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Topic: Is draw a "proper" result? (Read 1230 times) |
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aaaa
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Is draw a "proper" result?
« on: Jul 24th, 2007, 11:12am » |
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None of the rated human vs human games has ever ended in a draw due to mutual "cunicide" and I believe only 3 ended with one rabbit being left. This leads me to wonder whether such a occurrence can ever be the result of decent play by both sides or that in fact there being few rabbits left is a highly unstable situation and that a subsequent draw could only be the result of one side messing up in a winning situation.
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omar
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Re: Is draw a "proper" result?
« Reply #1 on: Jul 26th, 2007, 1:06am » |
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Weather or not a draw could occur in a well played game is an interesting question. I would venture to guess that in a suboptimal game it could; though we haven't seen one yet. Could it happen in an optimally played game; we may never know, but I hope it does. This would mean that ultimately Arimaa is a draw. When draws are rare events they become like gems in the state space of the game and seeing one happen becomes a spectacular thing.
In tournament games though we usually perfer that every game is decisive (to keep the tournament on schedule and avoid extra games) and thus introduce a rule that the first player to loose all the rabbits loses the game.
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| « Last Edit: Jul 26th, 2007, 1:08am by omar » |
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Fritzlein
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Re: Is draw a "proper" result?
« Reply #2 on: Jul 30th, 2007, 4:32pm » |
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My general experience is that, as the board empties out, the position becomes more and more unstable, so that even tiny mistakes can result in an immediate win for the opponent. I'm not sure what happens with perfect play, but "decent" play seems to result in the game getting sharper and sharper until one side or the other breaks through.
The one exception to this general rule is when the players end up trading rabbits, but don't trade any officers. Having all the officers on the board can mean that both sides still have a reasonably strong defense, while having few rabbits means that each side has limited offense. However, even when the game starts out with several rabbit trades, something seems to tip the balance eventually. Thus, if each player started with only four rabbits, I think offensive strategies would still be at least as effective as they are on a full board.
It is possible (although not certain) that trading rabbits makes the position more drawish.
It is possible (although improbable) that rabbit pulling is the only sound opening strategy.
It is possible (although quite unlikely) that the best thing to do when your own rabbit is pulled is always to give up that rabbit to capture while pulling an opposing rabbit in return.
If all three of these possibilities hold true, then we may someday see decent play leading to lots of drawish positions. In the current environment, however, a draw would be a fluke regardless of the level of the players.
on Jul 26th, 2007, 1:06am, omar wrote:| When draws are rare events they become like gems in the state space of the game |
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Ahh, but if optimal play leads to a draw, then we can expect draws to become less and less rare as the players improve. If expert play seems to approach a draw more and more closely, then draws are less like gems in the state space, and more like flaws in the gem. That's why I would just as soon adopt the tournament rule for all games, and abolish draws before they can ever become a problem.
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aaaa
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Re: Is draw a "proper" result?
« Reply #3 on: Aug 13th, 2007, 9:30pm » |
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on Jul 30th, 2007, 4:32pm, Fritzlein wrote:| Ahh, but if optimal play leads to a draw, then we can expect draws to become less and less rare as the players improve. If expert play seems to approach a draw more and more closely, then draws are less like gems in the state space, and more like flaws in the gem. That's why I would just as soon adopt the tournament rule for all games, and abolish draws before they can ever become a problem. |
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If Arimaa exhibits a strategic delicacy anywhere near comparable to go, the ratio of draws in competent play should remain relatively low, as in practice go games played with integral komi aren't exactly riddled with draws themselves. However, if this were not the case and Arimaa as it's played now would in the future cause a draw-epidemic, then eliminating them could possibly prove problematic in that it may cause an undue shift of the advantage to the one side benefited by the draw-eliminating rule change.
What portion of high-quality games could you accept being draws?
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The_Jeh
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Re: Is draw a "proper" result?
« Reply #4 on: Aug 13th, 2007, 10:43pm » |
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I will not have as high a regard for Arimaa if draws are not possible. If two players play perfectly, both should be rewarded equally. With no possible draws, there is no possibility of Arimaa being a perfectly level playing field.
As for a victory by eliminating all opposing rabbits first, I don't really think a player should be rewarded for not being able to finish the job. Eliminating all opposing rabbits should be a strategy for winning. It should not be the win itself.
At the far low end of the abilty spectrum, games go on and on and on and on, as neither player works toward advantage. It's happened between bots. It is possible that this is regular at the very high end of the spectrum, too, as neither player concedes advatage to the other. What is the solution to such games? There is currently no defined end except for the max game time, and time controls are (and rightfully so) arbitrary.
I think Arimaa is designed so that one grain of rice can usually tip the scale. And neither humans nor computers can count all the rice without error, so draws will continue to be very rare, I THINK. I just hope the Arimaa balance is perfectly callibrated.
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| « Last Edit: Aug 13th, 2007, 11:04pm by The_Jeh » |
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Fritzlein
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Re: Is draw a "proper" result?
« Reply #5 on: Aug 13th, 2007, 11:28pm » |
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It is persuasive at some level that if both players play perfectly, they should be equally rewarded. However, if anyone could play perfectly, or even verify perfect play after the fact, the Arimaa Challenge would be lost, and the game would already have less interest for me, regardless of the draw rule.
Furthermore, the fact that the rules permit draws doesn't mean that perfect play tends in that direction. As the opening post of this thread suggests, a draw might not be the natural outcome of excellent play, but rather something someone stumbles into by messing up a win. Even with the draw rule as it is, I suspect perfect play is more likely to lead to a win for Gold than it is to lead to a draw, and that draws really are flukes.
When I worry that the rules of Arimaa are imperfect, I don't worry that perhaps one side or the other has too great an inherent advantage. It doesn't matter who has a theoretically forced win if, when any two human players do battle, the better player has a greater than 50% chance of winning from either side.
What I do worry about is the (remote) possibility that no offensive play is sound, and that excellent players will maneuver endlessly without making progress. As you say, The_Jeh, deciding games with the time control is arbitrary and unsatisfactory. Even if that turns out to be a danger, however, it is possible that minor tweaks would restore the potency of offense. Two solutions I have suggested in the past are (1) to start each side with only one horse and one dog, i.e. 14 pieces instead of 16, or (2) to promote one horse on each side to a lion. Whether or not these proposals would help depends on the exact reason offense is ineffectual, if indeed it is ineffectual.
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Fritzlein
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Re: Is draw a "proper" result?
« Reply #6 on: Aug 13th, 2007, 11:32pm » |
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on Aug 13th, 2007, 9:30pm, aaaa wrote:| What portion of high-quality games could you accept being draws? |
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I guess I wouldn't complain too vigorously if only one percent of top-level games were draws. Right now draws never happen, so the rule is essentially irrelevant.
That said, I don't see how replacing the draw rule with the tournament rule could give too great an advantage to one side, since we can't even say with confidence which side the advantage would go to!
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UruramTururam
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Re: Is draw a "proper" result?
« Reply #7 on: Aug 14th, 2007, 3:03am » |
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on Aug 13th, 2007, 11:28pm, Fritzlein wrote:| What I do worry about is the (remote) possibility that no offensive play is sound, and that excellent players will maneuver endlessly without making progress. |
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In such case a rule like e.g. "a player who does not advance any rabbit in 30 consecutive turns loses" may help.
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aaaa
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Re: Is draw a "proper" result?
« Reply #8 on: Sep 10th, 2007, 9:23am » |
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One argument in favor of eliminating draws from the game is that there would no longer be the pathological possibility of having to kill one's own rabbits in order to prevent a loss by immobilization.
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Isaac Grosof
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Re: Is draw a "proper" result?
« Reply #9 on: Sep 11th, 2007, 5:26pm » |
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I think we should just adopt tournament rules for all games.
Some bots get messed up because of the rule change, such as http://www.arimaa.com/arimaa/gameroom/comments.cgi?gid=40733
game 40733
And also since winning the opponent's rabbits prevents a natural loss, it should therefor be a natural win. (immobilization is a side case).
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| « Last Edit: Sep 11th, 2007, 5:29pm by Isaac Grosof » |
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Sorry about that one thing.
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The_Jeh
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Re: Is draw a "proper" result?
« Reply #10 on: Sep 11th, 2007, 6:02pm » |
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Eliminating all opponent's rabbits prevents a natural loss, but it does not guarantee a natural win. I am slowly being persuaded that it should be a win, but I'm not theologically persuaded yet, if such a term can be applied.
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| « Last Edit: Sep 11th, 2007, 6:05pm by The_Jeh » |
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