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Title: Endgame Corner II (elephant vs. two cats) Post by Fritzlein on Apr 18th, 2005, 3:02pm 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by mouse on Apr 19th, 2005, 6:26am 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by 99of9 on Apr 19th, 2005, 8:35am Position 1, gold to move, gold wins in 3. Position 1, silver to move, gold wins in 5.5 ? |
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Title: Re: Endgame Corner II (elephant vs. two cats) Post by Fritzlein on Apr 19th, 2005, 8:21pm 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by 99of9 on Apr 20th, 2005, 2:27am 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by mouse on Apr 20th, 2005, 8:01am 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by 99of9 on Apr 20th, 2005, 8:27am 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by mouse on Apr 20th, 2005, 8:51am 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by Fritzlein on Apr 20th, 2005, 1:16pm 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by jdb on Apr 20th, 2005, 3:55pm 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by Fritzlein on Apr 20th, 2005, 9:45pm 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by jdb on Apr 21st, 2005, 8:32am 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by omar on Apr 27th, 2005, 3:15pm 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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Title: Re: Endgame Corner II (elephant vs. two cats) Post by jdb on Jan 12th, 2007, 6:32pm 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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