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We present a strong solution of the board game pentago, computed usingexhaustive parallel retrograde analysis in 4 hours on 98304 ($3 \times 2^{15}$)threads of NERSC's Cray Edison. At $3.0 \times 10^{15}$ states, pentago is thelargest divergent game solved to date by two orders of magnitude, and the onlyexample of a nontrivial divergent game solved using retrograde analysis. Unlikeprevious retrograde analyses, our computation was performed entirely in-core,writing only a small portion of the results to disk; an out-of-coreimplementation would have been much slower. Symmetry was used to reducebranching factor and exploit instruction level parallelism. Despite atheoretically embarrassingly parallel structure, asynchronous message passingwas required to fit the computation into available RAM, causing latencyproblems on an older Cray machine. All code and data for the project are opensource, together with a website which combines database lookup and on-the-flycomputation to interactively explore the strong solution.

Pentago is a First Player Win: Strongly Solving a Game Using Parallel In-Core Retrograde Analysis