MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

## Is there variance in chess? [closed]

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

-
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
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
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 HamkinsSep 30 2010 at 10:48

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.