Broderick Arneson

Fuego—An Open-Source Framework for Board Games and Go Engine Based on Monte Carlo Tree Search

FUEGO is both an open-source software framework and a state-of-the-art program that plays the game of Go. The framework supports developing game engines for full-information two-player board games, and is used successfully in a substantial number of projects. The FUEGO Go program became the first program to win a game against a top professional player in 9 × 9 Go. It has won a number of strong tournaments against other programs, and is competitive for 19 × 19 as well. This paper gives an overview of the development and current state of the FUEGO project. It describes the reusable components of the software framework and specific algorithms used in the Go engine.

Monte Carlo Tree Search in Hex

Hex, the classic board game invented by Piet Hein in 1942 and independently by John Nash in 1948, has been a domain of AI research since Claude Shannons seminal work in the 1950s. Until the Monte Carlo Go revolution a few years ago, the best computer Hex players used knowledge-intensive alpha-beta search. Since that time, strong Monte Carlo Hex players have appeared that are on par with the best alpha-beta Hex players. In this paper, we describe MoHex, the Monte Carlo tree search Hex player that won gold at the 2009 Computer Olympiad. Our main contributions to Monte Carlo tree search include using inferior cell analysis and connection strategy computation to prune the search tree. In particular, we run our random game simulations not on the actual game position, but on a reduced equivalent board.

Solving hex: beyond humans

For the first time, automated Hex solvers have surpassed humans in their ability to solve Hex positions: they can now solve many 9×9 Hex openings. We summarize the methods that attained this milestone, and examine the future of Hex solvers.

MoHex 2.0: A Pattern-Based MCTS Hex Player

In recent years the Monte Carlo tree search revolution has spread from computer Go to many areas, including computer Hex. MCTS-based Hex players now outperform traditional knowledge-based alpha-beta search players, and the reigning Computer Olympiad Hex gold medallist is the MCTS player MoHex. In this paper we show how to strengthen MoHex, and observe that—as in computer Go—using learned patterns in priors and replacing a hand-crafted simulation policy by a softmax policy that uses learned patterns significantly increases playing strength. The result is MoHex 2.0, about 250 Elo points stronger than MoHex on the 11\(\times \)11 board, and 300 Elo points stronger on the 13\(\times \)13 board.

WOLVE 2008 wins Hex Tournament

SIX, the gold medallist in each Hex competition since 2003, uses a two-ply truncated-width alpha-beta search and a Shannon-style electric-circuit evaluation function in which cell adjacencies are augmented by virtual connections. The virtual connection engine (VCE) uses Anshelevich and/or closure operations. From a list of moves to consider, SIX prunes dead cells with low degree; it also prunes cells outside of the virtual connection mustplay region, which are provably losing.

Hex, braids, the crossing rule, and XH-search

We present XH-search, a Hex connection finding algorithm. XH-search extends Anshelevichs H-search by incorporating a new Crossing Rule to find braids, connections built from overlapping subconnections.

Stronger Virtual Connections in Hex

For connection games such as Hex or Y or Havannah, finding guaranteed cell-to-cell connection strategies can be a computational bottleneck. In automated players and solvers, sets of such virtual connections are often found with Anshelevichs H-search algorithm: initialize trivial connections, and then repeatedly apply an AND-rule (for combining connections in series) and an OR-rule (for combining connections in parallel). We present FastVC Search, a new algorithm for finding such connections. FastVC Search is more effective than H-search when finding a representative set of connections quickly is more important than finding a larger set of connections slowly. We tested FastVC Search in an alpha-beta player Wolve, a Monte Carlo tree search player MoHex, and a proof number search implementation called Solver. It does not strengthen Wolve, but it significantly strengthens MoHex and Solver.

Automatic strategy verification for Hex

We present a concise and/or-tree notation for describing Hex strategies together with an easily implemented algorithm for verifying strategy correctness. To illustrate our algorithm, we use it to verify Jing Yangs 7×7 centre-opening strategy.