Michael Johanson

Strategy evaluation in extensive games with importance sampling

Typically agent evaluation is done through Monte Carlo estimation. However, stochastic agent decisions and stochastic outcomes can make this approach inefficient, requiring many samples for an accurate estimate. We present a new technique that can be used to simultaneously evaluate many strategies while playing a single strategy in the context of an extensive game. This technique is based on importance sampling, but utilizes two new mechanisms for significantly reducing variance in the estimates. We demonstrate its effectiveness in the domain of poker, where stochasticity makes traditional evaluation problematic.

Dead Cell Analysis in Hex and the Shannon Game

In 1981 Claude Berge asked about combinatorial properties that might be used to solve Hex puzzles. In response, we establish properties of dead, or negligible, cells in Hex and the Shannon game.

SOLVING 7x7 HEX: VIRTUAL CONNECTIONS AND GAME-STATE REDUCTION

We present an algorithm which determines the outcome of an arbitrary Hex game-state by finding a winning virtual connection for the winning player. Our algorithm performs a recursive descent search of the game-tree, combining fixed and dynamic game-state virtual connection composition rules with some new Hex game-state reduction results based on move domination. The algorithm is powerful enough to solve arbitrary 7×7 game-states; in particular, we use it to determine the outcome of a 7×7 Hex game after each of the 49 possible opening moves, in each case finding an explicit proof-tree for the winning player.