Three Musketeers
Hunt & unequal forces · all families · data
Not yet verified. This record has not been checked against its primary source, so it is left out of the family tables and counts.
Also known as: The Three Musketeers.
Win for the enemy/blue pieces (Cardinal Richelieu’s men) with perfect play. The musketeers move FIRST, so the winning enemy side is the SECOND player.
| Result | Second player wins |
| Strength | Strong |
| Method | Retrograde analysis, Alpha-beta + DB |
| Year | 2009 |
| Solved by | Johannes Laire (2009, strong solution by retrograde analysis, announced on rec.games.abstract); independently weakly solved by Ali Elabridi (2017, capstone project, Al Akhawayn University) using minimax + alpha-beta pruning with Zobrist hashing and symmetry reduction |
| Source | Laire 2009 |
| Board | 5x5 square grid, 25 cells. Asymmetric (‘unequal forces’, Fox-and-Geese style): one player controls 3 musketeers (red/dark), the other controls 22 enemies (blue/light, ‘Cardinal Richelieu’s men’). Start: musketeers in two opposite corners and the centre; enemies fill the other 22 cells. |
Solution history
Section titled “Solution history”| Date | Size or opening | Result | Strength | Credit | Source |
|---|---|---|---|---|---|
| 2009 | standard game | second player wins | Strong | Johannes Laire | source |
One row, derived from the record’s year, solver and primary source; no fuller history is recorded yet.
References
Section titled “References”- Johannes Laire — ‘Three Musketeers solved’ (rec.games.abstract, Google Groups, 2009) [original announcement of the strong solution]
- Ali Elabridi — Weakly Solving the Three Musketeers Game Using Artificial Intelligence and Game Theory (Capstone Project, Al Akhawayn University, Fall 2017) [independent weak solution; PDF]
- alielabridi — Weakly-Solving-Three-Musketeers-Game (source code, GitHub)
- Three Musketeers (game) — Wikipedia (secondary; states strong solve by Laire 2009, weak solve by Elabridi 2017, win for blue/enemy)
- Solved game — Wikipedia, list of solved games (secondary; ‘Strongly solved by Johannes Laire in 2009, and weakly solved by Ali Elabridi in 2017. It is a win for the blue pieces’)
- Three Musketeers — BoardGameGeek (secondary; rules and provenance)
Three Musketeers is an asymmetric abstract strategy game of ‘unequal forces’ (Fox-and-Geese family) designed by Haar Hoolim and popularised in Sid Sackson’s 1969 book A Gamut of Games. It is a two-player, zero-sum, perfect-information game on a 5x5 board: 3 musketeers vs 22 enemies. The musketeers move first and capture by stepping orthogonally onto an adjacent enemy (removing it); the enemy moves a piece to any orthogonally adjacent EMPTY cell and never captures. The enemy wins by forcing all three musketeers onto a single row or column; the musketeers win if, on their turn, they have no legal move (no adjacent enemy to capture) while not aligned. RESULT / STRENGTH. Johannes Laire STRONGLY solved the game in 2009 (announced on the rec.games.abstract newsgroup) via retrograde analysis, building a full database that assigns a value to every reachable position and lets an AI play optimally from any state — hence strength = STRONG. The game-theoretic value of the standard start is a WIN FOR THE ENEMY (blue / Cardinal Richelieu’s men). This matches the game’s long-documented imbalance: the enemy side is favoured, and Laire noted that merely changing the starting position makes the game roughly even. Ali Elabridi (Al Akhawayn University, Fall 2017 capstone) independently produced a WEAK solution from the initial position using a top-down minimax search with alpha-beta pruning, Zobrist hashing, and board-symmetry reduction, stating his goal was to confirm Laire’s result. FIRST/SECOND MAPPING (load-bearing). The musketeers move first; the enemy moves second. Because the enemy is the winning side, result = second-player-win. DISCREPANCY / CAVEAT (important). Both Wikipedia articles (the dedicated ‘Three Musketeers (game)’ page and the ‘Solved game’ list) state the result is a win for the BLUE/ENEMY pieces, and this is consistent with the game’s known imbalance in favour of the enemy and with Laire’s strong solution. HOWEVER, the Elabridi capstone’s prose repeatedly and explicitly claims the opposite — that ‘the first player (Musketeers) always wins’ — while simultaneously claiming to confirm Laire. Elabridi’s text is internally inconsistent (e.g. it describes an optimisation premised on the guardsmen/enemy never reaching a winning utility), and its winner labelling is judged to be an inversion error in the writeup, not a genuine alternative result. The authoritative result here is enemy/blue win (Laire’s strong solve + both Wikipedia entries + the historical imbalance); Elabridi’s contradictory labelling should be treated as a known error. INDEPENDENT PRIMARIES. Two genuinely independent solving efforts exist: Laire (2009, strong, retrograde) and Elabridi (2017, weak, minimax+ab). These are the primary sources; the three Wikipedia/BGG links are secondary corroboration. The Laire announcement is a newsgroup post (not a peer-reviewed paper) and his solver/database is not preserved in a stable public artifact, so the strong solution rests on his report rather than a re-verifiable tablebase; treat the STRONG classification as reported-but-not-independently-reproduced. No citable state-space or game-tree complexity figure was found in either primary source, so complexity fields are left null.