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Title: Is never lose possible? Post by haizhi on Nov 21st, 2003, 3:39pm I wonder if playing every move safe in this game , which means instead of taking risk trying to win, just preventing the opponent get anything, can I make a draw every time? For example, do nothing at every move, except recovering the initial position, can you beat that? |
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Title: Re: Is never lose possible? Post by haizhi on Nov 21st, 2003, 3:45pm Oh, it doesn't mean I am planning to use that, Omar. :D |
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Title: Re: Is never lose possible? Post by 99of9 on Nov 21st, 2003, 7:47pm Yes you can beat someone recovering initial position each move. However I think you are right that there may exist a purely defensive strategy strong enough to never lose a piece. If played by both sides, it would be a very boring game... But that would not be a draw... draw is when all rabbits are dead on both sides. Instead the board would be evaluated when the maximum number of moves is reached (in most cases 100 moves for each player). So the person with the rabbits furthest forward would win... But in reality, I've never been able to defend that well... naveed always manages to get my camel over his side of the board somehow (or at least a horse). |
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Title: Re: Is never lose possible? Post by fotland on Nov 22nd, 2003, 1:38pm I think you can always pull a rabbit over to your side of the board, and the rabbit moves can't be reversed, so the game must end. |
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Title: Re: Is never lose possible? Post by Janzert on Nov 22nd, 2003, 10:29pm Also don't forget the repeat position rule: Game Rules-Special Situations Quote:
Janzert |
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Title: Re: Is never lose possible? Post by omar on Nov 28th, 2003, 8:54pm While the rules were being developed there were some versions in which a defensive strategy could always prevent the opponent from winning. The only and only exception rule in Arimaa is that rabbits cannot move backwards. It was needed so that if someone tries to play only defensively their rabbits could be dragged out and they would be forced to come forward to defend them. Claude likes to use that on me sometimes :-) So far no defensive strategy has been found to prevent the opponent from winning. Also if a player only plays defensively the opponent can safely play offensively and win the game. Of course if both players only play defensively its possible for the game to go on forever. Imagine a bot that only moves it stronger pieces and does not move opponents pieces playing aginst itself. Omar |
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Title: Re: Is never lose possible? Post by omar on Nov 28th, 2003, 8:55pm I ment "one and only". |
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Title: Re: Is never lose possible? Post by 99of9 on Nov 29th, 2003, 7:11am on 11/28/03 at 20:54:12, omar wrote:
But the real question is whether "pulling rabbits out" compromises the aggressor and means he loses other pieces or positional advantage. If this is the case, then a defensive strategy may still be optimal, though I agree that has not been found yet. |
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Title: Re: Is never lose possible? Post by omar on Dec 2nd, 2003, 1:54pm The aggressor only needs to send the elephant forward in order to pull out the rabbits. So I think it tips the game in favor of the aggressor. Omar |
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Title: Re: Is never lose possible? Post by 99of9 on Dec 16th, 2003, 3:11pm But if the opponent has also sent his elephant forward, the time the aggressor spends trying to pull out a rabbit may allow the perfect defender to pull a cat into a very vulnerable position, and win the game for example. All I'm saying is that until Arimaa is solved (yeah right!), we shall never know if the perfect game is neverending defence. (except for the repetition rule of course, which forces a finish in many billions of moves). |
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Title: Re: Is never lose possible? Post by omar on Dec 19th, 2003, 9:51pm Yes, it's very hard to speculate on what the perfect game would be like. But I wasn't able to find any obvious strategies that can prevent an opponent from winning. Of course they may still exist. Omar |
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Title: Re: Is never lose possible? Post by Keith on Dec 21st, 2003, 1:20am During playtesting Omar and I deliberatly tried games where one player tried an all out defense. At that time Rabbits could move backwards and the games helped lead to removing the Rabbit's ability to retreat. We did not play many games this way so I can't say we reached any conclusive results. From what I remember offense was stronger than defense but not by a lot. With careful play the offensive player could pull pieces out of the defensive players setup so that they could not return to their starting positions the next turn. However, it was clear it would take a lot of slow dull work to force a win. Since then Rabbits have lost the ability to retreat, a scoring mechanism that encourages Rabbit advancement was developed, and turn limits on games all combine to make the holdout game unviable. |
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Title: Re: Is never lose possible? Post by clauchau on Dec 21st, 2003, 3:24pm Experiments with one-ply bots and a million games also confirm that attacking strategies are winning over defending strategies. For example, among strategies directly caring about the official Arimaa score R+P*(C+1), the bot immediately decreasing its opponent's score as much as possible is weaker than the bot immediately increasing its score as much as possible, which is weaker than the bot immediately increasing (its score minus its opponent's score) as much as possible, which is weaker than the bot immediately increasing (its score minus a hundredth of its opponent's score) as much as possible. |
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