Solved Game - Partially Solved Games

Partially Solved Games

Chess

Solved by retrograde computer analysis for all three- to six-piece, and some seven-piece endgames, counting the two kings as pieces. It is solved for all 3–3 and 4–2 endgames with and without pawns, where 5-1 endgames are assumed to be won with some trivial exceptions (see endgame tablebase for an explanation). The full game has 32 pieces. Chess on a 3x3 board is strongly solved by Kirill Kryukov (2004). It has been speculated that solving chess may be impossible with current technology.

International Draughts

All positions with two through seven pieces were solved. Positions with 4x4 and 5x3 pieces where each side had one king or less. Positions with five men versus four men, five men versus three men and one king, and four men and one king versus four men. Solved in 2007 by Ed Gilbert of the United States, computer analysis show that highly likely it always end in a draw if both players play perfectly.

Go

Board sizes up to 4×4 are strongly solved. The 5×5 board is weakly solved for all opening moves. Humans usually play on a 19×19 board which is over 145 orders of magnitude more complex than 7x7.

Reversi (Othello)

Weakly solved on a 4×4 and 6×6 board as a second player win in July 1993 by Joel Feinstein. On an 8×8 board (the standard one) it is mathematically unsolved, though computer analysis shows a likely draw. No strongly supposed estimates other than increased chances for the starting player (black) on 10×10 and greater boards exist.

m,n,k-game

It is trivial to show that the second player can never win; see strategy-stealing argument. Almost all cases have been solved weakly for k ≤ 4. Some results are known for k = 5. The games are drawn for k ≥ 8.