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        Arimaa >> General Discussion >> Arimaa Repetition rule and draws.
        
(Message started by: ddyer on Dec 26^th, 2010, 2:57pm)

Title: Arimaa Repetition rule and draws.
Post by ddyer on Dec 26^th, 2010, 2:57pm

I think the rule in Arimaa against repetition and intending to forbid draws is unsatisfactory, and ultimately unworkable. As evidence I offer this game played by my robot against itself. (Viewable on Boardspace.net) http://boardspace.net/arimaa/arimaa-viewer.shtml under "experiments/longgame.sgf")

This game is 390 moves long. For a long section in the middle (around move 270 for example) the bot is locked in a loop leading to repetitions, but is forced to break from the repetition by the rule, and eventually choose an inferior move to break the cycle. I'm not claiming that this is perfect play, but it is at least a passably competent game.

No human players would be able to reliable detect which moves were forbidden, or have the patience to slog through a game like this. Humans would agree to a draw, if they have the option. They ought to officially have the option.

Title: Re: Arimaa Repetition rule and draws.
Post by Fritzlein on Dec 26^th, 2010, 5:20pm

on 12/26/10 at 14:57:54, ddyer wrote:

I see the problem in this game. Given the option to repeat position, that is what both players would have done, resulting in an infinite-move draw. There have been bot vs. bot games in a similar vein on arimaa.com. Nevertheless, the rule forbidding draws has a substantial history of being perfectly satisfactory in games between two humans, and proving at least workable in games in which one of the players was human and the other a bot. Wouldn't it be the tail wagging the dog if incompetent computer play dictated what the rules of a game should be?

Quote:

This game is 390 moves long. For a long section in the middle (around move 270 for example) the bot is locked in a loop leading to repetitions, but is forced to break from the repetition by the rule, and eventually choose an inferior move to break the cycle. I'm not claiming that this is perfect play, but it is at least a passably competent game.

I have to disagree about the competence of the play in this game. On a very crude level, the bot routinely decided not to use all four of its steps, or have one of its steps undo another one of its steps, in positions where there was something constructive to do with those extra tempi. Also the bot several times used three steps that the opponent could undo in one, or four steps the opponent could undo in two. On a more sophisticated level, the bot seemed to usually be playing moves without a plan.

Looking at the game archive for the bot, I see it has won 5 games and lost 127. It hasn't beaten any human opponent twice. Some of the login names of the people who have dominated dumbot are unfamiliar to me, from which I infer that they are beginners at Arimaa and can nevertheless overwhelm the bot. I'm not sure how a bot that is thrashed by human beginners qualifies as "passably competent".

I am unsympathetic to the complaint that a bot that was making a slew of poor moves was forced into an inferior move by the repetition rule. Pick a position from that game in which you think the weaker side could have held out for a draw given the ability to repeat position, and I will show you a player rated in the 1500's that could beat the bot despite allowing the bot to repeat positions. In other words, at no point did the repetition rule turn a natural draw into a loss for the player forced to deviate.

There is a distinction between a position that is naturally drawn with competent play, and a position where the player with attacking possibilities is too timid or too clueless to make anything of those possibilities.

Quote:

No human players would be able to reliable detect which moves were forbidden, or have the patience to slog through a game like this. Humans would agree to a draw, if they have the option. They ought to officially have the option.

I agree that humans would have difficulty detecting repetition of position in this game, but they wouldn't agree to a draw from any of the game positions. Humans would recognize the futility of the moves they were making and would play more constructive moves instead. That's the experience we have had again and again on arimaa.com. Apparently it is also what is transpiring on boardspace.net. The evidence of the need for agreed draws would be much more persuasive if it involved a human player (and to be safe, one who isn't playing his first game ever). Otherwise, it appears that the problem of draws is confined to bot vs. bot play.

Title: Re: Arimaa Repetition rule and draws.
Post by Fritzlein on Dec 26^th, 2010, 5:28pm

You may be interested in this thread (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1274916361;start=0#0), where I analyzed the importance of the repetition rule to the games of the 2010 World Championship. The short summary is that no games had an outcome changed by the repetition rule (i.e. no natural draws). For a more nuanced discussion, one must read the full post.

Title: Re: Arimaa Repetition rule and draws.
Post by ddyer on Dec 26^th, 2010, 6:26pm

on 12/26/10 at 17:20:14, Fritzlein wrote:

Looking at the game archive for the bot, I see it has won 5 games and lost 127.

The overall win/loss record isn't representative, as almost all of the games were played with a much weaker version of the bot. Anyway, your argument really boils down to "a sufficiently advanced player wouldn't do that". Point taken.

Title: Re: Arimaa Repetition rule and draws.
Post by Fritzlein on Dec 26^th, 2010, 10:02pm

on 12/26/10 at 18:26:52, ddyer wrote:

The overall win/loss record isn't representative, as almost all of the games were played with a much weaker version of the bot.

Ah, I forgot that dumbot was under development. I should have realized, given that even ArimaaScoreP1 has a better record than that, and the linked game displayed better play than ArimaaScoreP1's level.

Title: Re: Arimaa Repetition rule and draws.
Post by 722caasi on Dec 26^th, 2010, 10:18pm

I'd just like to say, the simple (ko) repetition rule has always been enough in every game I've ever seen, except bot v. the same bot games.

Title: Re: Arimaa Repetition rule and draws.
Post by Belteshazzar on Dec 27^th, 2010, 12:45am

This is something that I've been wondering about in general. Occasionally, I will find myself in a stalemate with a bot in which we keep going back to nearly identical positions but with enough variation to avoid repeating a position three times in a row. The obvious way out of that is to try something different, which I usually do before too long, even if I have doubts as to whether it will be to my benefit. With two humans, this is even less of a problem, since chances are good that one or the other will decide to try something different within a few turns. But what if, when tactics and strategy are more established, a significant percentage of games between experienced players do enter such a loop, and neither is willing to deviate as they both see that whoever does so will be at a disadvantage? I suppose that would necessitate changing the rules to allow players to agree to a draw, and it may also prevent Arimaa from becoming all that it might have been.

Title: Re: Arimaa Repetition rule and draws.
Post by 722caasi on Dec 27^th, 2010, 3:32am

I think those loops (which I've fallen into too) are a product of having no plan. Nearly all tactics (taking over a trap, pulling a rabbit, gaining space, etc.) never fall into loops. Nevertheless, the problem is real.

Title: Re: Arimaa Repetition rule and draws.
Post by Fritzlein on Dec 27^th, 2010, 9:24am

on 12/27/10 at 00:45:42, Belteshazzar wrote:

But what if, when tactics and strategy are more established, a significant percentage of games between experienced players do enter such a loop, and neither is willing to deviate as they both see that whoever does so will be at a disadvantage?

I have thought about this question a lot, and I think you are probably correct that it will necessitate allowing agreed draws.

However, the exact implementation may depend on exactly how the infinite loops arise. For example, in Chinese Chess (xiangqi), almost every game would be drawn if they took the simple approach of letting each player repeat position when it was disadvantageous to deviate. In order to save xiangqi from death by draws, they have a complicated way of determining who is to blame for the repetition. Sometimes it even requires a referee to step in and say whose fault the repetition is. Then the player who is at fault (i.e. who is trying to draw rather than trying to win) is required to make a different move, and often loses the game as a result. (Dave, did you also petition the Xiangqi Federation to change their unworkable repetition rule? :P)

I mention this because it is possible that future infinite loops in Arimaa, if they arise, might seem to us like they are unnatural results that are the result of one player not trying to win. If so, and if there is an easy way to ban that sort of play, we might decide that we prefer to tweak the rules in a way that outlaws that kind of draw, thus preserving the decisive nature of Arimaa.

Perhaps it is more likely that future infinite loops in Arimaa will be too organic and too complicated to ban with the simple ko rule or anything similarly simple. In that case there will still be a serious debate about when agreed draws are appropriate. Supposing that 0.5% of all games were naturally reaching a drawn position that simple ko didn't handle. Would we then allow the players to agree to a draw on move three? I would think not, because we don't want to encourage the "grandmaster draws" that have plagued tournament chess to the detriment of the spectators.

Maybe, depending on how draws naturally emerge, something like the fifty-move rule from chess will be appropriate. For example, suppose we had the rule that either player could claim a draw after fifty moves by both players since the last capture. If that rule were in place, would it inadvertently include positions in which progress was happening, prematurely permitting a draw when there was no true deadlock?

I also have some hope that, depending on what causes infinite loops, there will be a scoring mechanism to break the tie. For example, after fifty moves with no capture, we might award the win to the player whose foremost rabbit is furthest advanced, and if that is tied, the second-foremost rabbit advanced, etc. Maybe this is a stupid scoring system, but maybe, depending on why the infinite loops were occuring, it would be a very satisfactory resolution.

Again, I think the appropriate response will depend on how the "drawn" positions are arising. We won't be able to decide until we see from experience what causes Arimaa games to fail to be decisive. Given the current state of affairs, I am quite persuaded that banning draws is appropriate. What will change my mind is probably not any theoretical argument, but a specific game that shows me how and why draws arise naturally in games with at least one competent human player who is trying to win.

Title: Re: Arimaa Repetition rule and draws.
Post by Sconibulus on Dec 27^th, 2010, 10:01am

I've done this before a couple times, not always because of a lack of plan. A plan involving blockading large amounts of enemies on their side of the board can occasionally lead to pointless juggling of pieces along the back of the fight, because just about everything else is usefully committed.

Title: Re: Arimaa Repetition rule and draws.
Post by omar on Dec 27^th, 2010, 12:19pm

I like the approach of waiting to see some high quality games where everyone agrees that disallowing repetition caused a problem and it should have been drawn.

I don't like allowing players to agree to draws since it opens up a loophole for intentional draws of games that otherwise should not have been drawn. In fact I would prefer the tradeoff of a small percentage of games being messed up by disallowing repetition over allowing mutually agreed draws.

Title: Re: Arimaa Repetition rule and draws.
Post by Fritzlein on Dec 27^th, 2010, 1:35pm

on 12/27/10 at 10:01:43, Sconibulus wrote:

Was this always against a bot, or also sometimes against a human? My apologies if you linked the relevant games in the past; I can't recall them now.

At the moment it does seem like draws are most likely to arise from one player swarming and sharing control of both opposing traps, but being too tied up to do anything with that shared control. On the other hand, I remember back in 2004 when there was a widespread, nagging fear that optimal play would result in both players hanging back with everything but the elephant, both preventing opposing rabbit pulls, and therefore never progressing. It is instructive to recall how worried we were about a prospect that had never resulted in a draw even then, and which today seems like hopelessly timid play by both players. Today is seems that symmetrical lone-elephant rabbit-pulling can easily be disrupted by advancing a flank horse to pull a rabbit, thus leading to asymmetrical setups, thus leading to sharp positions that are far more tense than the symmetrical ones ever were.

I wouldn't be surprised if our "swarm draw" fears prove equally unfounded in the long run as our strategic understanding of Arimaa evolves. I also wouldn't be surprised if natural draws emerge some day. Only time will tell.

Title: Re: Arimaa Repetition rule and draws.
Post by Sconibulus on Dec 27^th, 2010, 2:30pm

I've come close against a couple humans, I believe both vs. Nombril and vs. Nevermind in the first World League, but both times the blockade was never quite completed. I'm just worried that it might happen someday.

Title: Re: Arimaa Repetition rule and draws.
Post by ginrunner on Dec 27^th, 2010, 3:20pm

In my own experience I have learned to only swarm on a single side. I admit that I am far from being a perfect player but I have had games that I felt that i could not have played better where I swarmed both sides in hopes of blockading the enemy. What ends up happening unless the blockade is perfect is either the opponent can take advantage of already being by the traps and use fewer steps to prevent being locked in as well as use the advantage to maybe capture or hostage incoming pieces or another strategy against the blockade is simply mousing through and creating such an enormous goal threat that either A) there is a goal because your blockade is way to overcommited or B) to prevent the goal the blockader has to separate the troops so much that the blockade itself becomes weak and the blockader loses control of the traps and loses material that way.

I remember my first post ever was that an offensive style of play will eventually become the "best" and i still feel this way but since then I have learned that overcommiting is one of the worst things a player can do. i feel like the blockade strategy unless played perfect is a type of overcommitment and will almost always lead to a material disadvantage as well as sometimes a positional disadvantage.

"When you surround an army, leave an outlet free." Sun Tzu

My current strategy if to try and gain total or partial control of 3 traps and leave 1 to my enemy. I find that if I am allowed to do this the games go in my favor much more often.

Title: Re: Arimaa Repetition rule and draws.
Post by ddyer on Jan 1^st, 2011, 1:06pm

Here's another example, where the scenario is a threat to capture, where the threat is reversible in 3 and can be re-established in 3. Given that there's a wide open backfield, that extra move is being used to randomly shuffle pieces around, leading to an infinite length game.
http://boardspace.net/arimaa/arimaa-viewer.shtml under "experiments/longgame2.sgf")

You can poke holes in the details of this position - the game is lost for gold, silver can easily ignore the threat and do better; the threat itself is only a rabbit, etc.) but aside from these details, the basic scenario is sound - the threat could be a balance-tipping threat, where the losing player would have every motivation to continue.

Title: Re: Arimaa Repetition rule and draws.
Post by Sconibulus on Jan 1^st, 2011, 1:20pm

If there's one step free, that step can be used to create an additional, more severe threat, either by advancing a rabbit, threatening control of another trap, or getting in position to flip another piece.

Title: Re: Arimaa Repetition rule and draws.
Post by lightvector on Jan 1^st, 2011, 2:05pm

With a 3-step reversible threat that neither player wants to concede, the game usually continues just fine. There's almost always something constructive that can be done with 1 step per turn. It tends to be only the bots that spend their extra step uselessly shuffling pieces.

For instance, in that game, even if neither player wants to give up the 3-step reversible threat, silver can at least advance his horses 1 step at a time over to the C and B files to threaten the cat and rabbits there, or advance a dog to attack the H5 rabbit. Gold may similarly try to rotate his horses and camel out. Eventually, these threats will overwhelm the 3-step reversible threat.

I do agree though that there's something disconcerting about the repetition rules. If two bots/players truly believe that there's no useful way to progress in a position, it's certainly fair to argue that they should be allowed to draw. But it seems that until it happens frequently enough between human players, the rule's probably not going to be changed.

Title: Re: Arimaa Repetition rule and draws.
Post by Fritzlein on Jan 1^st, 2011, 4:50pm

on 01/01/11 at 13:06:45, ddyer wrote:

You can poke holes in the details of this position [...]

No one argues that a draw is theoretically impossible, just that draws don't happen in practice. You provide us with another practical position that isn't drawn, along with another theoretical plausibility argument about how a game could be drawn.

For every position that isn't drawn, one can argue that it is the "details" of the position that make it not a draw. On the other hand, if the details of every practical position make it decisive rather than drawn, why should those features of the position be called the details instead of the essence?