Following the Leader in Multiplayer Tabletop Games

In a two-player zero-sum game, players classically want to maximise their chance of winning. When a game has more than two players, using the binary win rate as an objective is no longer such an obvious choice. A player might instead have the objective of doing as well as possible in terms of ranked order, or in maximising their score. We investigate the impact of different game-agnostic objectives in several popular tabletop games, and whether it can be better to use the game score as a proxy for winning. We find that the games considered largely fall into two groups. In one it is helpful to focus just on one's own score during the game, and then shift to beating opponents only in the end-game. In the other, larger, group it is better to 'Follow the Leader' and constantly track one's relative position to the opponents throughout the game. Using the score as a proxy enables rollout simulations in Monte Carlo (Tree) Search to be terminated early, and we investigate the optimal length of these. Games in which long-term planning is required, or when the full score is only known at the end of the game benefit from a full rollout, while games with adversarial counter-moves benefit from a short rollout length.