Fabien Letouzey wrote:
BertTuyt wrote:
And last but not least, do you already have a gut feel whether this is (with perfect play) a white or black win?
No.
We already know that white wins in 8x8 (with checkers capture rules anyway), so that is a strong indication. On the other hand, I put Draughts into the "blocking game" category (with Othello) so it's also possible that white has to self-destruct first.
I think that the game result depend on the rules, in particular the king range. For what it's worth, about 6 years ago, I did some computations on the 6x6 board for all game variants. The results have not been published before, but I shared them with Ed in private communication (October 19, 2011).
Quote:
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I have weakly solved all 6x6 draughts and checkers variants, both the regular game and the suicide (AKA giveaway, misere or qui-perd-gagne) variety. This was a neglected corner of the solving small games literature
http://en.wikipedia.org/wiki/Solved_game The method used was a simple alpha-beta search (pvs and iterative deepening enhancements). No endgame databases were used. The games are therefore not strongly solved because there could conceivably be endgames which take more than reasonable resources to be resolved by forward search only. Strongly solving all these games (i.e. building the complete 12-piece databases) is also well within current technology (somewhat less than the 7-piece databases for the 10x10 game).
Compared to the Chinook project of solving 8x8 checkers (2007), Martin Fierz's probable draw solution for 8x8 suicide checkers (2010), and the recent announcement of the white win in 8x8 Russian suicide by Osipov and Morozev (2011), this was a nano-step for mankind. The searches took less than 15 minutes each on a 3.2 Ghz P4 with 1Gb of hash tables. The number of nodes are less than 1e9 per solution, somewhat in between solving 5x5 Amazons and 6x6 Othello.
Below are the results (W59 means white wins in 59 plies, L28 means white loses in 28 plies etc.). For a detailed description of the different rules, see the perft thread on this forum or the excellent website
http://www.mindsports.nl/index.php/on-t ... s-variants
Code:
Variant Regular Suicide
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International DRAW W36
Killer W59 W36
Frisian L28 L27
Pool DRAW W34
Russian DRAW W34
Thai DRAW W38
Czech DRAW W32
Spanish DRAW W32
Italian DRAW DRAW
Checkers DRAW DRAW
Interestingly, the results for 6x6 Russian suicide (white win) and 6x6 checkers suicide (draw) match the results for the 8x8 board. Also notable is that only the games with short ranged kings have drawn suicide games.
The drawn games in the table above are not 100% guaranteed because my search does not take care of Graph-History-Interaction. On the other hand, the search engine (a series of C++ templates) was extensively unit-tested on the 4-piece databases for International and Killer draughts, without encountering any discrepancies between the forward search and the database results (with forward searches of up to 77 plies). Nevertheless, any confirmation would be welcome!
These results should be taken with some disclaimer because of the Graph-History Interaction. With current technology, these 6x6 games could also be strongly solved (i.e. the opening position fits within the endgame databases). Also, I didn't compute the breakthrough results.
In any case, assuming correctness, note that Killer and Frisian are the only decided games on a 6x6 board, and with give-away, only the short-ranged king games (Italian and Checkers) are a draw. The Russian give-away game has also been solved to be a white win on a 8x8 game board (can't find the link anymore), most likely with far less resources than was required to proof 8x8 checkers to be a draw.
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Better hurry before Bert solves it on his computing monster, though.