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Topic: How many steps to goal without couter moves? (Read 1250 times) |
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clauchau
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How many steps to goal without couter moves?
« on: Mar 31st, 2006, 12:42pm » |
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How few steps are needed for Gold to reach the goal with a rabbit without Silver playing, once the two players set up their initial position -- Assuming Gold set up her position so that she'll goal in as few steps as possible and Silver set up his with the purpose to make Gold's minimum number of steps as high as possible?
I think 21.
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Fritzlein
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Re: How many steps to goal without couter moves?
« Reply #1 on: Mar 31st, 2006, 1:35pm » |
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Wow, I can't get it under 24. Then again, everyone knows how bad my goal attack is. 
Oh, wait, I think I can do it in 23 against any defense.
Ah hah! Down to 22. I feel much better now.
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| « Last Edit: Mar 31st, 2006, 1:38pm by Fritzlein » |
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PMertens
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Re: How many steps to goal without couter moves?
« Reply #2 on: Mar 31st, 2006, 1:36pm » |
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far far less I think (7) .... but I just got reminded, that I cannot read 
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| « Last Edit: Mar 31st, 2006, 2:15pm by PMertens » |
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jdb
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Re: How many steps to goal without couter moves?
« Reply #3 on: Mar 31st, 2006, 3:37pm » |
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I think 21 steps, but on one turn gold only uses three out of the 4 available steps. So depending on how that counts, either 21 or 22.
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Fritzlein
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Re: How many steps to goal without couter moves?
« Reply #4 on: Mar 31st, 2006, 3:47pm » |
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Just to clarify that I'm really missing something, can you still do 21 steps with the defensive elephant directly opposite your own? It doesn't matter to me how Gold's steps are divided into moves, because Silver isn't responding in between anyway. Even allowing 3-step moves doesn't get me down to 21. 
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| « Last Edit: Mar 31st, 2006, 3:49pm by Fritzlein » |
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clauchau
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Re: How many steps to goal without couter moves?
« Reply #5 on: Apr 1st, 2006, 1:06am » |
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on Mar 31st, 2006, 3:47pm, Fritzlein wrote:| can you still do 21 steps with the defensive elephant directly opposite your own? |
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Yes, you even can in 20 steps in that case, provided your elephant is on files b, d, e or g and Silver's isn't on... well I won't tell, but Silver's can be opposite yours and it won't prevent you to goal in 20.
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Fritzlein
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Re: How many steps to goal without couter moves?
« Reply #6 on: Apr 1st, 2006, 8:05am » |
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Thanks, I finally got it with a tip from JDB. Strangely, I got the 21-step goal in the "hard" case before I got the 20-step goal in the "easy" case.
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clauchau
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Re: How many steps to goal without couter moves?
« Reply #7 on: Apr 2nd, 2006, 3:13pm » |
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I wonder if there is any valid Arimaa position where Gold would need more than 21 steps to win without any counter-move.
I also wonder how long would a game last if the two players were now allowed to move but every move were allowed to be made of up to 20 steps instead of 4. I feel like Gold wins after Silver's first 20 counter-steps, but I'm not sure. If gold is leaving holes on his starting ranks, Silver may win during these first 20 counter-steps.
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