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        Arimaa >> General Discussion >> Endgame Study 2, Find the winning plan
        
(Message started by: jdb on Nov 25^th, 2006, 9:22am)

Title: Endgame Study 2, Find the winning plan
Post by jdb on Nov 25^th, 2006, 9:22am

Using the tournament ruleset, who wins the following position and in how many moves?

1w Rc1 Ea8
1b ea1 rf5

The planning window is located at
http://arimaa.com/arimaa/games/planGame.cgi

Title: Re: Endgame Study 2, Find the winning plan
Post by RonWeasley on Nov 25^th, 2006, 9:36am

Another great problem.

I see gold in 4.

Title: Re: Endgame Study 2, Find the winning plan
Post by Fritzlein on Nov 25^th, 2006, 10:39am

I also get Gold to win in four moves. It is unusual to think of advanced rabbits needing to defend: this is another very instructive position. Thanks, JDB!

Title: Re: Endgame Study 2, Find the winning plan
Post by jdb on Nov 25^th, 2006, 10:48am

Silver can last longer than four moves....

Title: Re: Endgame Study 2, Find the winning plan
Post by chessandgo on Nov 25^th, 2006, 12:21pm

The first moves seem to be forced :
2w :R to d4
2b : r to d5 and e to b2
3w E to b5 (the E can't come by below)
3b : e to c5 (to c4 would lose to gold pushing the r and capturing next turn)

and then both sides have to shift towards the eastern edge it seems. Silver has to get there first, so he will have to move in this position :
w : Eg4 Rh4
b : eg5 rh5

And apparently he has no way to prevent a more or less quick win by gold ... but I'm not sure of all this stuff ... or is there a simpler way ?

for the moment I'd say gold in 9 approximately ...

Title: Re: Endgame Study 2, Find the winning plan
Post by chessandgo on Nov 25^th, 2006, 12:22pm

Btw great problem Jeff :)

Title: Re: Endgame Study 2, Find the winning plan
Post by chessandgo on Nov 25^th, 2006, 12:45pm

(I meant gold wins around move 9, so maybe in 8 moves ... but that's with a big question mark ...)

Title: Re: Endgame Study 2, Find the winning plan
Post by DorianGaray on Nov 25^th, 2006, 12:59pm

This seems complicated. I am not sure that there is any quick foreseeable resolution.

Title: Re: Endgame Study 2, Find the winning plan
Post by Fritzlein on Nov 25^th, 2006, 2:06pm

Wow, it looks like I missed a fair bit in a position I already thought was interesting. I missed that the silver elephant could get to c5 on Silver's second move (and incidentally that the gold elephant couldn't approach the center around the other side of trap, because it blocks the d-file).

I tried turning to Bomb for help, but Bomb is playing under the old rules where all sixteen rabbits off is a draw, so Bomb concludes that Silver can engineer a rabbit trade and split the point. When I see how much tension it puts into this seemingly simple position that losing all eight of one's own rabbits is a loss, it makes me glad Omar changed the tournament rules.

I have never considered it important that the rules forbid passing a turn. Zugzwang is an essential concept in chess endgames, where the weaker side could often hold a fortress position if not compelled to move, but Arimaa endgames seem to be 100% races. How could it ever be possible that no constructive steps are available?

Admittedly, in the old days bot_Arimaanator would sometimes try to pass a turn and lose on timeout, but that was always in positions where it could have been crushed after the pass. bot_Arimaanator passed when it was not in a fortress position, i.e. when passing was not a good or necessary move.

If I am now correctly understanding the position, after Gold's fifth move in the main line, it will be mutual zugzwang. Silver has to move, so Silver will eventually lose, but if passing were allowed, Silver could hold out longer by passing. Indeed, if passing were allowed, the repetition rule would eventually force Gold to deviate. (In a weird sense, passing in response to a pass can be seen as undoing the previous player's move, so if one player were allowed to pass, the other wouldn't be.)

My current guess is that with best play on both sides, Gold will win in eight moves from the starting position. I'm just amazed at how many themes come into play to make this a tricky position. For example, it is also essential that rabbits can't move backwards: if rabbits could retreat Silver would have even more defensive resources. And if traps could be safely traversed, Silver would win easily.

How do you come up with these positions, JDB? Are you making an endgame tablebase, and picking out the positions with greatest distance to mate? But no, we decided long ago that tablebases would be infeasible for Arimaa due to repetition being a loss rather than a draw. Or have you found a way around that?

Title: Re: Endgame Study 2, Find the winning plan
Post by RonWeasley on Nov 25^th, 2006, 9:40pm

I also missed e to c5. So now I see gold in 8.

I very much like that I've come up with the wrong answer both times so far. This means I'm learning and that's fun. You guys are proving yourselves smarter than me, not that it's a big secret. Just be thankful Hermione doesn't play.