand than if there were only one opponent yet to act. Being in late position is an advantage because a player gets to see how his opponents in earlier position act (which provides the player more information about their hands than they have about his). Position is one of the most vital elements to understand in order to be a long-term winning player. As a player's position improves, so too does the range of cards with which he can profitably enter a hand. Conversely this commonly held knowledge can be used to an intelligent poker player's advantage. If playing against observant opponents in tournament style play (when the amount of chips one has is finite, which is to say there are no 'rebuys') then a raise with any two cards can 'steal the blinds,' if executed against passive players at a fortuitous time.

Reasons to raise

Unlike calling, raising has an extra way to win: opponents may fold. An opening bet may be considered a raise from a strategy perspective. David Sklansky gives seven reasons for raising, summarized below.[1]

* To get more money in the pot when a player has the best hand: If a player has the best hand, raising for value enables him to win a bigger pot.

* To drive out opponents when a player has the best hand: If a player has a made hand, raising may protect his hand by driving out opponents with drawing hands who may otherwise improve to a better hand.

* To bluff or semi-bluff: If a player raises with an inferior or drawing hand, the player may induce a better hand to fold. In the case of semi-bluff, if the player is called, he still has a chance to improve to a better hand (and also win a larger pot).

* To get a free card: If a player raises with a drawing hand, his opponent may check to him on the next betting round, giving him a chance to get a free card to improve his hand.

* To gain information: If a player raises with an uncertain hand, he gains information about the strength of his opponent's hand if he is called. Players may use an opening bet on a later betting round (probe or continuation bets) to gain information by being called or raised (or may win the pot immediately).

* To drive out worse hands when a player's own hand may be second best: Sometimes, if a player raises with the second best hand with cards to come, raising to drive out opponents with worse hands (but who might improve) may increase the expected value of his hand by giving him a higher probability of winning in the event his hand improves.

* To drive out better hands when a come hand bets: If an opponent with an apparent come hand (drawing hand) bets before a player, if the player raises, opponents behind him who may have a better hand may fold rather than call a bet and raise. This is a form of isolation play.

Reasons to call

There are several reasons for calling a bet or raise, summarized below.

* To see more cards: With a drawing hand, a player may be receiving the correct pot odds with the call to see more cards.

* To limit loss in equity: Calling may be appropriate when a player has adequate pot odds to call but will lose equity on money contributed to the pot.

* To avoid a re-raise: Only calling (and not raising) denies the original bettor the option of re-raising.

* To conceal the strength of a player's hand: If a player has a very strong hand, he might smooth call on an early betting round to avoid giving away the strength of his hand on the hope of getting more money into the pot in later betting rounds.

* To manipulate pot odds: By calling (not raising), a player offers any opponents yet to act behind him more favorable pot odds to also call. For example, if a player has a very strong hand, a smooth call may encourage opponents behind him to overcall, building the pot. Particularly in limit games, building the pot in an earlier betting round may induce opponents to call future bets in later betting rounds because of the pot odds they will be receiving.

* To set up a bluff on a later betting round: Sometimes referred to as a long-ball bluff, calling on an earlier betting round can set up a bluff (or semi-bluff) on a later betting round.[2]

Equity

A player's equity in a pot is his expected share of the pot, expressed either as a percentage (probability of winning) or expected value (amount of pot * probability of winning). Negative equity, or loss in equity, occurs when contributing to a pot with a probability of winning less than 1 / (number of opponents matching the contribution).

Example
Alice contributes $12 to a pot and is matched by two other opponents. Alice's $12 contribution "bought" the chance to win $36. If Alice's probability of winning is 50%, her equity in the $36 pot is $18 (a gain in equity because her $12 is now "worth" $18). If her probability of winning is only 10%, Alice loses equity because her $12 is now only "worth" $3.60.

If there is already money in the pot, the pot odds associated with a particular play may indicate a positive expected value even though it may have negative equity.

Texas hold'em example
Alice holds J♦7♠. Bob holds K♥6♠. After the flop, the board is 5♥6♥8♦. If both hands are played to a showdown, Alice has a 45% chance to win, Bob has a 53% chance to win and there is a 2% chance to split the pot. The pot currently has $51. Alice goes all-in for $45 reasoning Bob has to call to stay in game. Alice's implied pot odds for the all-in bet are 32%. Bob's simple pot odds for the call are also 32%. Since both have a probability of winning greater than 32%, both plays (the raise and the call) have a positive expectation. However, since Bob has more equity in the pot than Alice (53% vs. 45%), Alice would have been better off playing the pot as cheaply as possible. When Alice went all-in, she gave up the difference in equity on the money she contributed to the pot.