On the Importance of Pawns in Chess

It is said that there are more possibilities in chess than there are atoms in the universe. However, size may not be all that matters. The different rules according to which the different chess pieces move, impose a highly nontrivial structure on the game's configuration space. Clearly, direct sampling of even small portions of this space is out of reach. Yet, the task of figuring out properties of a state space that is too vast to enumerate, is a familiar one for statistical physics. In this talk I will show how we applied transition-path sampling, an advanced Monte-Carlo simulation method that is usually used to study crystallization, protein folding or the flow behavior of polymers, to chess. The simulations show that chess' state space decomposes into a large number of weakly connected "pockets" that reflect the pawn structures emphasized by good chess players.