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The fundamental theorem of poker

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 their cards differently from the way they would play them if they could see your cards, you 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

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 their $10 call), their pot odds are 4-to-1. To have a positive expectation, a player's odds of winning must be better than their pot odds. If the player's odds of winning are also 4-to-1 (20% chance of winning), their expected return is to break even (on average, losing four times and winning once for every five times they play such a pot).

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 the one 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 their opponent(s) to act differently than they would if they could see their cards. Bluffing is a form of deception where players bet strongly on a weak hand, to induce opponents to fold superior hands. Related is the semi-bluff, in which a player who does not have a strong hand, but has a chance to improve it to a strong hand in later rounds, bets strongly on the hand in the hopes of inducing other players with weaker "made" hands to fold. Slow-playing is deceptive play in poker that is roughly the opposite of bluffing: checking or betting weakly with a strong holding, attempting to induce other players with weaker hands to call or raise the bet instead of folding, to increase the payout.

Even if a bluff or slow play fails, they can benefit a player in future hands. If opponents observe that a player never bluffs, they won't call their bets unless they have very good hands. If opponents observe that a player never slow plays, they can pounce at any sign of weakness.

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 yet to act 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 their 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 they 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 the right time

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.

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 them 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 their 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, they still have 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, their opponent may check to them on the next betting round, giving them a chance to get a free card to improve their hand.

To gain information: If a player raises with an uncertain hand, they gain information about the strength of their opponent's hand if they are 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 their hand by giving them a higher probability of winning in the event their hand improves.

To drive out better hands when a drawing hand bets: If an opponent with an apparent drawing hand bets before a player, if the player raises, opponents behind them 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. However, this is only completely safe in case the player is last to act (i.e. "closing the action").

To conceal the strength of a player's hand: If a player has a very strong hand, they might smooth call on an early betting round to avoid giving away the strength of their 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 them more favorable pot odds to also call. For example, if a player has a very strong hand, a smooth call may encourage opponents behind them 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. A recent online term for "long-ball bluffing" is floating.

Concepts Explained

The gap concept states that a player needs a better hand to play against someone who has already opened (or raised) the betting than they would need to open himself. The gap concept reflects that players prefer to avoid confrontations with another player who has already indicated strength, and that calling only has one way to win (by having the best hand), whereas opening may also win immediately if your opponent(s) fold.

Sandwich effect Related to the gap effect, the sandwich effect states that a player needs a stronger hand to stay in a pot when there are opponents yet to act behind him. Because the player doesn't know how many opponents will be involved in the pot or whether they will have to call a re-raise, they don't know what their effective pot odds actually are. Therefore, a stronger hand is desired as compensation for this uncertainty.

Loose/tight playLoose players play relatively more hands and tend to continue with weaker hands; hence they don't often fold. Tight players play relatively fewer hands and tend not to continue with weaker hands; hence they often fold. The following concepts are applicable in loose games (and their inverse in tight games) Bluffs and semi-bluffs are less effective because loose opponents are less likely to fold. Requirements for continuing with made hands may be lower because loose players may also be playing lower value hands. Drawing to incomplete hands, like flushes, tends to be more valuable as draws will often get favorable pot odds and a stronger hand (rather than merely one pair) is often required to win in multi-way pots.

Aggressive/passive playAggressive play refers to betting and raising. Passive play refers to checking and calling. Unless passive play is being used deceptively as mentioned above, aggressive play is generally considered stronger than passive play because of the bluff value of bets and raises and because it offers more opportunities for your opponents to make mistakes

Hand reading is the process of making educated guesses about the possible cards an opponent may hold based on the sequence of actions in the pot. The term 'hand reading' is actually a misnomer due to the fact that a professional poker player does not attempt to put a player on an exact hand. Rather they attempt to narrow the possibilities down to a range of hands which makes sense based on the past actions of their opponent. A tell is a detectable change in an opponent's behavior or demeanor that gives clues about their hand. Educated guesses about an opponent's cards can help a player avoid mistakes in their own play, induce mistakes by their opponent(s), or influence the player to take actions that they would normally not take under the circumstances. For example, a tell might suggest an opponent has missed a draw, so a player seeing it may decide a bluff would be more effective than usual.

By observing the tendencies and patterns of one's opponents, one can make more educated guesses about others' potential holdings. For example, if a player has been playing extremely tightly (playing very few hands), then when he/she finally enters a pot, one may surmise that he/she has stronger than average cards. One's table image is the perception by one's opponents of one's own pattern of play. A player can leverage their table image by playing out of character and thereby inducing his/her opponents to misjudge his/her hand and make a mistake.