Strong solutions for the morris family, computed with the game-solver engine in this repo.
Six men's morris is a draw under perfect play, over all 42,372,745 reachable positions. As far as I can find this is the first published solution: six men's is absent from the academic work (Gasser 1993; Gévay and Danner 2014) and from the open-source solvers Malom and Sanmill, which cover nine, twelve and Lasker morris plus Morabaraba but not six.
These files are published so the result can be checked rather than believed.
Files
Two variants per board size: standard rules, and flying (a player reduced to three men may move to any empty point).
| File | Board | Reachable | Start value |
|---|---|---|---|
morris4.wld |
two-ring, 4 men | 4,111,151 | Draw |
morris4-flying.wld |
two-ring, 4 men, flying | 4,111,327 | Draw |
morris5.wld |
two-ring, 5 men | 17,844,721 | Draw |
morris5-flying.wld |
two-ring, 5 men, flying | 17,846,785 | Draw |
morris6.wld |
two-ring, 6 men | 42,372,745 | Draw |
morris6-flying.wld |
two-ring, 6 men, flying | 42,383,945 | Draw |
Each .wld ships with a .meta.json giving the exact encoding, state counts, and win/loss/draw breakdown.
Format
2bit-le, addressed by dense index: 0=unreachable 1=win 2=loss 3=draw, two bits per state, little-endian within each byte. Values are from the perspective of the side to move. num_states is the size of the index space; reachable is how many of those a legal game can produce.
Verifying
The solver that produced these is in engine/. Rerunning it from scratch should reproduce each file byte for byte. The interactive explorer queries the same tablebases in the browser.