No of HU LHE paths for one hand - Poker Theory

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No of HU LHE paths for one hand

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11-24-2014 , 07:49 PM

DecisionMade

grinder

Join Date: Nov 2012 Posts: 557

Could someone tell me if the number of paths one hand of HU LHE can be played from start to finish is known? Is the number too big to work out or can a formula give you an idea? What would be that formula?

Factors being:
1. A hand starts preflop with the SB and ends when one player folds
2. No player can fold if they have the option to check

e.g. where F=fold, X=check, C=call, B=bet, R=raise:
the first and shortest way would be [F]; the second [R, F]; third [C, R, F]; etc.

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11-24-2014 , 08:16 PM

yaqh

Pooh-Bah

Join Date: Aug 2007 Posts: 5,745

If you count different hole cards being dealt as different "paths", apparently the number is about 3*10^17. See

http://arxiv.org/pdf/1302.7008.pdf

and references therein.

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11-24-2014 , 09:39 PM

yaqh

Pooh-Bah

Join Date: Aug 2007 Posts: 5,745

Well I guess game states isn't quite the same as paths -- number of paths will be the same as number of states that correspond to the end of the hand (leaves) -- but the order of magnitude and counting methodologies should be similar.

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11-25-2014 , 09:58 AM

DecisionMade

grinder

Join Date: Nov 2012 Posts: 557

Thanks. That's an interesting document.

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