No-Limit_Holdem

# No-Limit_Holdem - Mathematics of No-Limit Holdem William...

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Mathematics of No-Limit Holdem William Wilding

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Description of Texas Holdem Each player receives two cards. Two player are required to post live blinds (antes) called the big blind and small blind. To continue in the hand, each player must at least match the current bet size which is initially the size of the big blind. In no-limit poker a player can bet any amount up to their current chip stack.

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Four Betting Rounds Preflop Flop Turn River
An All-in Problem You are the BB with X chips of which pX are posted in the blind. Everyone folds to the SB who raises to a total of X How big does p need to be for you to call with a bad hand like 32 offsuit?

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Some All-In Probabilities VS 34% (2 to 1 against) 24% (3 to 1 against) Random Hand 31% (2.2 to 1 against) 14.8% (5.8 to 1 against)
Expected Value of Stack Size [ ] [ ] (1 ) (.7)(0) (.3)(2 ) [ ] [ ] .4 E Fold p X X pX E Call X E Fold E Call p = - = - = + = = If the raise comes from the button and the small blind folds, p = .35

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## This note was uploaded on 11/11/2011 for the course MATH 112 taught by Professor Jarvis during the Winter '08 term at BYU.

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No-Limit_Holdem - Mathematics of No-Limit Holdem William...

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