The fundamental theorem of poker


The fundamental theorem of poker, introduced by David Sklansky, states: Every time you play your hand the way you would if you could see your opponents' cards, you gain, and every time your opponents play their cards differently from the way they would play them if they could see your cards, you gain.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 from how 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.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 from how they would if they could see their cards. David Sklansky has argued that winning at poker is often decided by how much one player can force another to change his/her style while successfully maintaining their own strategy.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.


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/raise or call 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). This information, coupled with a low bet to a late player, may allow the player to "limp in" with a weaker hand when they would have folded the same hand if they'd had to act earlier. 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, then a raise with any two cards can 'steal the blinds,' if executed against passive players at the right time.


Reasons to raise


• 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: A player raises with an inferior or "trash" hand attempts to deceive other players about the strength of their hand, and hopefully induce a better hand to fold.

• To semi-bluff: A player with a drawing hand may raise both to bluff and for value. While technically still a bluff, as the player may not end up with a made hand and is primarily trying to drive out players, the player still has the opportunity to make his or her hand and win the pot if the bluff is called.

• To block: Players on drawing hands may put out a "blocking bet" against players who are likely to bet when checked to, but unlikely to raise when bet into. This is a small bet made on a drawing hand to lessen the likelihood of having to call a larger bet from a player in late position.

• To get a free card: If a player raises with a drawing hand, their opponent may call the bet and 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: A combination protection and probe raise, a player with a strong hand but not the "nuts" (the hole cards that make the best possible hand given the current face-up cards) may raise, both to induce drawing hands that may improve to the "nut hand" to fold, while also testing to see if another player has the "nuts".

• To drive out better hands when a drawing hand bets: If an opponent with an apparent drawing hand has bet before the player to act, if the player raises, opponents behind them who may have a better hand may fold rather than call two bets "cold". This is a form of isolation play, and has elements of blocking and protection.


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 additional money contributed to the pot with a raise.

• 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 or even raise, 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. For instance, a player with a strong initial hand may call instead of raise to see the flop cheaply. That flop may not benefit the player, but the player may still have many "outs" (cards left to deal that could make a strong hand), or even if the odds are slim they can try to bluff. By raising, this scenario may appear to an opponent like a player who has "limped in" with a weak initial hand, but after the flop now has a strong made or drawing hand. A recent online term for "long-ball bluffing" is floating.


Gap concept


The gap concept states that a player needs a better hand to play against someone who has already opened (or raised) the betting than he would need to open himself.The gap concept reflects that players prefer to avoid confrontations with other players who have 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 does not know how many opponents will be involved in the pot or whether he will have to call a re-raise, he does not know what his effective pot odds actually are. Therefore, a stronger hand is desired as compensation for this uncertainty. A squeeze play exploits this principle.


Loose/tight play


Loose players play relatively more hands and tend to continue with weaker hands; hence they do not 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 play


Aggressive 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, tells and leveling


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, as skilled players do not attempt to assign a player to an exact hand. Rather they attempt to narrow the possibilities down to a range of probable hands based on the past actions of their opponent, during both the current hand and previous hands played by this opponent.

Tells are detectable changes in opponents' behavior or demeanor which provide clues about their hands or their intentions. Educated guesses about opponents' cards and intentions can help a player avoid mistakes in his own play, induce mistakes by the opponents, or influence the opponents to take actions that they would not normally take under the circumstances. For example, a tell might suggest that an opponent has missed a draw, so a player seeing it may decide a bluff would be more effective than usual.

Leveling or multiple level thinking is accounting for what the other opponents think about the hands. This information can then be used to the player's advantage. Some players might be able to make educated guesses about opponents' hands; this could be seen as the first level. The second level could be thought of as the combination of the first level and deducing what the opponents think the player's hand may be. Skilled players can adjust their game play to be on a higher level than that of less skilled opponents.

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