Goofspiel is a simple two-person zero-sum game introduced by Merrill Flood in the Mathematics Department in Princeton in the 1930ties.
As far as we know there exist no known equilibrium strategies.
We conducted round-robin tournaments in which participants (students and faculty) were asked to provide computer programs they designed to play the game with or without carryover. Each of the games variants was played under different objective functions, namely, maximization of the
cumulative number of points won across all opponents (as in Axelrod’s tournament), and maximization of the probability of winning any given round. Our results show that there are more successful strategies. Inherent differences in the results exhibit levels of sophistication, depth, and balance that are not captured by present models of adaptive learning.