Editing Pot odds (section)

==Using pot odds to determine expected value==
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. 

=== Example (Texas hold'em) ===
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 [[List of poker hands|flush]]. Excluding her two [[Community card poker|hole cards]] and the four [[Community card poker|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.

==== Validity of strategy ====
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 [[List of poker hands|two-pair]] or a [[List of poker hands|set]]. In these cases, her opponent could have been drawing on a higher flush, a [[List of poker hands|full house]], or [[List of poker hands|four of a kind]], all of which would win even if Alice made her flush. This is where considering the [[Poker strategy|range]] of an opponent's hands becomes important. If, for example, Alice's opponent raised multiple times [[Texas hold 'em starting hands|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 [[Poker strategy|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.