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Topic: DCR vs dcr (Read 4733 times) |
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chessandgo
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Re: DCR vs dcr
« Reply #15 on: Feb 25th, 2010, 3:38am » |
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Digging up this old (awesome) thread.
I'm considering giving an example of EMR vs edcrr in my book to illustrate the importance of the number of pieces over their strength in an endgame, perhaps something like:
1w Ed4 Rd1 Mf2
1b ed5 ra8 rh8 cf7 dc7
I wonder whether a bot or some kind of exhaustive search can prove that silver is winning even with gold to play in a position like the above. What do you programming wizards think?
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| « Last Edit: Feb 25th, 2010, 3:39am by chessandgo » |
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jdb
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Re: DCR vs dcr
« Reply #16 on: Feb 25th, 2010, 6:54am » |
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The current bots are not able to solve a position with 8 pieces still on the board. However, with rabbits new GUI it would be easy enough to play against a bot offline, starting from any position. This would let you play out some lines to demonstrate the proper technique in your book.
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chessandgo
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Re: DCR vs dcr
« Reply #17 on: Feb 25th, 2010, 7:24am » |
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Ok. I was just checking, I'm not going to go into any line in the book, I merely wondered whether someone would come up after the book is released and say: well, the position you assess as won for silver is actually a goal in 15 for gold 
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Hippo
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Re: DCR vs dcr
« Reply #18 on: Feb 25th, 2010, 8:40am » |
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What about other databases with 6 pieces? The most important are with both having the same strongest piece (HCR/hdr).
There were 2 symmetries in DCR/dcr (East-West, North-South) which can be used so ~ 65*64*63*62*60*59*2/4>234 ... roughly 4GB of resulting space with 1 bit per position. But you need a bit indicating not known result yet ... so around additional 4GB of space during computation required. I suppose most of positions lead to "immediate" end so the "unknown result yet" shrinks fast.
... The computational time is not so surprising .
In HCR/hdr the North-South symmetry vanishes.
I am happy that Arimaa game ends mostly with 10 or more pieces on the board.
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| « Last Edit: Apr 5th, 2010, 7:47am by Hippo » |
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RonWeasley
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Re: DCR vs dcr
« Reply #19 on: Feb 25th, 2010, 8:54am » |
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I really like these kind of results. While some folks have expressed disinterest, I think there are those of us who would like to see more. jdb is my hero.
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jdb
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Re: DCR vs dcr
« Reply #20 on: Feb 25th, 2010, 1:22pm » |
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on Feb 25th, 2010, 8:40am, Hippo wrote:What about other databases with 6 pieces? The most important are with both having the same strongest piece (HCR/hdr).
There were 2 symmetries in DCR/dcr (East-West, North-South) which can be used so ~ 65*64*63*62*60*59*2/4>234 ... roughly 4GB of resulting space with 1 bit per position. But you need a bit indicating not known result yet ... so around additional 4GB of space during computation required. I suppose most of positions lead to "immediate" end so the "unknown result yet" shrinks fast.
... The computational time is not so surprising .
In HCR/hdr the North-South symmetry vanishes.
I am happy that Arimaa game ends mostly with 10 or most pieces on the board. |
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Only 1 bit per position is required for computation. I don't remember off the top of my head how it worked. I'd have to look it up.
4Gb is enough memory to do the 6 piece tablebases (barely).
The initial gold rabbit can only go on 28 squares. The board has left/right symmetry. The gold rabbit can't be on the 8th rank, since the game would be over. It also can't be off the board, since the game would also be over.
The initial silver rabbit can only go on 48 squares. It can't be on the first rank, since the game would be over.
The other pieces can be on 65 squares. Anywhere on the board, plus off the board.
Tighter indexing is possible. This method allows the 6 piece tables to be done using 4Gb. Even with better indexing 7 pieces takes alot of memory.
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jdb
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Re: DCR vs dcr
« Reply #21 on: Feb 25th, 2010, 1:24pm » |
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on Feb 25th, 2010, 8:54am, RonWeasley wrote:| I really like these kind of results. While some folks have expressed disinterest, I think there are those of us who would like to see more. jdb is my hero. |
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It should be possible to do something with rabbits GUI to allow people to play around with the endgame puzzles.
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Hirocon
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Re: DCR vs dcr
« Reply #22 on: Feb 25th, 2010, 2:55pm » |
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Do these results take into consideration the 3-repeat rule? I remember seeing a ER v. r position where silver to move has a forced win, but only because of the 3-repeat rule (without the rule the position would be a draw). Do situations like that ever arise on any DCR v. dcr positions?
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jdb
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Re: DCR vs dcr
« Reply #23 on: Feb 25th, 2010, 3:31pm » |
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on Feb 25th, 2010, 2:55pm, Hirocon wrote:| Do these results take into consideration the 3-repeat rule? I remember seeing a ER v. r position where silver to move has a forced win, but only because of the 3-repeat rule (without the rule the position would be a draw). Do situations like that ever arise on any DCR v. dcr positions? |
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The tablebase ends up recording 3-repeat positions as "unknown". When the engine probes the tablebase it has to figure out itself which side wins using repetition. In practice these types of positions are easy to figure out.
The 3-repeat type positions occur in all the tablebases I have made so far.
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Fritzlein
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Re: DCR vs dcr
« Reply #24 on: Feb 25th, 2010, 4:27pm » |
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on Feb 25th, 2010, 3:38am, chessandgo wrote:1w Ed4 Rd1 Mf2
1b ed5 ra8 rh8 cf7 dc7
I wonder whether a bot or some kind of exhaustive search can prove that silver is winning even with gold to play in a position like the above. What do you programming wizards think? |
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I'm not a programming wizard, but this looks like a goal in at least six for Silver with Gold to move. That's a 48-step search. Even with reduced branching factor deepening the possible search, and even with static goal evaluation knocking (say) 8 steps off the end of the search, I'm guess the 40-step exhaustive search proof you are looking for is not forthcoming.
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rabbits
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Re: DCR vs dcr
« Reply #25 on: Feb 26th, 2010, 8:33am » |
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on Feb 25th, 2010, 1:24pm, jdb wrote:| It should be possible to do something with rabbits GUI to allow people to play around with the endgame puzzles. |
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This would be cool! If you want any particular feature added, let me know.
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Hippo
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Re: DCR vs dcr
« Reply #26 on: Apr 5th, 2010, 6:25am » |
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http://arimaa.com/arimaa/gameroom/comments.cgi?gid=140298 is a game where this analysis could be helpful.
BTW:
20b rh7w cf1e rg7e cg1e = 20b cf1e cg1e
23w Ce6s Df5e Ce5n = 23w Df5e
We get the same position after 23w as after 20b so that must be one sided zugzwang!
31b rg7e cf7s cf6n cf7e = 31b rg7e cf7e
33w Cf4e Cg4s Cg3e Ch3n = 33w Cf4e Cg4e
34b rh7w dh5w dg5n rg7e = 34b dh5w dg5n
35w Ch4s Ch3s Ch2w Cg2n = 35w Ch4s Ch3w
40b df5s df4e dg4n = 40b df5e
41w Ce1w Cd1n Cd2e = 41w Ce1n
41b dg5s Rh5w dg4w df4n = 41b dg5w Rh5w
48w Cd6s Dg5e Rh6n Rh7n is illegal, should be
48w cg6w Dg5n Rh6n Rh7n or 48w Cd6n re6w rd6w rc6x Cd7s
Wow 44w capturing the silver cat would lead to gold elimination.
A lot of one sided zugzwangs.
I suppose most of the positions remain in state "unknown".
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| « Last Edit: Apr 5th, 2010, 7:46am by Hippo » |
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