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Morabaraba

Morris / mill family · all families · data

Part of the morris (mill) family — see the family page for the scaling table and a playable explorer.

Also known as: Twelve Men’s Morris, Mlabalaba, Umlabalaba, Morabaraba (South African Morris).

First-player win — the standard starting position is a win for the player to move first, with a game-theoretic value of win in 49 (moves). Most starting positions in which both players place an equal number of stones (including the standard one) are first-player wins, in contrast to Nine Men’s Morris and Lasker Morris, which are draws.
Result First player wins
Strength Strong
Method Retrograde analysis
Year 2015
Solved by Gábor E. Gévay (Eötvös Loránd University) & Gábor Danner (University of Szeged); arXiv:1408.0032 (2014), published IEEE Trans. on Computational Intelligence and AI in Games, 2016
Source Gévay 2015
Board Nine Men’s Morris board with the four diagonal lines added (24 points / intersections, all corners of the three nested squares connected by diagonals); 12 men per player
State space 112,000,000,000
Distance to result Win in 49 (the game-theoretic value of the standard starting position, expressed as moves-to-win in the depth-to-win database)

Solution history

Section titled “Solution history”
Date Size or opening Result Strength Credit Source
2015 standard game first player wins Strong Gábor E. Gévay source

One row, derived from the record’s year, solver and primary source; no fuller history is recorded yet.

Engines

Section titled “Engines”

References

Section titled “References”

Resources

Section titled “Resources”

Tablebases

Notes

Section titled “Notes”

Strongly solved. Morabaraba is the southern-African variant of Twelve Men’s Morris: it is played on the Nine Men’s Morris board with the four diagonal lines added (each corner of the three nested squares is connected through to the center cross), and each player places 12 stones (“cows”) rather than 9. Standard rules include the “flying” rule — a player reduced to three stones may move a stone to any empty point rather than only along adjacent lines. Gábor E. Gévay (Eötvös Loránd University) and Gábor Danner (University of Szeged) strongly solved the game with a multi-valued retrograde analysis over a partitioned state space, computing a complete depth-to-win database. The game-theoretic value of the standard starting position is WIN IN 49 for the first player — a notable contrast with Nine Men’s Morris (Gasser 1996, a draw) and Lasker Morris (Stahlhacke 2003, a draw), both of which the same paper also re-solved. They report that most starting positions where both players place an equal number of stones (including the standard position) are first-player wins; the extra diagonals make the game sharper and the first move decisive. The Morabaraba state space is roughly four times that of Nine Men’s Morris (about 112 billion states in the standard solution database per their Table I; ~284 billion across the extended/alternative-stone-count solutions), and the computation took on the order of days on a single machine (~3.2 GHz, ~20 GB RAM). Because the solution is a full depth-to-win tablebase holding a value for every reachable position, it qualifies as a STRONG (not merely weak) solution; the authors additionally computed an ULTRA-strong solution that, by subclassifying drawn/won positions, improves practical results against a fallible opponent. The ultra-strong Morabaraba database is published for download (~41 GB compressed / ~324 GB uncompressed). This is the SAME paper that strongly re-confirms Lasker Morris (see lasker-morris.yaml). Independent primary confirmations of the Morabaraba result: one (the Gévay–Danner work; the Szeged “mills” website is the project’s own tablebase distribution page, not an independent re-solution). The exact state-space figure is an approximate value reported in the paper, not an exact enumerated cardinality.