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Topic: Endgame Corner II (elephant vs. two cats) (Read 1218 times) |
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Fritzlein
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Endgame Corner II (elephant vs. two cats)
« on: Apr 18th, 2005, 3:02pm » |
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In order from easy to difficult:
Position 1: Ra1 Cd1 Ce1 Rh1 ra8 ed8 rh8
Position 2: Ra1 Cd1 Ce1 ra8 ed8
Position 3: Ra1 Rb1 Cd1 Ce1 Rg1 Rh1 ra8 rb8 ed8 rg8 rh8
Who wins in each case with Gold to move and with Silver to move?
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mouse
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #1 on: Apr 19th, 2005, 6:26am » |
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I guess this link should be available from the gameroom so people could easily set up the position. I think it is only in the forum.
http://arimaa.com/arimaa/games/planGame.cgi
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99of9
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #2 on: Apr 19th, 2005, 8:35am » |
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Position 1, gold to move, gold wins in 3.
Position 1, silver to move, gold wins in 5.5 ?
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Fritzlein
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #3 on: Apr 19th, 2005, 8:21pm » |
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99of9, I think your half-moves must be switched around. When folks say, "Gold to move and win in 3 moves", they usually mean 2.5 moves, i.e. 3 moves by Gold and 2 by Silver. That is my evaluation of the first position too. But when you say "Silver to move and Gold wins in 5.5 moves", do you mean after 5 moves by Silver and 5 by Gold, or do you mean 6 moves by Silver and 6 by Gold?
Not that I was asking for the exact number of moves when I posted the positions. The interesting thing is that Gold wins no matter who moves first, so two small pieces are definitely superior to one big piece in Position 1.
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| « Last Edit: Apr 19th, 2005, 8:29pm by Fritzlein » |
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99of9
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #4 on: Apr 20th, 2005, 2:27am » |
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Right, obviously gold isn't going to win on silver's turn  .
It should have been 2.5 moves and 5.0 moves. (I'd be interested to hear if the bots agree with me about the number of moves where silver plays first).
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| « Last Edit: Apr 20th, 2005, 2:29am by 99of9 » |
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mouse
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #5 on: Apr 20th, 2005, 8:01am » |
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Will you post your moves for silver to move. I keep getting a win in 6 and not 5 moves. So I am interested in the one move shorter version.
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99of9
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #6 on: Apr 20th, 2005, 8:27am » |
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To me it seems like there are many ways to finish it in 5 moves. So I'll publish one long line, but you can tell me where you would have deviated as silver in order to delay the finish to 6, then I'll say how I would respond, etc. It might take us a while to figure this out.
1b) ra8s ra7s ra6s ra5s
1w) Cd1w Cc1n Ce1e Ra1n
2b) rh8s rh7s rh6s rh5s
2w) Cf1n Rh1n Rh2n Ra2n
3b) ed8s ed7s ed6s ed5s
3w) Rh3w Rg3n Rg4n Cf2e
4b) ed4e ee4e ef4e rh4s
4w) Ra3e Rb3n Cc2w Cg2e
5b) Rg5w eg4n Rf5n Rf6x eg5w
5w) Rb4n Rb5n Rb6n Rb7n
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| « Last Edit: Apr 20th, 2005, 8:40am by 99of9 » |
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mouse
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #7 on: Apr 20th, 2005, 8:51am » |
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I think the reason is I counted setup as one move. This time around I cant find any way to delay to 6 moves.
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Fritzlein
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #8 on: Apr 20th, 2005, 1:16pm » |
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When I started this thread I thought that Position 2 was a draw no matter who goes first, and that Position 3 was a win for Gold no matter who goes first. Now I am unsure of both answers. I'm obviously not as careful as JDB, who worked out the exact answers to his positions in Endgame Corner One before posting them.
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jdb
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #9 on: Apr 20th, 2005, 3:55pm » |
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Position 2, Silver's Move
I think silver has the win.
The following should cut & paste into Omar's great planning window.
1w Ra1 Cd1 Ce1
1b ra8 ed8
2w pass
2b ed8s ed7s ed6s ed5w
3w Ra1n Ra2e Cd1w Cc1w
4b ra8s ra7s ra6s ec5s
Gold has a bunch of options for their 3w move, but Silver's elephant is very well placed.
Opinions?
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Fritzlein
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #10 on: Apr 20th, 2005, 9:45pm » |
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The cut and paste is awesome, JDB. From now on when I pose I problem I will give the setup moves in a format that can be pasted into Omar's cool plan window.
Anyway, what about
1w Ra1 Cd1 Ce1
1b ra8 ed8
2w pass
2b ed8s ed7s ed6s ed5w
3w Cd1w Cc1w Cb1n Ra1e
The general idea is for Gold to try to play on both wings since Silver can only play on one. It doesn't seem to me Silver can push through on the a-file fast enough to ignore the gold rabbit on the other wing or even up the center.
On the other hand, the absence of a quick win doesn't make it a draw. The strategy I had overlooked for Silver was to keep its own rabbit back while manuevering to neutralize the opposing rabbit with its elephant. It isn't clear that Gold can keep the gold rabbit safe long enough to threaten the Silver rabbit and force an exchange. Proabably you are right and it is a Silver win in the end.
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jdb
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #11 on: Apr 21st, 2005, 8:32am » |
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Once Silver's elephant blocks Gold's rabbit, Gold is in trouble.
1w Ra1 Cd1 Ce1
1b ra8 ed8
2w pass
2b ed8s ed7s ed6s ed5w
3w Cd1w Cc1w Cb1n Ra1e
3b ec5w eb5s eb4s ra8s
According to clueless, this is a win for Silver.
For position 2, Gold to Move:
I think the best Gold can hope for is a draw. Silver leaves its rabbit on a8 and goes after Gold's rabbit.
1w Ra1 Cd1 Ce1
1b ra8 ed8
2w Ra1n Ra2e Rb2e Rc2e
2b ed8s ed7s ed6s ed5s
3w Rd2e Re2e Rf2e Rg2e
3b ed4e ee4e ef4e eg4s
I think there is enough time for silver to capture the rabbit and get back to save its own rabbit. Although, I have no convincing proof of this.
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omar
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #12 on: Apr 27th, 2005, 3:15pm » |
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My gut feel says that position 2 is a win for gold regardless of who moves first. I think the key for gold is to get the rabbit to the right side (away from the silver rabbit) while using the cats to slow down the silver rabbit. If the silver elephant trys to assist its own rabbit the gold rabbit will have an open goal shot. If the elephant goes after the rabbit then one of the cats can go to assist it, while the other holds back the silver rabbit. I haven't worked out the details, so I could be wrong.
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jdb
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Re: Endgame Corner II (elephant vs. two cats)
« Reply #13 on: Jan 12th, 2007, 6:32pm » |
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Position Two revisited.
Using the tournament ruleset
It turns out silver has alot of winning choices.
With Gold To Move:
1w Ra1 Cd1 Ce1
1b ra8 ed8
2w Ra1e
2b ed8s ed7w ec7w eb7s
3w Ce1n Ce2n Ce3n Ce4n
3b eb6s eb5s eb4s eb3w
4w Ce5w Cd5w Cc5w Cb5n
4b ea3s ea2e eb2e ec2s
5w Cb6n Cb7n Cb8s ra8e
5b ec1n Rb1e ec2e Rc1n
6w Cb7s Cb6s Cb5s Cb4e
6b ed2n Rc2e Rd2e ed3s
7w Cc4e Cd4e Ce4e
7b rb8s rb7s rb6s rb5w
8w Cf4e Cg4n Cg5n Cg6n
8b Re2n ed2e Re3e Rf3x ee2n
With silver to move:
1w Ra1 Cd1 Ce1
1b ra8 ed8
2w
2b ra8s ra7s ra6s
3w Ra1e Rb1n Rb2w Cd1w
3b ra5s ed8s ed7s ed6s
4w Ra2e Cc1w Cb1w Ca1n
4b ra4e rb4e ed5w
5w Rb2e Ce1w Rc2w Ca2s
5b rc4e rd4e re4w ec5s
6w Rb2w Ra2n Ra3n Cd1n
6b rd4e re4e ec4w
7w Ca1e Cb1e Cd2e Ce2e
7b eb4s Ra4e Rb4n eb3n
8w Cc1w
8b Rb5e eb4n Rc5n Rc6x eb5e
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