Allowing two moves in succession increases the game's bias: A theorem

Chess is probably the best known example of a game which is “biased”—in the sense that whoever starts the game has an advantage. From the commonsense viewpoint, the resulting bias should be the same whether we allow the players to play as usual: 1st, 2nd, 1st, 2nd, or whether we allow each player to make two moves at the same time. However, in practice, if we allow each player to make two moves in succession, the bias increases. In this paper, we provide a theoretical explanation for this empirical phenomenon. © 2001 John Wiley & Sons, Inc.