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Title: Replace the Scoring Function Post by browni3141 on Apr 19th, 2013, 3:13am I have created this thread because I want to discuss replacing the scoring function, because I find it a very distasteful part of the Arimaa rules. " I suggest nothing since in my opinion there´s no need to open such discussion. So far, the score function wasn´t an issue. In a game between humans it may almost never occur that this function will decide a game. That´s the most important point."-odin73 from http://arimaa.com/arimaa/gameroom/comments.cgi?gid=261898 I think this is the opinion held by a lot of you. It has never decided an important game, so it is not a problem. I completely disagree. I think it would be harmful to the game of Arimaa (to what degree depends on the importance of the game being played) if a game ever ends on score. Think of it as car insurance. Most of us are not expecting to need it anytime soon, but we want to be prepared for the possibility of a crash. Also, I believe that odin is wrong in saying that the scoring function has never been an issue in the past. Remember that it is not only games that end on score that are an issue; it is any game where score enters the players thoughts! I think most can agree that ideally score should play no role in the game whatsoever. In this case score has been a problem in the past. The games could be hard to find, but I recall at least two in the past year or so (one of them my own other than the joke game) So now I'd like to compare options, some of which are old and some my own ideas. They are ordered in what I believe is worst to best. I already have an opinion on which one is best, and I'm amazed it hasn't been suggested before, at least as far as I know. 1. The current scoring function Pro:
Con:
2. Use a material evaluator such as DAPE Pro:
Con:
3. The players each get to use whatever time they have remaining to make the rest of their moves Pro:
Con:
4. Accelerating time controls Pro:
Con:
And now for my (and in my opinion, the best) solution! Use a human adjudicator (or panel of adjudicators)! Pro:
Con:
Note that none of these really solves the problem of "drawn" positions. I would like to discuss that also, but that should probably be left to another thread, or at least until we talk about the main topic first. I see no reason right now not to use a human adjudicator. My "Con" is practically meaningless considering how massively superior this is to score. Discuss! |
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Title: Re: Replace the Scoring Function Post by Boo on Apr 19th, 2013, 6:17am Quote:
How would you adjudicate this game http://arimaa.com/arimaa/gameroom/comments.cgi?gid=201392 , if gold had been able to push rabbit into a4 on 19g and just shuffle the pieces in home teritory? Quote:
As it is equally hard for both players, I don't see what's the problem with that. Moving quickly requires some skill & training ;) |
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Title: Re: Replace the Scoring Function Post by Manuel on Apr 19th, 2013, 9:09am Some other cons of a human adjudicator: - availability of a human (assuming you are not only discussing event games!) - Also for an unbiased human it is not always easy to decide who is winning. I actually like the idea of switching to a sudden death time-control. |
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Title: Re: Replace the Scoring Function Post by Nombril on Apr 19th, 2013, 10:33am Thanks for putting these suggestions all in one place. Since you saved your best suggestion for last, I'll save my biggest critique for last ;) I do agree with much of what you have said, the following highlights my disagreements and additional comments. I'm curious which two games you thought would be close to requiring resolution on score. I think it would also help if we could describe what sort of game we expect to reach the time limit. Any proposed solution should be considered in light of each of them. In the interest of completeness, I have also seen suggestions for using the most advanced rabbits in place of the score function. Personally, I think this is a non-starter, since it is by definition gives preference to away players. An advanced rabbit can be liability or advantage depending on the position. on 04/19/13 at 03:13:09, browni3141 wrote:
Right, giving up your elephant in order to capture two rabbits could be a winning trade if evaluated by score. BUT if we were to check the material balance for all finished games, I suspect the player with more pieces has won a vast majority of the games. From this standpoint, if we don't have a good definition of why a game to be decided on score will be so different from the general population of games, this score function is very reasonable. (NOTE: I think a game decided on score would certainly look different from the general population of games...but I don't know how to define the difference yet.) on 04/19/13 at 03:13:09, browni3141 wrote:
I disagree with the pro of "end naturally". If a game turns towards blitz movements, games more often end by time out or blunder. Maybe my definition of a natural end is different? Con: This would reward a player that has banked a larger reserve, thus rewarding a time management preference rather than any playing ability. (Though I suspect any game reaching the point of needing a score resolution would see both players with max reserve remaining.) Con: If both players start the period with same reserve, the player with faster interface and/or faster internet connection will win. I definitely agree with your stated con. I can't see any time control related solutions being viable with current technology and online play. on 04/19/13 at 03:13:09, browni3141 wrote:
I think the idea of a "drawn" position might be more closely linked than you want to admit. Besides positions that are close to a draw, what else would take the entire time limit? If it is a closed position where rabbits/blockades/phalanxes/etc are preventing movement, I'm not sure I'd be comfortable with an expert evaluation of who is "winning". If it is players not trying to reach victory by goal/elimination/immobilization, then I'm not too concerned about how to evaluate who won the game. I'm also not sure that expert evaluation of board position is accurate. It is my opinion that hanzack was able to win so many games against other top players because he evaluated positional advantages differently. During many games, commentators and spectators thought hanzack's opponent had achieved a good position (frame, hostage, etc), only to later watch hanzack turn it into a devastating attack. And my final critique: But even if a human adjudicator can simply determine which side had a better position, then why didn't the player with the better position win the game? It actually seems ludicrous to me to award a win to a player that wasn't able to see how to use an advantage that could be seen by another player but not themselves. |
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Title: Re: Replace the Scoring Function Post by browni3141 on Apr 19th, 2013, 1:48pm on 04/19/13 at 09:09:41, Manuel wrote:
I do not see the availability of a human to be a problem. I have already volunteered to do it because I know I would only be called upon once every several thousand games :) I'm sure it would not be difficult to get other reasonably strong players to volunteer so that there is no problem of adjudicator availability. I pretty much agree with Nombril on sudden death time controls. They do not treat all players equally enough to be fair, they aren't compatible with time controls with a max reserve time, and they are just no fun when it takes most players around 5-6 seconds minimum to make a move. They work better for chess because you can move in under a second and pre-moves are possible. I still prefer it over the scoring function, though. Nombril wrote: Quote:
But isn't it still more accurate than any other evaluation method? Maybe it is not perfect, but I can not think of better in terms of adjudication. I think it would be most fair to allow the adjudicator to award a draw if the position is so close that it's very hard to tell who is winning. Quote:
We should not fault a player trying to win by score because they are taking advantage of the rules. However what should we do about players who have opportunities to try to progress but do not take them, knowing that the game would be adjudicated? I disagree that this is not an important question to answer. What if it is a tournament game? The result doesn't affect just those two players. Either a draw or a double loss seems appropriate. Quote:
The fact that he won doesn't mean his early play was sound. My opinion is that a lot of the time he did get himself into a bad position and turned it into a win with skill and some luck. Quote:
If allowed, I would award a draw. Isn't that is the most fair result? Unfortunately, some people here seem to have a hatred towards draws, even if they would almost never occur. If not allowed to award a draw, I guess I would give it to the player that was objectively better. Even if it's not fair it's better than rolling a die with a score function. Since I said that I thought bias could be mitigated, and somebody brought it up anyway, then I put forth the suggestion that the two players of a game must agree on an adjudicator, and if they can not agree then one will be selected for them. This won't eliminate the chance for bias, but it will attempt to make things as fair as possible. Another suggestion to try and minimize bias is that multiple adjudicators are used and they vote. These are the two games I was thinking of where score played a part. http://arimaa.com/arimaa/gameroom/comments.cgi?gid=231123 I had a way to make progress but could not see it. If this were to make it to score it would be most fair for it to be a draw I think. I didn't really deserve to win. Of course I might have eventually found the way to make progress and won naturally. http://arimaa.com/arimaa/gameroom/comments.cgi?gid=246143 Ocmiente's style seems to tend to make for very long games. The game may very well end on score and still be "alive." What about a panel of collaborating adjudicators who are allowed to award draws and take input from the players? Majority vote would win after deliberation. |
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 19th, 2013, 8:04pm Thanks for starting this browni! My two cents: 1. Some positions are just drawn. on 04/19/13 at 00:06:50, mattj256 wrote:
If the board is in that position the only fair outcome is a draw or double loss. 2. A player shouldn't be forced to sacrifice material to open up the position. on 04/19/13 at 19:48:32, mattj256 wrote:
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 19th, 2013, 9:03pm on 04/19/13 at 03:13:09, browni3141 wrote:
(1) IMO the worst-case scenario would be a bot winning the Arimaa Challenge because it won the last game on score. More generally, it would suck for any high-profile game to be decided by score. As I said in my last post, some positions are just drawn. So you're either going to have an arbitrary procedure to break ties which will sometimes be unfair, or you allow draws or double losses, or you change the rules to make it less likely that the scoring function will ever be used. (2) on 04/19/13 at 06:17:18, Boo wrote:
In the comments for the game above, Fritzlein said:
(3) I'll make my own counter-proposals.
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Title: Re: Replace the Scoring Function Post by Boo on Apr 20th, 2013, 3:31am Quote:
Those 2 don't look drawish. In the first one gold can play Ee1-->f3, next move Ef3-->f4 and capture some rabbits in the next 2 moves. In the second one gold can play Rg3-->e3+Cg1-->g3 and capture rg4 next. Quote:
If the players were to play such a game in a World Arimaa Championship in the hopes of avoiding a loss for both players, I think the outcome definetily should be the double-loss. But what if the case is not so straight-forward abuse? Where is the limit between adjudicating a draw or a double loss in an event game? Therefore I don't like the adjudication idea at all, I think scoring function is better than any adjudication, because it doesn't leave space for interpretation. Quote:
I think this holds true only if the game reaches time limit, because both players can't find a way to make progress. (turtling-up) What if the limit is reached with both players seeing the way to progress? I suspect both players to be low on reserve then. They would have to make a choice of making a fast 'any' move, or think extra 10 sec and try to find a better one. Thus playing ability is still a big factor. |
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Title: Re: Replace the Scoring Function Post by odin73 on Apr 20th, 2013, 2:33pm on 04/19/13 at 03:13:09, browni3141 wrote:
That´s surely a very intuitive and reasonable proposal concerning e.g. event games in a competition played in the gameroom. However, since Arimaa is a strategy game with perfect information such a rule will never be an option. I don´t know exactly what Omar´s thoughts forbidding any draw in this game, but probably a draw may serve best for the case of reaching the maximum game time. Hence, I guess that the current rule may be some trade-off to that. Beside this: The finding of a good and reasonable function for a position taking into account number of pieces and space advantage is a very interesting issue for now and for sure in future as well. :) |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 21st, 2013, 5:54pm Yes, there is a problem. I continue to maintain, however, that we can't know the best way to fix it until we know what the problem is. Maybe we want to allow draws, because Arimaa draws occur naturally, and imposing a win on a position that is naturally drawn is too arbitrary for us to stomach. But we can't know that until we see the games. Maybe we need sudden death. Maybe accelerating time controls are sufficient. But both of those are the wrong answer if neither player can make progress on the board, i.e. if it is a natural draw. Wouldn't it be silly for a drawn game to be determined by who could shuffle pieces faster after the position locked up? Bots would automatically get the win in any draw situation, due to faster-than-human reflexes. Maybe there is a decent scoring function that will pick who would have won eventually. But how can we know with no examples? Or rather with only two examples, neither of which was decided on score, but both of which would have been correctly decided by the current scoring function if it had come to that. Nothing has broken yet, unless you believe that someone who doesn't know how to win a won position should not be awarded a win on score, or by arbiter, or by any other means, because a draw on the board should be a draw in fact. To the last point, if we allow arbiters, we don't even know how to instruct them until we see the scoring function break. Do you think an arbiter who knows how to win a position the player didn't know how to win should give the clueless player the point? Is that fair, or could the other player say, hey, he couldn't beat me, so the arbiter's intervention is like giving advice? When, if ever, should an arbiter be allowed to assign a draw? When he thinks neither player would have been able to win, or only if it is drawn with perfect play? If the level of players enters into the decision, is that fair? Again, I am not saying there is no problem. I am saying that neither you nor anyone else knows in advance how to fix the problem. We already have a rule. Probably it is a stupid rule, but at least we won't ever be stuck not knowing who has won a game, so that catastrophe is not looming. If the rule we have sucks once every ten thousand games, then we have to let the rule break at least once, to see how it breaks, before we can know what fix is appropriate. Or we can be guided by a consistent pattern of cases in which the rule almost broke. But at the moment we are essentially flying blind in trying to find a solution. |
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 22nd, 2013, 12:03am By the way, not to change the subject, but can someone move this thread from "Site Discussion" to "General Discussion"? Site Discussion: "Problems, suggestions or questions relating to the web site, game client, bots, etc" General Discussion: "relating to Arimaa rules, strategy, questions, comments, announcements, etc" |
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Title: Re: Replace the Scoring Function Post by browni3141 on Apr 22nd, 2013, 1:09am on 04/22/13 at 00:03:00, mattj256 wrote:
By one viewpoint this discussion doesn't have to do with rules of Arimaa, but specifically how unfinished games are resolved on arimaa.com :) I'm not convinced it doesn't belong here. I think it could fit in either forum. |
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Title: Re: Replace the Scoring Function Post by Hippo on Apr 22nd, 2013, 6:02am on 04/19/13 at 20:04:12, mattj256 wrote:
The first one is clearly lost on repetition for the player making the last rabbit step. Opponent just alternates two positions till the player remains without moves :) |
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Title: Re: Replace the Scoring Function Post by Nombril on Apr 22nd, 2013, 10:05am on 04/19/13 at 13:48:53, browni3141 wrote:
But it isn't rolling a die. In the vast majority of games (I'm assuming here :) ) the player with the most pieces wins the game. Until we can define what/how the games leading to using the score function look different, I still maintain that the score function provides a simple, predictable way to evaluate the position, that is very likely to be correct. It is always possible to find isolated counter examples, but that doesn't prove something wrong. Oh, a potential concern for adjudication: In a bot vs human game, does this give an unfair advantage to the human player? How could a bot take into account for the evaluation function something that can't be hard defined ahead of time? And note that all three of mattj256's examples are not draws. As Hippo pointed out, the "typical" draw of rabbits in the middle was proven by Hippo to not actually be a draw, but there will be a winner based on the repetition rule leading to "immobilization". And for the other two examples, it is easy to open the position without sacrificing material. The player just needs to be willing to take steps with pieces other than rabbits ;) . It sounds like the games that could be the most concerning are tournament games that should be deemed either a draw or a double-loss. So maybe that discussion is more related than I originally thought. |
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Title: Re: Replace the Scoring Function Post by browni3141 on Apr 22nd, 2013, 2:13pm on 04/22/13 at 10:05:38, Nombril wrote:
Okay, okay, the die is loaded, but it's still a die. ;) The reason I like adjudication is that trying to "win by adjudication" ideally coincides with trying to win on the board. This is not the case with score. Score is not a part of Arimaa to me. It's just a hacked out safety net. Having the most pieces or the most advanced rabbit is not what Arimaa is about. It shouldn't be a factor in deciding games. The winner should be the player that actually won, or the player with better position if the game could not be completed. If we ever find a function to suit our needs here then Arimaa will be broken. Quote:
I don't understand what you mean. Both players are trying to win the game. Likely ALL of the bot's evaluation is intended to help it do this. The win conditions are hard defined ahead of time. Are you trying to say that a human might try to make his position look pretty before adjudication, which is something a bot can't do? There isn't really a way around this, except to trust that the adjudicator is trying to be as objective and critical as possible. Quote:
Well, technically the first is not a draw, but what does you think it should be? What does your intuition tell you? From my perspective that position "is" a draw, even if it isn't :) |
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Title: Re: Replace the Scoring Function Post by clyring on Apr 22nd, 2013, 3:55pm on 04/22/13 at 14:13:08, browni3141 wrote:
My intuition tells me that the player who made the move to create such a position in the first place (here, Silver) has a forced loss that is very easy. Gold can just shuffle his elephant one step north then one step south every move and win by immobilization because he will not repeat any position without Silver repeating a position at least as many times. (But my intuition only told me this because I took it on as a problem with you in the chatroom in the past. :)) (That said, I would have no problems as a player calling these positions drawn, either, but calling these positions drawn with the current repetition rule seems somewhat silly to me given that it naturally produces an easily predictable winner with no need to actually play out the ridiculous number of moves involved. That said, if Gold doesn't know the winning technique, I of course have no problem calling it drawn. :D) |
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 22nd, 2013, 10:58pm on 04/22/13 at 10:05:38, Nombril wrote:
I was wrong about the last two cases and I probably should have acknowledged that earlier. The first case, while theoretically a win for one player, would take a couple gazillion years to play under best play. on 04/22/13 at 10:05:38, Nombril wrote:
It seems to me that the only time the scoring function comes up in practice is when the human is much better than the bot and chooses to prolong the game rather than end it. Or when two humans are totally fooling around and neither has any intention of winning. I personally don't care if a regular (non-event) gameroom game is decided by score, even if that score leads to the "wrong" player winning. This is my attempt to eliminate the scoring function from event games. Proposed rules (1) If a tournament game lasts longer than X amount of time, the game is adjourned and recontinued at a later time as determined by the Tournament Director and both players. If a non-event game takes longer than X amount of time it is decided by a scoring function that might or might not be accurate. (2) If a player goes 50 consecutive turns without moving a rabbit forward, pushing or pulling an opponent's rabbit forward, capturing an opponent's piece or having his/her own piece captured, that player loses. Sacrificed pieces are treated exactly the same as any other capture. (3) If one player has all eight rabbits on the same rank, the other player may not end his/her turn with all eight rabbits on the rank immediately in front unless doing so leads to an immediate win by immobilization. |
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Title: Re: Replace the Scoring Function Post by Boo on Apr 23rd, 2013, 2:04am Quote:
I don't think so. Suppose the position is stalemated at the beginning. 1g Ra1 Rb1 Rc1 Cd1 Re1 Rf1 Rg1 Rh1 Ha2 Hb2 Cc2 Ed2 De2 Df2 Mg2 Rh2 1s ha7 mb7 cc7 cd7 ee7 hf7 dg7 dh7 ra8 rb8 rc8 rd8 re8 rf8 rg8 rh8 2g Ed2n 2s ee7s 3g Ed3s 3s ee6s 4g Ed2n 4s ee5n ee6n 5g Ed3s 5s ha7s 6g Ed2n 6s ha6n 7g - if gold moves Elephant back, this repeats the position, so gold has to play another move. |
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Title: Re: Replace the Scoring Function Post by clyring on Apr 23rd, 2013, 6:54am on 04/23/13 at 02:04:19, Boo wrote:
This produces the initial position with Silver to move only for the second time (Side to move is important in these repetition fights--That the position has appeared once with Gold to move does not limit Gold and can only hinder Silver.), and to put Gold in this situation he has needed to create the same position after 4s and 6s. |
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Title: Re: Replace the Scoring Function Post by omar on Apr 23rd, 2013, 8:55am >Use a human adjudicator (or panel of adjudicators)! Thanks for the suggestion Mathew. Please consider these points and see if it might change your mind. 1. It adds a burden of having to pick human adjudicators for every important game just in case the game ends on time. Most of the time it won't be needed; so we will get lazy and not always do it and get away with it. Except one day when we are least expecting it a game will end on time and we will have forgotten to pick the human adjudicators before hand and find ourselves in a mess. The reason I got rid of draws (even though they were so rare) was because it adds a burden to planning a tournament. In case a draw happens you have to have all the rules in place to deal with it. The tournament coordinators and players have to be ready to deal with it. As a tournament coordinator you find yourself hoping that a draw does not happen. "However, in practice I was finding that for elimination type tournaments (like the finals of our world championship tournament) I did not want there to be any possibility of draws, because another game has to be played to break the draw and that makes the tournament schedule less predictable." Getting rid of things that add a burden to running a tournament can only be appreciated after you've run some tournaments :-) Also this proposal breaks a couple of fundamental truths you expect from perfect information games: 2. The result of the game must be consistently reproducible. 3. The result of the game must be completely in control of the players. If a different set of human adjudicators were selected the result of the game could turn out different; violating #2. Now we could have the rules specify that particular bots running in a controlled environment would make the decision so that it is always consistent (also this would eliminate the burden of having to pick adjudicators), but it would still violate #3. One could argue that if the evaluation function was deterministic and made public it does not violate #3 because that's also what a simple scoring function is. That's theoretically true, but practically if as a dumb human I can't figure out in real time during the game how it would be evaluated then I am lacking the information I need to make the move decisions during the game. So the game essentially feels like it's not in my control. This is why the current scoring function is dead simple and doesn't even use any formulas. I hope my explanation will convince you. I appreciate you bringing this up though. It's always good to question why things are the way they are. |
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Title: Re: Replace the Scoring Function Post by Boo on Apr 23rd, 2013, 11:00am Quote:
I meant that if it can be produced for the second time, it can also be produced for the 3rd time. You need to repeat the same sequence 5g-6s once more: 5g Ed3s 5s ha7s 6g Ed2n 6s ha6n 7g Ed3s 7s ha7s 8g Ed2n 8s ha6n 9g - gold cant move Ed3s. |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 23rd, 2013, 3:30pm on 04/23/13 at 11:00:09, Boo wrote:
1g Ra1 Rb1 Rc1 Cd1 Re1 Rf1 Rg1 Rh1 Ha2 Hb2 Cc2 Ed2 De2 Df2 Mg2 Rh2 1s ha7 mb7 cc7 cd7 ee7 hf7 dg7 dh7 ra8 rb8 rc8 rd8 re8 rf8 rg8 rh8 2g Ed2n 2s ee7s 3g Ed3s 3s ee6s 4g Ed2n 4s ee5n ee6n 5g Ed3s 5s ha7s 6g Ed2n 6s ha6n 7g Ed3s 7s ha7s 8g Ed2n 8s ha6n Quote:
Isn't move 8s illegal, creating the same position that move 4s and move 6s also created? |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 23rd, 2013, 3:33pm on 04/22/13 at 22:58:02, mattj256 wrote:
This could delay an elimination tournament an entire week if the players live in different time zones and have incompatible schedules. |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 23rd, 2013, 3:56pm on 04/22/13 at 14:13:08, browni3141 wrote:
So if you were the human adjudicator, you would rule this position a draw? What if it were an elimination tournament in which a draw would mean all other players have to wait a week for the drawn game to be replayed? There is a tremendous convenience to having no draws; if you want to allow draws you have to make a pretty strong case for it, in addition to your case for using a human adjudicator rather than using a scoring function. In my opinion, Arimaa should not allow for draws until we exhaust all reasonable options for determining a winner by other means. In Chinese chess (xiangqi) they use a human arbiter to prevent draws that would otherwise occur over the board. That is to say, if the two players are just shuffling pieces, an arbiter is permitted to tell one of the players that it is his fault the game is not making progress. The player deemed at fault has to make a different move or lose. In a sense, the current repetition rule is like that. If one player locks up a position, the other player can do the "Hippo shuffle" until the first player is forced to repeat. Thus whoever puts the last brick in the wall loses. Translation: You lose because it is your fault the game stalemated. You had no plan to make progress. You decided to merely block the other guy's progress instead of trying to make headway yourself. Exactly as you aren't allowed to create an infinite loop by undoing the other guy's move, you aren't allowed to perfect a stalemate position. But this might not seem like an intuitive rule once we see how draws actually emerge in practice. Maybe the way drawn positions emerge would make the current rule reward turtling rather than punishing it. |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 23rd, 2013, 4:00pm on 04/19/13 at 13:48:53, browni3141 wrote:
By the way, this game has a simple fix other than changing the scoring function: change the time control from 1d/60d/100/0/300d/21d to 1d/60d/100/0/360d/21d. I would rather have Postal Mixer games spilling over into the next calendar year than have them cut off prematurely. Why not allow a full year? They will still be over before the next Postal Mixer starts. The game in question would have ended naturally by move 120. |
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 24th, 2013, 1:23am on 04/23/13 at 08:55:58, omar wrote:
Thanks for indulging me Omar and Fritzlein. I think I'm finally convinced to abandon the proposal to change the scoring function: 1. Running a tournament is already a lot of work, and if I'm going to push for a procedure that will make more work for the tournament director there has to be a stronger rationale than that it MIGHT be useful. 2. Arimaa is currently a perfect information game and it should stay that way. 3. The people that are actually running the tournaments don't want to allow draws, or allow long tournament games to be postponed, or move to "sudden death" time controls, and none of those are things I feel strongly about. If I were dead-set on removing the scoring function I would be pushing for one of those three. Which I'm not. on 04/22/13 at 22:58:02, mattj256 wrote:
I'm abandoning #1. Proposed rule #2 is the "you lose if you don't make progress in 50 moves" rule. And proposed rule #3 prevents the pathological setup which I still dislike. If you ignore #3 and produce that setup, then rule #2 says that the FIRST player to make the row of eight has to sacrifice his pieces one by one and then lose by immobilization. Maybe #2 should be tweaked, or maybe that's an acceptable outcome? Sorry if I'm being pedantic but I really don't like the way the rules handle that particular board setup. |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 24th, 2013, 1:36pm Your rule #2 doesn't obviate the need for a repetition rule. Imagine a stalemate position in which each side has a hostaged rabbit behind enemy lines. Every 48 moves or so each player could dislodge the enemy rabbit forward to reset the clock, then dislodge it back the next move. Thus you haven't found a way to determine a winner, in a guaranteed reasonable number of moves, for all positions in which neither player is making progress. |
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Title: Re: Replace the Scoring Function Post by clyring on Apr 24th, 2013, 3:33pm on 04/23/13 at 08:55:58, omar wrote:
on 04/24/13 at 01:23:06, mattj256 wrote:
Yes, but browni3141 is Mathew. You are but one of three members named Mat(t)hew who have participated in this thread. I thought your name was spelled more like mine with two T's, anyway! :P |
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 24th, 2013, 9:14pm on 04/24/13 at 15:33:06, clyring wrote:
on 04/24/13 at 13:36:22, Fritzlein wrote:
You're right that my rule #2 as written doesn't address the case where both players do the hokey-pokey with an enemy rabbit. Do you agree with the sentiment behind rule #2? These billion-move situations are maybe not relevant for tournament play but they still bother me... |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 25th, 2013, 8:26am on 04/24/13 at 21:14:41, mattj256 wrote:
If it turns out there are positions where both players are unable (or unwilling) to force goal, and the repetition rule takes an unreasonably long time to determine a winner, and there is a simple rule that determines a winner in a reasonable amount of time, but that simple rule doesn't accidentally change the result of games that were working their way toward a natural conclusion, then yes, I'm all for it. I'm afraid, however, that if you construct a rule to address a specific position that will never, ever happen (sixteen rabbits deadlocked on ranks four and five), then there is a low probability that it will help in situations that actually arise. Most likely a fifty-move rule in Arimaa would never be invoked, so it would be extra complexity for no gain. If it were ever invoked, there's a fair chance it would be in a situation unlike the ones we have anticipated so far, and we would realize then it isn't the best fix for the problem at hand. In a nutshell, those are my two reasons for not solving the problem now. 1) Extra complexity is an immediate, tangible evil; the good we are trying to attain is distant and uncertain. 2) We can have no confidence we are addressing the problem correctly when we have almost no data as to what the problem is. I applied the same logic to persuade Omar not to change the setup rules. He wanted to put to rest any possible speculation that Gold has an advantage over Silver or vice versa. His proposal for setup was i) Gold places one piece and one rabbit ii) Silver places two pieces and two rabbits iii) Gold places two pieces and two rabbits iv) Silver places two pieces and two rabbits ... ix) Gold places his final piece and final rabbit and takes two steps. x) Silver takes four steps, and the game proceeds normally from there. My argument was that, admittedly, the current rules might favor Gold or might favor Silver. But imbalance hasn't been a problem yet. If one side has the advantage, we can't tell which it is. So (1) don't add the immediate evil of four extra turns for each player at the beginning of every game, complexity which hassles us immediately in exchange for an uncertain future benefit. And (2) we aren't even sure why the setup phase leads to unbalance, supposing it does, so even though the proposed procedure is completely logical, we can't sure it would fix the unbalance if it ever emerged. I'm glad that Omar left the setup phase in it's current simple, pure form. Are you glad too? |
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 26th, 2013, 12:47am on 04/25/13 at 08:26:03, Fritzlein wrote:
Yes I am glad about that. There is a fascinating thread somewhere else trying to figure out what, if any, is Gold's advantage in rating points from moving first. Through your willingness to waste YOUR time on this, I'm realizing that I'm wasting MY time on it, too. I can see the only way I'm going to make progress here is if I write a bot that turtles up and doesn't attempt to make progress, but I don't have the time or inclination to work on that now. There are so many more productive things I could be doing, and instead I'm scattering my energies... |
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Title: Re: Replace the Scoring Function Post by chessandgo on Apr 26th, 2013, 2:48am on 04/23/13 at 15:30:06, Fritzlein wrote:
It seems so, however silver playing 6s ha6e instead of north (and obviously 7s hb6w instead of 7s ha7s) works for silver? Intuitively, clyring's parity idea should fail to some kind of triangle idea to reverse parity. I agree Gold should be winning though, you need to find a clever map between the possible silver moves and Gold's I guess. If the rabbits blockade was shifted of one line, say all silver rabbits on the 4th row and all gold Rabbits on the 3rd row, then silver should win regardless of who starts playing? It feels logical but I can't convince myself 100%. Simple proof anyone? |
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Title: Re: Replace the Scoring Function Post by chessandgo on Apr 26th, 2013, 2:58am Oh, btw, I seem to remember that in case of a tie in the current score, the player who had the higher score before the tie occured wins? If that's correct, then position 1 is actually awarded on score to the player who actualy has the forced win. Position 1' being the same position with all rabbits shifted one line shouth, favours silver on score. If silver does indeed win, then again the score function indicates the actual theoretical winner. Position 1'' (that's a double prime) being the same as position 1 with Gold missing a Cat. Is silver winning? If that's so, then again the scoring function is correct. If all the above is true, then you at least have to a find one blockaded position where the scoring function fails to pick the theoretical winner if you really want it changed :) |
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Title: Re: Replace the Scoring Function Post by harvestsnow on Apr 26th, 2013, 5:00am Quote:
I think Suppose that Silver creates a stalemate position on move (m)s, and Gold's strategy loses the shuffling game. Then, there is a move where Gold will repeat a position for the third time. Let (x)g, (y)g and (z)g be the three moves in question. But Gold always makes the same move; that means the positions after moves (x-1)s, (y-1)s and (z-1)s were also identical. In other words, Silver can only make Gold repeat a position by repeating one as many times before him. Therefore the hypothesis is wrong and Gold's strategy wins. The only way Silver could break this pattern is if he could prevent Gold from looping like he does, but then the position wouldn't be a stalemate. Also, Silver can't use the same strategy, because he would have to cancel the move (m)s somehow. If he can do that without letting Gold make any progress, then Gold's position was already blocked after (m)g. Reverse the argument and Silver wins. It's counter-intuitive, because you'd think the number of possible moves each player has would matter. Quote:
The current score rule (http://arimaa.com/arimaa/learn/matchRules.html) only takes into account the number of pieces left, not rabbit advancement. Quote:
Of course, I checked it (http://i.imgur.com/tCPFjqf.png)... |
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Title: Re: Replace the Scoring Function Post by Hippo on Apr 26th, 2013, 12:58pm on 04/26/13 at 05:00:47, harvestsnow wrote:
Actually this was my argument :) ... yes even with silver 8 rabbits on row 3 with 8 gold rabbits on rank 2, one piece captured and remaining pieces on row 1 the player finishing the blockade loses. More interesting position would be with 2 pieces sacrified, but with silver elephant on rank 1 ... http://arimaa.com/arimaa/notconv/old/boardimg.php?orient=n&size=150&imgtype=jpg&ranks=mhhddcc/////rrrrrrrr/RRRRRRRR/1CCeDDHH http://arimaa.com/arimaa/notconv/old/boardimg.php?orient=n&size=150&imgtype=jpg&ranks=mhhddcc/////rrrrrrrr/RRRRRRRR/1CCDeDHH it seems silver is winning in first one but losing in second ... when the last step was silver rabbit to a3 in both cases. |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 26th, 2013, 10:10pm on 04/26/13 at 12:58:46, Hippo wrote:
Indeed, which is why I call the winning technique the "Hippo Shuffle". Also I think of this song in my head: http://www.youtube.com/watch?v=FKAfXdb5LsA |
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Title: Re: Replace the Scoring Function Post by harvestsnow on Apr 27th, 2013, 1:53am on 04/26/13 at 12:58:46, Hippo wrote:
Sorry for that! Fixed. |
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Title: Re: Replace the Scoring Function Post by chessandgo on Apr 27th, 2013, 4:24am Oh, sounds good. I guess I got confused with the fact that the same (piece) position with a different player to play is not the same position. |
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Title: Re: Replace the Scoring Function Post by chessandgo on Apr 27th, 2013, 4:28am Hmmm there used to be somehting like a "sum of cubes of rabbits advancement" in the scoring formula. When did that disappear? |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 27th, 2013, 12:34pm on 04/27/13 at 04:28:33, chessandgo wrote:
Jean, the rule was changed almost five years ago: http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;num=1213818953;start=0 It says something about the importance of a rule when someone can win three consecutive World Championships without knowing what the rule is! :D on 04/26/13 at 00:47:32, mattj256 wrote:
Discussing with someone who is trying to learn and understand rather than trying to win an argument is seldom a waste of time. |
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Title: Re: Replace the Scoring Function Post by Janzert on Apr 27th, 2013, 6:20pm on 04/26/13 at 00:47:32, mattj256 wrote:
No need to write a bot, if you can just do this consistently yourself against top players it would be... well maybe not an advance but certainly a bit of a breakthrough in Arimaa strategy. If you look back at the early Arimaa play (what I'll call the lone Elephant era) this was basically the strategy for a while. Turtle up as best you could while looking for your opponent to leave an opening. Fritzlein said: Quote:
Oh man how have I not seen that till now. Janzert |
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Title: Re: Replace the Scoring Function Post by Hippo on Apr 28th, 2013, 3:16am http://arimaa.com/arimaa/notconv/old/boardimg.php?orient=n&size=150&imgtype=jpg&ranks=////dhCccChd/rrrrrrrr/RR1RRRRR/HHRmMEDD seems to be won for silver ... with the last move H<m<>Rv. Silver stays still in the rest of the game (rotating west hd each turn) while gold shuffles out of the possible positions ... except gold allows traditional immobilisation. |
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Title: Re: Replace the Scoring Function Post by hyperpape on Apr 29th, 2013, 11:42am My thought processes: Me: "Oh, I'm totally going to write something saying that a draw is the obvious best solution." Me: "Wait. I haven't played a game in six months, it's pretty silly for me to participate in this discussion." Me: "I guess I'll go play a game." ...so this discussion has been fruitful for me. :) |
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Title: Re: Replace the Scoring Function Post by mattj256 on Apr 29th, 2013, 10:44pm on 04/27/13 at 12:34:03, Fritzlein wrote:
on 04/27/13 at 18:20:31, Janzert wrote:
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Title: Re: Replace the Scoring Function Post by chessandgo on Apr 30th, 2013, 2:32am No, it wouldn't be rude to the least extent to bunker down ... just bad strategy ;) |
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Title: Re: Replace the Scoring Function Post by browni3141 on Apr 30th, 2013, 2:40am on 04/29/13 at 22:44:02, mattj256 wrote:
A bot might be able to pull that off against other bots and maybe weaker humans, but against any decent human it should flop. I'm assuming the bot is allowed to move past the fourth rank when it needs to to avoid losing material. Being purely defensive is a really poor strategy because you are ignoring many good options while the opponent's options aren't limited. It only takes a few inaccurate moves before you're at a tangible disadvantage, and pure passivity is probably not even close to optimal. If any of the top bots implemented a strategy of pure passivity then they would probably be several hundred points weaker. Bots are probably only slightly better than top humans on average when it comes to tactics anyway. Regarding the stamina issue, 30-60 minutes of playing shouldn't wear out the average person. The average player probably wouldn't start to notice much fatigue for at least 4-5 hours. Personally I think that I could last many, many hours and maintain a strong level of play, because I can play well with little mental effort and I can play well when fatigued. If anybody wants to provide an incentive I will gladly prove it :) A 24+ hour marathon might be fun, but it would be hard to schedule it ;) |
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Title: Re: Replace the Scoring Function Post by browni3141 on Apr 30th, 2013, 3:49am on 04/26/13 at 12:58:46, Hippo wrote:
The first silver wins regardless of who is to move. Silver to move: 1s ma8s 2g Cb1w 2s ma7n 3g Ca1e 3s ma8s 4g Cb1w 4s ma7n 5g Cc1w 5s ed1w Rd2s rd3s Gold to move: 1g Cb1w 1s Cc1w ed1w ec1e 2g Cb1e 2s Cc1w ed1w ec1e 3g Cb1e Ca1e (now it is the original position with silver to move) 3s ma8s 4g Cb1w 4s ma7n 5g Ca1e 5s ma8s 6g Cb1w 6s ma7n 7g Cc1w 7s ed1w Rd2s rd3s The second position gold to move wins by shuffling b1-a1-b1 until silver runs out of moves. Silver to move also wins the second position, using the same method as in position 1 with gold to move. I'll post my thoughts on what's been said about the scoring function later. I have not given up, I've just been busy with coursework :) @odin: I find your argument a little unsporting, you act as if you've dealt a death blow :P I will post my reasoning later as to why I don't think the point regarding Arimaa being a perfect information game carries much weight. |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 30th, 2013, 9:07am on 04/29/13 at 22:44:02, mattj256 wrote:
Back in 2004, when we all attacked with only the elephant, there was a sneaking suspicion among top players that a purely defensive strategy might be possible. The tacit assumption was that if the opponent advanced anything other than his elephant, it would be to his disadvantage. You would switch gears, take his second advanced piece hostage, and have an advantage yourself. Of course pure defense involves keeping all rabbits back, because rabbit pulls can't be reversed. It requires keeping a solid second layer of pieces in front of the rabbits so they are not exposed. It involves keeping your own elephant on the fourth rank to unfreeze and retreat any non-rabbit pieces the opposing elephant pulls out to the third rank. However, with all that said, it apparently doesn't quite work to prevent all hostages even if the opponent isn't allowed to advance anything except his elephant. The community was sporadically exploring the finer points of this debate when elephant-horse attacks started popping up on the wing away from the defensive camel, which made the conversation moot. If your strategy must insure (A) the opposing lone elephant can't ever pull a hostage back to his side and (B) the opposing horses must be kept out of both the b3 and g3 squares and (C) an opposing horse can't ever pull a hostage back to his side, then far from being a "really robust" strategy, pure defense is downright impossible. And from there it got worse for defense-only strategy. We now know that there are some situations in which even camel advances can't be punished by taking the camel hostage. If your opponent is allowed to advance elephant, horses, and camel, it is completely hopeless to think "no piece of mine goes past the fourth rank". There are too many ways for your pieces to get pulled out, too many holes to plug. If you don't generate some threats of your own, you are dead duck. Unlike in 2004, there is no longer sneaking suspicion among top players. The debate is completely over. Like browni says, your opponent has too many ways to hurt you for pure defense to be viable in Arimaa. |
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Title: Re: Replace the Scoring Function Post by Hippo on Apr 30th, 2013, 12:14pm on 04/30/13 at 03:49:53, browni3141 wrote:
Oh interesting ... silver passed moving his pieces moving just gold to make his move legal. |
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Title: Re: Replace the Scoring Function Post by Brendan_M on Apr 30th, 2013, 5:09pm There is another option - the result of a game that ends on time is a loss for both players This satisfies the following criteria:
I also think it is aesthetically pleasing for the game of arimaa. Here is a simple definition of arimaa which is very similar to the first line on the arimaa homepage: 'Arimaa is a race against your opponent to force a rabbit to the other side' Why not change this to: 'Arimaa is a race against your opponent and the clock to force a rabbit to the other side' I think it nicely solves several of the example problems in this thread too. Why should a game where both players have placed all their rabbits on the 4th row be a victory for one of them? Neither of them deserve to win. You only deserve to win if you actually win within the allotted time |
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Title: Re: Replace the Scoring Function Post by Hippo on Apr 30th, 2013, 6:34pm on 04/30/13 at 17:09:59, Brendan_M wrote:
Yes, I like this idea. Except in that case rating systems could be confused. Is this problem of rating systems? The sum of ratings should be maintained. |
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Title: Re: Replace the Scoring Function Post by Fritzlein on Apr 30th, 2013, 8:05pm on 04/30/13 at 17:09:59, Brendan_M wrote:
This would unfortunately give an incentive for stalling, on the theory "I'm not going to win, but I'm at least going to take the other guy down with me." Players might choose to pass up a desperate counter-attack, might give up hopes of a swindle, in exchange for the most tortuous defense that is certain not to win. Zero-sum games have different incentives than games which are not zero-sum. In the former, by definition the only way you can hurt the other player is to help yourself. In the latter you can choose to hurt the other player even if doing so hurts you too. |
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