Arimaa Forum - Print Page


    
      
        Arimaa Forum
        (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi)
      

        Arimaa >> General Discussion >> Endgame Puzzle 5
        
(Message started by: jdb on Apr 1^st, 2011, 3:56pm)

Title: Endgame Puzzle 5
Post by jdb on Apr 1^st, 2011, 3:56pm

Who wins?

1w Ca1 Ra3
1b ra6 da8

http://arimaa.com/arimaa/games/planGame.cgi

Title: Re: Endgame Puzzle 5
Post by Hippo on Apr 2^nd, 2011, 2:51am

Rh4, Ca5 and gold capures faster. If silver steps ra5, Ca4 and again gold is faster, but the game is one turn prolonnged.
That one seems to be the easiest.

But with rb6?
Oh there is no differece as Ca5 prevents rabbit escape. And Ca2 could be played instead the Rh4 step.

Title: Re: Endgame Puzzle 5
Post by jdb on Apr 2^nd, 2011, 8:29am

Hippo, I do not understand your solution. Could you please explain it again?

Title: Re: Endgame Puzzle 5
Post by chessandgo on Apr 2^nd, 2011, 10:58am

I think Hippo means (with spoiler):

2g Ra3neee, and on any other move than 2s ra6seee, play 3g Rd4eeee, and then if silver defends against the goal play 4g Ca1nnnn, and I agree that it wins for gold. However, 2g Ra3neee 2s ra6seee seems very tense. I can't resist from looking at 3g Ca1neee da8seee, and silver's rabbit can simply follow gold's rabbit if it slides along the 4th row, and advancing the Rabbit to a5 on 4g doesn't seem to work.

I got excited with 3g Ca1nee Rd4e, as there might be a very cute win after silver's mirror answer 3s da8see rd5e 4g Re4een Cc2e 4s dc7eeee 5g Cd2enn (no 4th step, adding a Rg5e step loses to 5s dg7ssw Rh5w) 5s dg7s 6g re5nw Ce4nn. Unfortunately, 3g Ca1nee Rd4e 3s da8seee seems to defend, as Gold can only transpose in the losing variation, not in the winning one, since silver's dog can reach f5 in just 4 steps.

Well, I think 2g Ra3neee is the only viable move for Gold, and 3g Ca1nee Rd4e or 3g Ca1neee are the only 2 alternatives for 3g. For the moment I'm betting on silver, but I'm bound to have missed a lot of things.

Title: Re: Endgame Puzzle 5
Post by Hippo on Apr 2^nd, 2011, 11:03am

OK, I have again missed the correct defense :) OK it is not as easy as I have expected :).

Title: Re: Endgame Puzzle 5
Post by jdb on Apr 2^nd, 2011, 12:24pm

@chessandgo

Nice analysis, but incorrect.

Title: Re: Endgame Puzzle 5
Post by UruramTururam on Apr 2^nd, 2011, 12:59pm

It seems to me that it's a zugzwang position: the second to move wins...

Title: Re: Endgame Puzzle 5
Post by chessandgo on Apr 2^nd, 2011, 3:44pm

on 04/02/11 at 12:24:19, jdb wrote:

@chessandgo

Nice analysis, but incorrect.

Hehe, thanks. I wish I knew in which way it is incorrect :)

Title: Re: Endgame Puzzle 5
Post by Fritzlein on Apr 2^nd, 2011, 11:35pm

I agree with all of chessandgo's analysis except the conclusion. Here's why (spoiler):
Thanks for all the analysis, Jean. I couldn't find the flaw in it.

To my eyes, Silver starts with the threat of 2s d->b5, which would be crushing. The gold rabbit has to get away from the dog for Gold to have any hopes. And it is hopeful for Gold, as you and Hippo noted, that the silver dog can't afford to defend the gold rabbit, because then the gold cat captures the silver rabbit before the silver dog captures the gold rabbit. Tempo trumps strength in that kind of asymmetry.

So 2g R->d4 seems like the best hope. Yet I can't punch holes in your analysis that the mirror move 2s r->d5 defends it. If the rabbits stalemate each other, the gold cat is necessary to break the deadlock, but the silver dog seems to arrive just in time to pwn the gold cat.

But wait. What about 2g R->c4, C->a2? The gold rabbit has still emerged from under the threat of 2s d->b5. Just as before, it seems the silver dog can't defend against the gold rabbit, so the Silver rabbit must take on the defense. But 2s r->c5 to mirror rabbits is not stalemate, even giving the silver dog a free step, because the silver rabbit doesn't indirectly threaten goal from c5. So it seems 2s r->d5 would be forced.

In that case, we already know some losing lines for Gold, but we have a new option of 3g C->d3 that looks promising. Suddenly the silver rabbit is in danger of capture. Strategically it must be bad for the silver rabbit to run east; that creates the piece alignment that Gold wants after 3s r->h5 4g C->g4, and tactically, too, this seems to work out against Silver.

If the silver rabbit can't run, then the Silver dog must centralize. But it seems 3s d->b5 loses to 4g R->e5, C->d4, whereas 3s d->d7 loses to 4g R->a5, C->d4.

Obviously this is a very loose analysis, but if I have the main line right, it may be possible to dot the i's and cross the t's.
But probably I missed something key... :P
P.S. For spoilers on this parity, use "color=lightsteelblue" rather than "color=lightblue". Or to get an even more perfect match, according to my color picker, "color=#AFC6DB", if you can remember it.

Title: Re: Endgame Puzzle 5
Post by Fritzlein on Apr 2^nd, 2011, 11:43pm

For spoilers on this parity, it appears "color=ghostwhite" works better than "color=white", and "color=#F8F8F8" is the exact match according to my color picker. What do you think?

Testing spoilers; can you see this? This is the color #F8F8F8, so if you can't see it, then #F8F8F8 is for you.

Testing spoilers; can you see this? This is the color ghostwhite, so if you can't see it, then ghostwhite is for you.

Testing spoilers; can you see this? This is the color white, so if you can't see it, then white is for you.

Also, nobody may delete a post from early in the thread, as it would uncloak all spoilers by changing parity, and nobody may quote a spoiler from either parity. :)

Title: [quote author=Fritzlein link=bRe: Endgame Puzzle 5
Post by Eltripas on Apr 3^rd, 2011, 12:33am

on 04/02/11 at 23:43:19, Fritzlein wrote:

Both #F8F8F8 and ghostwhite are completely invisible for me.

Title: Re: [quote author=Fritzlein link=bRe: Endgame Puzz
Post by Fritzlein on Apr 3^rd, 2011, 1:08am

on 04/03/11 at 00:33:00, Eltripas wrote:

Both #F8F8F8 and ghostwhite are completely invisible for me.

Likewise, Eltripas, your lightsteelblue is totally invisible to me, even though it is supposedly not quite #AFC6DB. But I was afraid it was just my poor old monitor and poor old eyes. :)

Title: s
Post by ginrunner on Apr 3^rd, 2011, 1:34am

gold

My move list:
[color= lightsteelblue]Ra3n Ra4e Rb4e Rc4e
ra6s ra5e rb5e rc5e
Ca1n Ca2e Cb2e Rd4e
rd5e da8e db8e dc8e
Re4e Rf4e Cc2e Rg4e
dd8e de8e df8e dg8s
Cd2n Cd3n Cd4n
dg7s
Cd5w re5w Cc5w rd5w[/color]
spoiler
every line I have found forces Cd5 Rh4 dg7 re5 with silver to move or some variation of gold rabbit on the far east to win and gold cat threatening the rabbit in the west to win.

I have yet to find a counter

Title: Re: Endgame Puzzle 5
Post by Hippo on Apr 3^rd, 2011, 1:55am

So my solution before reading the thread:
[edit]color changed[/edit]
A) 2 Rd4 d* 3 Rh4 * 4 C a5 * 5 * rc6x
B) 2 ... rd5 3 Re4 Cc2 dc7 re5 4 Rg5 Ce2 * 5 rfrozen(and C,R cannot be) * 6 rx
C) 3 ... * 4 Rh5 * 5 rfrozen * 6 rx
(the goal in 1 variants not emphasized)

Title: Re: Endgame Puzzle 5
Post by Fritzlein on Apr 3^rd, 2011, 9:24am

To both ginrunner and Hippo; does reading chessandgo's spoiler above change your evaluation of the key move you both proposed? Neither of you refute his proposed 3s da8e db8e dc8e dd8s 4g Re4e Rf4e Rg4e Rh4n 4s dd7e de7e df7e rd5e.

Title: Re: Endgame Puzzle 5
Post by Hippo on Apr 3^rd, 2011, 1:17pm

I have either stopped reading merely after realising the mirror answer to Rd4. Or the variant with Cc2 Re4 were not in the post when I have read it.

Hmm, now it seems to me gold's hopes all lose by [color=#F8F8F8 ]df5 pulling Rg5[/color]. As chessandgo have written ... .

[color=#F8F8F8 ]If white rabbit ends on 4th rank, silver's rabbit can stand on the fifth rank and dog could stay in cat's opposition (strating from d,e rabbits). If white rabbit end's on 5th rank, dog could protect the goal (from g7) and escape with it's own rabbit to e5 to be able to protect it next turn while freezeing the Rabbit.
With centralised dog the board is too narrow :).
[/color]

Wow, I like your analysis Fritzlein.

With Rc4 Ca2 dog defense is impossible as the silver rabbit has no time to escape from the c6 trap neighbourhood. (Rg4, d at least f7 required, but 2 r steps are not enough.)
So the rabbit defense, but rc5 is not sufficient due to trap defending c1 so Rf5 wins.
The only remaining defense is rd5 with counterthreat.
Cd3 is threatening freezing the rabbit with R attack back on the a file.
So let us consider that position as the starting point.

There is very strong threat of
block Re5 rd5 Cd4 forcing d not to be on the b file.
(Together with Cat able to catch the rabbit while Rabbit running away from dog).

So we could expect silver moves dog to at least c7.
But at that case C could freeze the rabbit by two steps treatening capture with Rabbit going to a4 by the remaining two steps. Silver could not prevent both goal and (forked rabbit/rabbit capture in distant trap).

We are in the mirror of the variant discussed by chessandgo, but with Rabbit on 4th rank favourising gold.

Variant with db7 rb5 looks may be more interesting than variants with 3 dog steps ..., but Cb4 Rd4 where capture threat at c6 prevents dog from freezing Rd4 so Rabbit can run to h4 and finally rabbit would be captured at c6.

So definitely that was not the easiest one :). But now, I am almost sure the answer is correct.

Title: Re: Endgame Puzzle 5
Post by ginrunner on Apr 3^rd, 2011, 3:02pm

my reply to C&G's 3s of da8e db8e dc8e dd8s

move that eventually wins
Rd4e Re4e Rf4e Ca1n
spoiler
because the rabbits are on the rows with traps their movement is hindered and gold has the ability to get itself out first and put pressure which allows gold to win. With the move silver needs to spend 3 moves to defend the goal and only gets one move to either try and move to threaten sooner capture of the gold rabbit or try and free the silver rabbit. Gold is then allowed 4 moves to move to threaten capture of the silver rabbit or move the gold rabbit west again. The silver dog can never leave the 7th row because it will always be required to move 3 east or west and if it ever moves south the gold cat can start to threaten the silver rabbit. Gold has two long term threats it can always choose between whereas silver must always defend against one and can never make a threat of its own without a mistake from gold. --- There are some variations where the silver dog only moves 2 east or west to defend but it can never come fast enough to threaten a rabbit capture faster than the gold cat can.

Title: Re: Endgame Puzzle 5
Post by chessandgo on Apr 3^rd, 2011, 4:59pm

I agree with your analysis too Karl, I can't see any way for Silver to get out of it.

Title: Re: Endgame Puzzle 5
Post by jdb on Apr 3^rd, 2011, 5:41pm

on 04/03/11 at 16:59:32, chessandgo wrote:

I agree with your analysis too Karl, I can't see any way for Silver to get out of it.

I agree too. ;D

Title: Re: Endgame Puzzle 5
Post by Fritzlein on Apr 3^rd, 2011, 6:18pm

Thanks for the confirmation, jdb. It's too bad the puzzle tool allows only one line in the solution. It's at least as instructive how other lines including 2g Ra3n Ra4e Rb4e Rc4e don't work. For the full beauty of the analysis one needs a full tree of variations.