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Topic: Fixing the rules / eliminating draws (Read 12389 times) |
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Fritzlein
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Re: Fixing the rules / eliminating draws
« Reply #15 on: Apr 8th, 2005, 12:05pm » |
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on Apr 5th, 2005, 1:30pm, Arimanator wrote:I don't know if I agree with the rule that in case of abandonnement ( I read the article this time  )of your own rabbit before trapping the last rabbit adverse should be a win for the one who does it. To me it's like uncover your king to mate the king adverse, you can't do that because you king dies first (I believe that checkmate initially meant "the king is dead"). Same thing here your rabbit is dead first so it doesn't matter whether you get the other's rabbit or not. To me it's either a draw or the one who moves loses. Sometimes the remedy causes more damage than the disease it is meant to heal, in our quest for eliminating draws we shouldn't create rules that go against intuition as this one would. You may as well say that in case of a draw the victor will be decided by flipping a coin. |
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That's a good point. We don't want to eliminate draws in a way that goes against the spirit of the game. Mouse's examples don't really persuade me, becuase it is already the case that someone with more material could lose due to an opposing goal, so it doesn't bother me that someone with more material could lose due to losing their last rabbit. It's in keeping with the spirit of the game. In fact it extends the "no draws" part of the spirit of the game without costing anything elsewhere.
But I see your point about giving the win to one player or the other if both lose their last rabbit on the same move. If two winning conditions are met simultaneously, intuitively it feels like a draw. So I guess the "last rabbit rule" wouldn't necessarily eliminate all draws if you give it in the most intuitive form.
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omar
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Re: Fixing the rules / eliminating draws
« Reply #16 on: Apr 10th, 2005, 9:25am » |
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Very interesting discussion; this and also the one on Bram's blog. You might be suprised to learn what my views are on the topic of draws.
First of all, having Arimaa be a game with no draws at all was not one of my goals. My primary goals for Arimaa were:
1 It should be playable with a standard chess set
2 It should be difficult for computers
3 The rules should be simple and intuitive to understand
4 The game should be interesting to play
Goal number 4 is very subjective and that's where I spent a lot of time trying out different sets of rules. But eliminating all possibility of draws was not one of my primary goals. If a set of rules resulted in a game that had a high draw percentage, I would have rejected it based on goal 4. In my opinion a game that has a very high frequency of draws is not very interesting.
But if a set of rules also had no chance of a draw I would also reject it due to goal 4. In my opinion a game that has no possibility of draws could eventually become non-interesting even though the game itself is interesting in every other way. It would eventually be known that one side or the other will win; in all such games it's always been white or first to play that wins. So as the quality of the game play improved you would begin to notice an increase in the number of games won by white. To make such games more balanced the second player usually has the option to switch sides after the first players move. But with perfect play it doesn't really change anything; the second player should always be able to win. In such games the black player can always argue that he lost not because of a flaw in his play, but rather because of a flaw in the game that black is destened to lose.
Anyways my view of draws is that a game should allow some draw positions that can be reached with perfect play by both sides. But the frequency of reaching such positions with non-perfect play should be very low. In such a game, a draw becomes a gem and witnessing one is quite a spectacular thing. For the spectators the possibility of a draw actually adds to the excitement of an end game. I feel quite lucky that Arimaa does have the potential for a draw, but has a very low draw percentage even with very good quality of play.
So I guess by now, you can tell that I would not want to eliminate draws from Arimaa; in my opinion they're gems. However, there are many practical situations when we don't want a game to end in a draw and must some how resolve a draw (such as elimination tournaments). You may be suprised to know that Arimaa already does have such a rule to eliminate draws if needed. But it is part of the match rules and not a core game rule. If you look near the bottom of the match rules page there is a rule for breaking draws. It says that if both sides lose all the rabbits the first player who lost the first rabbit loses the game. I can't recall now all the reasons why I chose that, but I do remember also considering a few other options; one being the first player who had lost all the rabbits loses the game and another being the last player to lose all the rabbits wins the game. I think my main reason for chosing this one was because this rules causes the players to avoid a draw type situation to begin with. Initially both players would not want to lose even a sigle rabbit. But once one of the players has lost a rabbit that player would want to protect the remaining rabbits very strongly. So when playing with this rule the players would avoid losing rabbits from the begining and thus there is less chance of having a situation where both players have lost all the rabbits. Also all three of these rules can put one of the players in a situation where they do not want to trap the opponents last rabbit. With the rule I chose which player will be in that situation is known as soon as the first rabbit is trapped; so there is plenty of time to avoid that situation from occuring. Finally I don't think we will see this rule getting invoked so much that it really matters.
So my view on draws is that I would not want to eliminate them from Arimaa. However, I can always be persuaded to change my view if someone can give a good argument that a game with any chance of draws is theoretically flawed. In my view a game that has a high frequency of draws with good quality, non-perfect play is flawed and also a game with no chance of draws is theoretically flawed due to the black player arguement I mentioned above; unless somehow both players have an equal chance of winning which I don't think is possible in a deterministic game. A game with any chance of a draw always results in a draw with perfect play, but I think I perfer that over the white player always winning with perfect play.
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Fritzlein
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Re: Fixing the rules / eliminating draws
« Reply #17 on: Apr 10th, 2005, 11:47am » |
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Very interesting, Omar! I didn't realize that you would prefer the game to be drawn with perfect play. Now that I think about it, I probably agree with you, as long as draws are quite rare. Ideally both sides would have an equal chance of winning, but no one could lose unless they made a mistake.
If I had to lay a bet right now, I would bet that Arimaa is NOT drawn with perfect play on both sides, but in fact Gold has enough of an initiative to win. Setting up the pieces second doesn't seem to quite compensate for the first move. I believe the near 50-50 win percentage for the two colors in the past was partly due bots playing more games as Gold than as Silver (because humans were seeking a greater challenge). One notices that when the bots were broken and only playing Silver, the win percentage for Gold shot way up.
But this poses a new question: If it is a design flaw for the first player to have a forced win with perfect play on both sides, and if I'm right about my hunch, how could the game be rebalanced? One idea would be to allow Silver to take one step after setting up the pieces, or even two steps with two different pieces. This would go some distance to disrupting any Gold initiative, if only because it would allow Silver to block an initial "elephant forward 4" opening. Perhaps one could allow Silver an unrestricted two steps, but then I suspect Silver would just play "elephant forward two" and claim a miniscule advantage.
Anyway, this is all hypothetical discussion with minimal practical impact, because the game seems very well balanced as is, with even marginally better play likely to tip the balance towards a win from an even position.
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omar
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Re: Fixing the rules / eliminating draws
« Reply #18 on: Apr 13th, 2005, 6:37pm » |
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It is possible for a game to be drawn with perfect play and still show a significant advantage for the white (first to move) player with non-perfect play. The advantage is greatest at random play and diminishes slowly as the quality of play improves and more and more games become drawn. It eventually disappears at perfect play where all games are drawn. I noticed that when I was experimenting with tic-tac-toe. See the discussion about rating of a perfect chess player for some numbers.
Im not sure what happens in games where perfect play is a win for white.
It may well be that Arimaa is a win for white with perfect play even though the potential for draws is there with non-perfect play. Connect4 turned out to be this way. It is possible for a game to be drawn in Connect4, but with perfect play it is always a win for the first player.
Experiments with connect4 might show what happens to the white advantage and frequency of draws for games that are win for white with perfect play. Does the white player advantage continue to increase as the quality of play increases or does it first decrease from the random play level before increasing again?
The idea proposed by Karl of giving the first player only 2 steps on the first turn is an interesting one. It was also proposed by R. Wayne Schmittberger (editor of GAMES magazine). I am open to modifying the core rules of Arimaa to add this if we find that there is a significant advantage of about 4 or 5 percent for the first player in high quality games.
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99of9
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Re: Fixing the rules / eliminating draws
« Reply #19 on: Apr 14th, 2005, 8:52am » |
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on Apr 13th, 2005, 6:37pm, omar wrote:| The advantage is greatest at random play and diminishes slowly as the quality of play improves and more and more games become drawn. It eventually disappears at perfect play where all games are drawn. I noticed that when I was experimenting with tic-tac-toe. |
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Maybe I'm just an over-cautious scientist, but I think the first sentence in the quote above is unjustified. It may well have happened this way for tic-tac-toe, but I don't think it's necessarily generally true. For example in arimaa, if high quality human games turn out to have a bigger advantage than the 0.3% that random steppers show, that doesn't necessarily mean that arimaa is a theoretical win for gold. It may still be a theoretical draw - we just aren't playing it well enough yet. The reason the split opens up may just be some peculiarity about who gets to choose the path of the game.
About changing the rules. I think the 2 step idea is a good one, and if you were inventing arimaa now, I'd say you should go with it. But I agree with Arimanator that it's very desirable to have a continuity of rules, and not to change them on a suspicion of an advantage! Even 20-30% would be acceptable as long as tournaments mix up the gold and silver or use double rounds (eg chess).
Which reminds me of one of the gripes I had this year in the WC. I really don't think it is good to make the top rated players play all silver. If nothing else it should be randomized. (Not that I'm blaming my poor performance on that of course - Naveed played a spectacular game to knock me out in round 1.) I do have another gripe, but I'll save it for another day and another posting topic.
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Fritzlein
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Re: Fixing the rules / eliminating draws
« Reply #20 on: Apr 14th, 2005, 9:11am » |
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I, too, am suspicious of the claim that the advantage of going first is greatest with random play and diminishes as the quality of play improves. I think I recall reading that in chess the 55%-45% advantage for white holds more or less steady throughout the spectrum, even as the percentage of draws increases. Of course, if chess is theoretically drawn then this advantage for white will go away with perfect play, and diminish with near-perfect play, but on the scale at which humans play, I believe that 2500-rated players and 1000-rated players show about the same advantage for white in games between equally rated players.
The data to verify this should be out there somewhere. In fact, Omar, didn't you acquire a huge database of chess results for a different purpose? I'm curious to see if my recollection is correct.
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| « Last Edit: Apr 14th, 2005, 3:03pm by Fritzlein » |
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omar
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Re: Fixing the rules / eliminating draws
« Reply #21 on: Apr 14th, 2005, 12:53pm » |
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on Apr 14th, 2005, 1:00am, Arimanator wrote:Omar, I would be wary before changing the rules in a way that would make the old games invalid, especially after a 3 year history worth of database ( all the more after we've seen in another topic that Gold has no significant advantage !)
That might confuse people who want to study the game.
So please, don't do it lightly. |
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No I would not do it without a lot of play testing and only if it made a significant improvement. Our current estimate of the first player advantage is less than 1% so I don't think it would make much of a difference.
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omar
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Re: Fixing the rules / eliminating draws
« Reply #22 on: Apr 14th, 2005, 1:05pm » |
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What if it turns out that for every gold setup there is a counter silver setup that can defeat it. Since gold has to go first and silver can see golds setup, it may even be possible that Arimaa is a win for silver with perfect play.
But I hope that is not the case and that Arimaa is a draw with perfect play. So it is necassary to not eliminate draws if we hope to have a chance that the game is a draw with perfect play.
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omar
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Re: Fixing the rules / eliminating draws
« Reply #23 on: Apr 14th, 2005, 1:27pm » |
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on Apr 14th, 2005, 9:11am, Fritzlein wrote:I, too, am suspicious of the claim that the advantage of going first is greatest with random play and diminishes as the quality of play improves.
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I posted a reply to this, but in the
'How great an advantage is the first move?' thread.
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| « Last Edit: Apr 14th, 2005, 1:29pm by omar » |
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omar
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Re: Fixing the rules / eliminating draws
« Reply #24 on: Apr 14th, 2005, 1:38pm » |
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on Apr 14th, 2005, 9:11am, Fritzlein wrote:
The data to verify this should be out there somewhere. In fact, Omar, didn't you acquire a huge database of chess results for a different purpose? I'm curious to see if my recollection is correct. |
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Yes, it was for the 'Rating of a perfect chess player' thread.
See the notes in this file for where to get the data.
http://arimaa.com/arimaa/rating/humanChessDrawPerc.xls
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omar
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Re: Fixing the rules / eliminating draws
« Reply #25 on: Jun 7th, 2005, 9:40pm » |
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Bram's comments regarding the tie break rule have caused me to re-evaluate the situation. The way I was thinking about it before is that only after a game has ended in a draw (i.e. both players have lost all the rabbits) the tie break rules kicks in. However, I now think that in games where draws are not acceptable, it might be better to just use the rule Bram suggested and declare the first player who captures all of the opponents rabbits as the winner right away and the game does not progress any further. Though this introduces an additional way to win the game, I don't think it will impact the main objective of the game. I've modified the 'Match Rules' page to reflect this.
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Fritzlein
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Re: Fixing the rules / eliminating draws
« Reply #26 on: Jun 8th, 2005, 12:24am » |
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I also was persuaded by Bram's arguments. This is quite a separate issue from whether draws are a bad thing that should be totally eliminated from Arimaa. I personally would favor wiping out the possibility of any draws ever, but I respect your position, Omar, that draws need not be eliminated and can be an interesting side show if they ever happen. But because there are cases (e.g. a single-elimination tournament) where we all agree that draws are not acceptable, it makes it an important question how to eliminate draws in those cases.
The "first to capture a rabbit" rule seems less desirable than the "first to capture all opposing rabbits" rule for reasons Bram outlined and other reasons as well. Since losing all rabbits happens very deep into the game, it is almost surely indicative of inferior skill, whereas losing one rabbit early could happen for all kinds of reasons, for example sacrificing a rabbit to gain a camel hostage. Also Bram's rule gives less advantage to Gold. Also Bram's rule won't kick in except in situations where both players know very well what is on the line. And finally, if rulebook draws occurred with regularity, and if they were decided by the first rabbit capture, then opening play would be weirdly influenced by a reluctance to lose the first rabbit, even for material gain, i.e. winning a dog for a rabbit in the opening. Bram's rule, in contrast, won't affect opening play at all, which makes it a much better rule for that reason alone.
So, in brief, I heartily applaud the change you just made, Omar.
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jdb
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Re: Fixing the rules / eliminating draws
« Reply #27 on: Jun 23rd, 2005, 3:45pm » |
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I just played a game against shallowblue, where I lost all my rabbits. The game was not over.
Has the server been updated to reflect this new rule?
If so, I have mistunderstood the rules. Is capturing all your opponents rabbits an automatic win, or does it only win under certain circumstances? (I certainly hope the rule applies at all times!)
Thanks
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Fritzlein
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Re: Fixing the rules / eliminating draws
« Reply #28 on: Jun 23rd, 2005, 9:29pm » |
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on Jun 23rd, 2005, 3:45pm, jdb wrote:Is capturing all your opponents rabbits an automatic win, or does it only win under certain circumstances? (I certainly hope the rule applies at all times!)
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If I understand Omar's intent, it is that the rule only applies in situations (e.g. single-elimination tournaments) where draws are unacceptable. Otherwise, you can still play on hoping for a draw after you lose all your rabbits.
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omar
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Re: Fixing the rules / eliminating draws
« Reply #29 on: Jun 26th, 2005, 9:36am » |
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Capturing all of the opponents rabbits does not equal a win. By default the game continues. However in tournaments where draws are not acceptable then this rule can be used to prevent a draw situation from occuring.
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