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Topic: Reverse puzzles and impossible positions (Read 4018 times) |
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Fritzlein
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Re: Reverse puzzles and impossible positions
« Reply #30 on: May 27th, 2010, 4:32pm » |
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Hippo, I am not sure I understand your puzzle. You might mean to say this:
"From the given position and the information that it is Gold's move, you can deduce that Gold is winning. Explain this deduction."
But that conclusion doesn't follow, does it? So instead I am guessing that you mean to say this:
"From the given position and the information that it is Gold's move and the information that Gold is winning, you can deduce exactly why Gold is winning."
In this case, the only reason that Gold could be winning is that the repetition rule will force Silver to sacrifice a rabbit or move away the cat from blocking goal. Is there something more specific that we should be able to deduce in addition? It seems that, depending on prior moves, Gold might have more than one "winning strategy". For example, it might be that the move Ra6e forces Silver to immediately sacrifice a rabbit because other moves all result in 3-fold repetition or immediate goal. Or it might be that this move loses while Ra6e Rb6e wins.
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| « Last Edit: May 27th, 2010, 4:52pm by Fritzlein » |
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Hippo
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Re: Reverse puzzles and impossible positions
« Reply #31 on: May 27th, 2010, 10:48pm » |
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on May 27th, 2010, 4:32pm, Fritzlein wrote:Hippo, I am not sure I understand your puzzle. You might mean to say this:
"From the given position and the information that it is Gold's move, you can deduce that Gold is winning. Explain this deduction."
But that conclusion doesn't follow, does it? So instead I am guessing that you mean to say this:
"From the given position and the information that it is Gold's move and the information that Gold is winning, you can deduce exactly why Gold is winning."
In this case, the only reason that Gold could be winning is that the repetition rule will force Silver to sacrifice a rabbit or move away the cat from blocking goal. Is there something more specific that we should be able to deduce in addition? It seems that, depending on prior moves, Gold might have more than one "winning strategy". For example, it might be that the move Ra6e forces Silver to immediately sacrifice a rabbit because other moves all result in 3-fold repetition or immediate goal. Or it might be that this move loses while Ra6e Rb6e wins. |
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This is among retrograde analysis. Yes, it has a lot of solutions so it is not correct retrograde puzzle. Yes you must know the game history to decide who wins, who's turn it is is not important.
722cassis statement ... last turn move describtion ends with x ... the player to move wins. Is the shortest describtion of sufficient history information.
So the current version of puzzle says:
If the last move ended with x. Show the strategy of player to move leading to victory. (Try to find as easy describtion as possible).
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Oops I was trying to make some other puzzle and it is not correct (neither version) ... how could I delete it from the collection? I have not linked them yet to any page.
But following one is OK:
http://arimaa.com/arimaa/puzzles/show.cgi?p=p55.
I have forgot how to link it to the puzzle page. ... (goal in more than 15 ... exact value is ..).
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| « Last Edit: May 28th, 2010, 2:23am by Hippo » |
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jdb
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Re: Reverse puzzles and impossible positions
« Reply #32 on: May 28th, 2010, 6:10am » |
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Nice puzzles Hippo.
Silver can suicide a rabbit and still maintain the blockade. I think this means silver wins with either side to move.
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Manuel
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Re: Reverse puzzles and impossible positions
« Reply #33 on: May 28th, 2010, 7:23am » |
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on May 28th, 2010, 6:10am, jdb wrote:Nice puzzles Hippo.
Silver can suicide a rabbit and still maintain the blockade. I think this means silver wins with either side to move. |
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I don't think silver can suicide a rabbit and keep maintaining the blockade, is it? Silver has to do some move in every next turn...
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Fritzlein
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Re: Reverse puzzles and impossible positions
« Reply #34 on: May 28th, 2010, 7:50am » |
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on May 28th, 2010, 6:10am, jdb wrote:| Silver can suicide a rabbit and still maintain the blockade. I think this means silver wins with either side to move. |
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Yes, it looked like that to me too at first, but after suiciding a rabbit Silver no longer has an extra piece to shuffle, and thus gets hit by the no-pass rule.
on May 27th, 2010, 10:48pm, Hippo wrote:So the current version of puzzle says:
If the last move ended with x. Show the strategy of player to move leading to victory. (Try to find as easy describtion as possible). |
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So we are allowed to give only the last move that occurred before the position, and that addition by itself must be sufficient to prove that the current player on move is winning? I see how to do this for Silver to move, but not for Gold to move in the same position.
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| « Last Edit: May 28th, 2010, 7:51am by Fritzlein » |
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Hippo
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Re: Reverse puzzles and impossible positions
« Reply #35 on: May 28th, 2010, 9:06am » |
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 I have trained a bit to win on 3 repetitions . The strategy for Gold is the same as for Silver . Seems study of this is not well known so far.
P.S.: The only important thing is gold and silver plays on independent playgrounds. Sacrifying any number of pieces would not change the result.
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| « Last Edit: May 28th, 2010, 9:12am by Hippo » |
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Fritzlein
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Re: Reverse puzzles and impossible positions
« Reply #36 on: May 28th, 2010, 10:27am » |
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on May 28th, 2010, 9:06am, Hippo wrote:| I have trained a bit to win on 3 repetitions . The strategy for Gold is the same as for Silver . |
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I believe you that you understand this type of position better than any of us. Good job! Thanks for the puzzle! But would you be so kind as to clarify exactly what the puzzle is asking? I don't want to think I have solved it (or busted it) and then have you tell me you meant something else. Are you now saying the second puzzle consists of explaining how Gold can win given that Silver moved last and that move was a capture?
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| « Last Edit: May 28th, 2010, 10:48am by Fritzlein » |
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jdb
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Re: Reverse puzzles and impossible positions
« Reply #37 on: May 28th, 2010, 10:51am » |
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on May 28th, 2010, 7:50am, Fritzlein wrote:
Yes, it looked like that to me too at first, but after suiciding a rabbit Silver no longer has an extra piece to shuffle, and thus gets hit by the no-pass rule.
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The shuffle is still possible, it just has to involve at least two pieces.
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Fritzlein
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Re: Reverse puzzles and impossible positions
« Reply #38 on: May 28th, 2010, 11:24am » |
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on May 28th, 2010, 10:51am, jdb wrote:| The shuffle is still possible, it just has to involve at least two pieces. |
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No, because if e7 or d7 is left unoccupied by Silver, then Gold can occupy it, curtailing Silver's shuffle strategy. Only c7 and f7 can be left unoccupied, but Silver would need six steps to swap between those two.
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Hippo
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Re: Reverse puzzles and impossible positions
« Reply #39 on: May 28th, 2010, 12:02pm » |
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on May 28th, 2010, 10:27am, Fritzlein wrote:
I believe you that you understand this type of position better than any of us. Good job! Thanks for the puzzle! But would you be so kind as to clarify exactly what the puzzle is asking? I don't want to think I have solved it (or busted it) and then have you tell me you meant something else. Are you now saying the second puzzle consists of explaining how Gold can win given that Silver moved last and that move was a capture? |
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OK, I was asking how to apply the advantage caused by your opponent moving to the position when players play on separate playgrounds.
I surely enjoy to explain some thing about arimaa to you ... but may be it's rather some abstract graph theory game?
Let denote such positions by two letters ... lower case for our position and upper case for opponent's one.
We start at position a* and move to position b*. We move only between a* and b*. Why we cannot lose on 3 times repetition in position xY? Because opponent plays to zY third time turn before us. ({x,z}={a,b}).
Induction ... we play to xX k-th time move after opponent payed to zX k-th time...
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| « Last Edit: May 28th, 2010, 1:53pm by Hippo » |
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Fritzlein
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Re: Reverse puzzles and impossible positions
« Reply #40 on: May 28th, 2010, 12:29pm » |
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Er, I was still trying to clarify the question, but thanks anyway for giving me the answer, which indirectly tells me that my last guess at the question was in fact correct. I had a strong intuition that the player with more squares to shuffle between would always win, but I had just seen that was not the case for two versus three, so I was just starting to understand that as long as I have two squares to shuffle between, it doesn't matter how many squares my opponent has, or in general how many positions my opponent can reach. I might have gotten all the way to the correct answer in a few more iterations.
Potentially you have just provided us with a way to resolve some practical draws, i.e. games in which both players can't or won't do anything but shuffle pieces. For example, in the position below, assuming Silver just completed the rabbit wall, we could allow Gold to claim a win by declaring an intention to play Ea1n and Ea2s on alternate turns from here on out. Although Silver could avoid repetition for many lifetimes, Hippo's Theorem proves it is theoretically won for Gold.
Quick, upload the puzzle "Gold to move and win in seven trillion".
Note this is different from the current rules which would require the game to be played until time was exhausted and then award the win to Silver based on the game having been captureless. Depending on how and whether such a rule could be applied in practice, it would be an attractive feature that whoever creates a divided-board situation is theoretically the loser. Thus both players have an incentive not to do it, and instead keep open a channel for engagement.
Even if there is no good way to apply the theory in general, it could practically decide some games even within the time limit. For example in Arimaa World League game Nevermind vs. Sconibulus, it appeared around move 21 that if Nevermind wasn't careful, Sconibulus could complete a swarm to lock up the board and create a piece-shuffling contest. But even if Sconibulus has created such a deadlock, perhaps Nevermind, armed with the knowledge from this thread, could have forced Sconibulus to deviate even within the game time controls by simply alternating Rh1w and Rg1e.
Thanks for teaching me something about Arimaa! (But of course you don't need a puzzle to do that; you are teaching me something about Arimaa simply by beating me in our Postal Mixer game.)
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| « Last Edit: May 28th, 2010, 1:19pm by Fritzlein » |
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Hippo
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Re: Reverse puzzles and impossible positions
« Reply #41 on: May 28th, 2010, 1:12pm » |
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on May 28th, 2010, 12:29pm, Fritzlein wrote:Er, I was still trying to clarify the question, but thanks anyway for giving me the answer, which indirectly tells me that my last guess at the question was in fact correct.
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Sorry about that (my poor English )
on May 28th, 2010, 12:29pm, Fritzlein wrote: For example, in the position below, assuming Silver just completed the rabbit wall, we could allow Gold to claim a win by declaring an intention to play Ea1n and Ea2s on alternate turns from here on out. Although Silver could avoid repetition for many lifetimes, Hippo's Theorem proves it is theoretically won for Gold.
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Yes, it would be nice to be able to declare victory on 3-times repetition based on my theorem . The player who divides the board to independent playgrounds loses.
(If the opponent declares this kind of victory (and has at least 2 positions)) ... (rabbit step forward creates another playground as it is irreversible by rabbit's owner, as well as removing a piece ... own or opponent's).
In this position taking a piece is losing move (the player completting the wall was losing after that move, but he is probably not lost after inaccurate opponent's play).
on May 28th, 2010, 12:29pm, Fritzlein wrote:
Thanks for teaching me something about Arimaa! (But of course you don't need a puzzle to do that; you are teaching me something about Arimaa simply by beating me in our Postal Mixer game.) |
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It's very far to say that Adanac is used to give a horse to win afterwards against much better player than I am, you are better than him and you gave me much less ...
It's probable it's just a matter of time a blunder of me would decide the game ... but surelly I would try to avoid that.
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| « Last Edit: May 28th, 2010, 1:44pm by Hippo » |
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