Micro Shogi (4×5)

Open problem: Micro Shogi (4×5)


Status	Open
Solved so far	Reduced-material sibling games only: king and pawn a side (457,993 positions) and king, pawn and gold a side (869,287,068 positions), both draws from the start; no value for the full game
Next target	Full Micro Shogi (about 5×10^14 reachable positions), after a smaller distributed rehearsal
Barrier	compute, storage, memory: Reachable positions from the start are estimated at 3.0×10^14 to 6.2×10^14 (point estimate about 5×10^14). A dense-rank solver must index every arrangement, about 3.9×10^15 slots after the left-right fold, so the working value table is about 1 PB, with about 660 to 1,200 core-years of compute and $40,000 to $70,000 on bare metal. Memory was already the wall on the K+P+G rung: the stored-predecessor solver needed about 60.5 GiB on a 64 GB machine, and a dense-rank rerun that generates predecessors on demand cut that to about 6.86 GiB.
Latest result	Liou 2026 (2026-06-12)*
Last checked	2026-10-25
Record	data/open/micro-shogi.yaml

Searches for newer work:

2026-10-25: looked for web search for a solution, tablebase or perfect-play result for Micro Shogi; found none; the nearest result was a 2024 estimate of the reachable positions of Minishogi (5×5), which is also unsolved.

Solution history

Date	Size or opening	Result	Strength	Credit	Source
2026-06-05	reduced game: king and pawn a side	draw from the start; 135,804 wins, 2,956 losses, 319,233 draws (457,993 positions), longest mate 29 plies	Strong	Brian Liou	source
2026-06-11	reduced game: king, pawn and gold a side	draw from the start; 606,922,331 wins, 142,074,547 losses, 120,290,190 draws (869,287,068 positions), longest mate 155 plies; reproduced by a dense-rank rerun on 2026-06-12	Strong	Brian Liou	source

Superseded rows stay in the table.

References

Brian Liou, “Micro Shogi: A Dense-Rank Rerun Cut Memory 8.8×” (2026-06-12): the K+P and K+P+G draws and the full-solve sizing (2026-06-12)
micro-shogi README
micro-shogi rules spec: board, setup, capture-flip promotion, unrestricted drops, king-capture terminal and the repetition default
micro-shogi findings: the state-space estimate, the calibration runs and the arrangement-basis cost
Wikipedia, Micro shogi

* Self-archived: the result is available only from its authors (a repository, a post, a deposit), not yet refereed, formally verified or reproduced by someone else. The mark comes off when one of those happens. It applies to this repo’s own results too.

Notes

Rules as solved (the repo’s rules spec, from English Wikipedia’s Micro shogi and Japanese Wikipedia’s 五分摩訶将棋, which agree on every substantive rule). A 4-file by 5-rank board. Each player has King, Gold, Silver, Bishop and Pawn: the home rank reads S G B K with the King in the right corner and the Pawn in front of the King. Pieces move as their shogi namesakes. There is no promotion zone: a non-king piece flips to its reverse whenever it captures, and flips back on its next capture (Gold and Rook, Silver and Lance, Bishop and Tokin, Pawn and Knight); the King never flips. A captured piece goes to the captor’s hand and may be dropped on any empty square with either face up; there is no two-pawn rule, no ban on a pawn drop giving mate, and no last-rank restriction, so a dropped piece may have no legal move. The sources give checkmate as the win; the solver uses king capture, which gives the same win and loss values. Neither source states a repetition rule, so positions unresolved after the win/loss fixpoint are draws, with no perpetual-check rule; whether to model orthodox shogi’s perpetual-check loss is left open. The solved rungs are reduced games with fewer pieces on the same board and rules, not endgames of the real game, since drops recycle material; they give no value for Micro Shogi from the start. This is the maintainer’s own work, available only from the micro-shogi repository and the post, so it carries the self-archived mark.