Go (5×5)
Go · all families · data
Also known as: 5x5 Go, Five-by-five Go, Small-board Go (5x5).
Black (first player) wins by 25 points — the entire board — with the optimal opening on the center point (C3); no komi, Japanese rules
| Result | First player wins |
| Strength | Weak |
| Method | Alpha-beta + DB, Knowledge-based |
| Year | 2002 |
| Solved by | Erik C. D. van der Werf (program MIGOS), with H. Jaap van den Herik and Jos W. H. M. Uiterwijk |
| Source | van der Werf 2002 |
| Board | 5x5 square Go board (25 intersections) |
| State space | 414,295,148,741 |
| Distance to result | Win proven at 22 plies for the center opening (23 plies for the empty board, i.e. all openings); not a fixed-ply line — a full-game alpha-beta proof from the start |
| Evidence | refereed |
Solution history
Section titled “Solution history”| Date | Size or opening | Result | Strength | Credit | Source |
|---|---|---|---|---|---|
| 2002 | 5×5, Japanese rules, no komi | first player wins by 25 points (the whole board) | Weak | Erik C. D. van der Werf, H. Jaap van den Herik & Jos W. H. M. Uiterwijk | source |
| 2024 | 5×5, positional superko | first player wins the whole board | Weak | Owen Randall, Martin Müller, Ting-Han Wei & Ryan Hayward | source |
Superseded rows stay in the table.
Open problem: Go (6×6)
Section titled “Open problem: Go (6×6)”| Status | Smaller board solved |
| Solved so far | 5×5 (weak): first player wins the whole board under Japanese rules (2002) and under positional superko (2024); rectangular boards up to 5×6 |
| Next target | 6×6 under positional superko |
| Barrier | compute, algorithmic: Square boards above 5×5 are unsolved. Superko cycles make the search history dependent (the graph-history interaction problem), and the state space grows far past the 5×5 solve. |
| Latest result | Randall et al. 2024 (2024) |
| Last checked | 2026-10-17 |
| Record | data/open/go-6x6.yaml |
Searches for newer work:
- 2026-10-17: looked for a 2025 or 2026 solution of 6×6 Go; found none.
References
Section titled “References”- E. van der Werf, J. van den Herik, J. Uiterwijk — Solving Go on Small Boards, ICGA Journal 26(2):92-107, 2003 (the MIGOS primary paper)
- Erik van der Werf — 5x5 Go is solved (author’s announcement / writeup page, Oct 2002)
- O. Randall, M. Müller, T.-H. Wei, R. Hayward — Expected Work Search (arXiv:2405.05594, 2024): first solution of empty 5x5 Go under positional superko, independently confirming a first-player full-board win
- Erik van der Werf — Chessprogramming wiki (MIGOS, method and result, secondary)
- R. Hayward — Solving Go on Small Boards (course notes / history, secondary)
Resources
Section titled “Resources”Write-ups
5x5 Go is the largest square Go board solved from the empty board for a clearly specified ruleset. Erik van der Werf’s program MIGOS (“Mini Go Solver”) solved it in October 2002 (published in ICGA Journal 2003). Under Japanese rules with no komi and the optimal opening on the center point (C3), the first player Black wins the WHOLE board: a 25-point win. Passes and seki are handled — it is full Go, not a simplified variant. MIGOS solved all of the (by symmetry, 6) distinct opening moves on the empty board and for several rule sets; the empty-board proof reaches depth 23 plies and the center-opening win is proven at 22 plies. The solving search examined about 4.472 x 10^9 nodes in ~4 hours on a 2.0 GHz Pentium 4. Method: iterative-deepening alpha-beta / principal-variation search with transposition tables, enhanced transposition cutoffs, symmetry lookups, two killer moves, the history heuristic, a Go-specific heuristic evaluation, and — critically — Benson’s algorithm for unconditionally alive stones / static recognition of unconditional territory, which let proven full-board wins be detected several plies early. The super-ko rule introduces a Graph-History-Interaction (GHI) problem that the paper addresses explicitly. STRENGTH = weak. This is a weak solution: the game-theoretic value of the start plus a strategy to achieve it, proven by full-game search. It is NOT a strong solution — there is no published tablebase giving the optimal value for every one of the ~4.1 x 10^11 legal 5x5 positions (legal-position count from John Tromp’s enumeration; state_space here is the number of LEGAL 5x5 positions, not reachable). The “strong” label would require such a full tablebase. Ruleset caveat: the headline result is under van der Werf’s Japanese-style rules (situational/positional super-ko variants were also analyzed). In 2024 Randall, Müller, Wei and Hayward (Expected Work Search, arXiv:2405.05594) reported the FIRST solution of the empty 5x5 board under the commonly used POSITIONAL SUPER-KO ruleset and likewise found a first-player full-board win — an independent confirmation of the qualitative result under a different ruleset and a different solver. Related small/rectangular boards (van der Werf et al.): 1x1 draw (value 0), 2x2 Black wins by 1 (the 4x4 territory minus, with no winning capture beyond +1 under some rule conventions; Tromp’s exact 2x2 transition graph is known), 3x3 Black wins by 9 (whole board), 4x4 Black wins by 2; rectangular boards up to 5x6 were later solved (van der Werf & Winands, “Solving Go for Rectangular Boards”, ICGA Journal 32(2), 2009 — e.g. 5x6 solved). 6x6 and larger square boards are NOT solved.