Computing Strong Game-Theoretic Strategies in Jotto

TL;DR

This paper introduces a novel method for approximating equilibrium strategies in the complex, large-scale game of Jotto using an oracular strategy representation and an extended fictitious play algorithm, outperforming benchmark strategies.

Contribution

It presents a new approach combining oracular strategy representation with an extended fictitious play algorithm to handle extremely large imperfect information games like Jotto.

Findings

Strategies computed outperform benchmark algorithms in head-to-head matches.

The approach effectively handles the large state space of Jotto.

Demonstrates the feasibility of equilibrium computation in large imperfect information games.

Abstract

We develop a new approach that computes approximate equilibrium strategies in Jotto, a popular word game. Jotto is an extremely large two-player game of imperfect information; its game tree has many orders of magnitude more states than games previously studied, including no-limit Texas hold 'em. To address the fact that the game is so large, we propose a novel strategy representation called oracular form, in which we do not explicitly represent a strategy, but rather appeal to an oracle that quickly outputs a sample move from the strategy's distribution. Our overall approach is based on an extension of the fictitious play algorithm to this oracular setting. We demonstrate the superiority of our computed strategies over the strategies computed by a benchmark algorithm, both in terms of head-to-head and worst-case performance.