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Quite a simple question, but can't decide either way. Does the game of chess have mathmatical variance in it? (Like poker does?)

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5 
 what is "mathmatical (sic) variance"? – Robin Chapman Sep 30 2010 at 9:50
en.wikipedia.org/wiki/Variance "In probability theory and statistics, the variance is used as one of several descriptors of a distribution. It describes how far values lie from the mean. In particular, the variance is one of the moments of a distribution. In that context, it forms part of a systematic approach to distinguishing between probability distributions. While other such approaches have been developed, those based on moments are advantageous in terms of mathematical and computational simplicity." – Tom Sep 30 2010 at 9:55
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 Sure, when I try to hit opponent's head with a rook, there is a variance in how far they fly from the head... – Bugs Bunny Sep 30 2010 at 10:17
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 Whenever I try to hit my opponent's head with a rook, then it always flies away before it hits their head. Or it turns round and tries to peck my eye out. – Andrew Stacey Sep 30 2010 at 12:10

closed as not a real question by Gjergji Zaimi, Robin Chapman, Yemon Choi, Tony Huynh, Joel David Hamkins Sep 30 2010 at 10:48

1 Answer

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While Rasmus is definitely right, you can get some variance in an implementation of the game (say if you program uses random numbers) or in a model of the game. The latter could be useful because the size of the game tree is unmanageable (in the region of $10^{140}$ variants). You may consider the tree that goes down 5-15 semimoves and just build a probabilistic model for the rest of the tree.

I gather that chess programs go along this route.

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1 
 Would two humans have variance? One might have a hangover or a bruise on his head from a rook, that causes deviation from their stategy? – Tom Sep 30 2010 at 10:55

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