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Topic: Replace the Scoring Function (Read 8128 times) |
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mattj256
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Re: Replace the Scoring Function
« Reply #30 on: Apr 26th, 2013, 12:47am » |
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on Apr 25th, 2013, 8:26am, Fritzlein wrote:| I'm glad that Omar left the setup phase in it's current simple, pure form. Are you glad too? |
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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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chessandgo
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Re: Replace the Scoring Function
« Reply #31 on: Apr 26th, 2013, 2:48am » |
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on Apr 23rd, 2013, 3:30pm, Fritzlein 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
Isn't move 8s illegal, creating the same position that move 4s and move 6s also created? |
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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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chessandgo
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Re: Replace the Scoring Function
« Reply #32 on: Apr 26th, 2013, 2:58am » |
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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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harvestsnow
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Re: Replace the Scoring Function
« Reply #33 on: Apr 26th, 2013, 5:00am » |
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Quote:| clyring's parity idea should fail to some kind of triangle idea to reverse parity |
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I think clyring'sHippo's argument is correct.
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:| 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. |
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The current score rule only takes into account the number of pieces left, not rabbit advancement.
Quote:| If a game is stopped due to reaching the time control limit then the winner is determined by scoring the game as follows: the player who currently has or most recently had more pieces left after the completion of a turn wins. Otherwise the player to move second (silver) wins. |
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Of course, I checked it...
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| « Last Edit: Apr 27th, 2013, 1:53am by harvestsnow » |
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Hippo
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Re: Replace the Scoring Function
« Reply #34 on: Apr 26th, 2013, 12:58pm » |
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on Apr 26th, 2013, 5:00am, harvestsnow wrote:
I think clyring's argument is correct.
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.
The current score rule only takes into account the number of pieces left, not rabbit advancement.
Of course, I checked it... |
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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 ...
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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| « Last Edit: Apr 26th, 2013, 1:12pm by Hippo » |
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Fritzlein
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Re: Replace the Scoring Function
« Reply #35 on: Apr 26th, 2013, 10:10pm » |
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on Apr 26th, 2013, 12:58pm, Hippo wrote:| Actually this was my argument |
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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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harvestsnow
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Re: Replace the Scoring Function
« Reply #36 on: Apr 27th, 2013, 1:53am » |
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on Apr 26th, 2013, 12:58pm, Hippo wrote:
Actually this was my argument ... |
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Sorry for that! Fixed.
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chessandgo
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Re: Replace the Scoring Function
« Reply #37 on: Apr 27th, 2013, 4:24am » |
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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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chessandgo
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Re: Replace the Scoring Function
« Reply #38 on: Apr 27th, 2013, 4:28am » |
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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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Fritzlein
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Re: Replace the Scoring Function
« Reply #39 on: Apr 27th, 2013, 12:34pm » |
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on Apr 27th, 2013, 4:28am, chessandgo wrote:| 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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Jean, the rule was changed almost five years ago: http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=talk;action=display;nu m=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! 
on Apr 26th, 2013, 12:47am, mattj256 wrote:| Through your willingness to waste YOUR time on this, I'm realizing that I'm wasting MY time on it, too. |
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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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Janzert
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Re: Replace the Scoring Function
« Reply #40 on: Apr 27th, 2013, 6:20pm » |
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on Apr 26th, 2013, 12:47am, mattj256 wrote:| 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. |
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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:
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Oh man how have I not seen that till now.
Janzert
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Hippo
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Re: Replace the Scoring Function
« Reply #41 on: Apr 28th, 2013, 3:16am » |
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 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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hyperpape
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Re: Replace the Scoring Function
« Reply #42 on: Apr 29th, 2013, 11:42am » |
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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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mattj256
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Re: Replace the Scoring Function
« Reply #43 on: Apr 29th, 2013, 10:44pm » |
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on Apr 27th, 2013, 12:34pm, Fritzlein 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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Thanks for understanding. You're a good teacher.
on Apr 27th, 2013, 6:20pm, Janzert wrote:| No need to write a bot, if you can just [turtle up] consistently yourself against top players it would be... well maybe not an advance but certainly a bit of a breakthrough in Arimaa strategy. |
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I'm really not rude enough or patient enough to try this tactic in a live game against a human. But it would be fun (if I ever had time) to write a really passive-aggressive bot. Given that bots are so good at tactics, I wonder what would happen if you intentionally program the bot to keep all the pieces safe at home? I don't mean an elephant-only attack but a really robust strategy of "nothing goes past the fourth rank." If nothing else, a bot that was able to stall for 30-60 minutes might gain an advantage over a human because the person would get mentally tired but the bot wouldn't be affected.
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chessandgo
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Re: Replace the Scoring Function
« Reply #44 on: Apr 30th, 2013, 2:32am » |
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No, it wouldn't be rude to the least extent to bunker down ... just bad strategy 
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