When there are no pieces on the board except one Bishop for each side (Kings and Pawns don't count!) and those Bishops travel on different color squares, then the likelihood of a draw is very high. It sometimes happens that a game is drawn even with an advantage of as many as two Pawns. This is for two reasons:
- The Pawns have difficulty advancing over squares controlled by the enemy Bishop, and
- the Bishop can control both the Kingside and the Queenside at the same time.
If there are any other pieces on the board, then the dynamics change considerably. In these cases a Pawn advantage or a positional advantage can be enough to win the game. The stronger side should always be careful before simplifying into Bishops of opposite color.