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        Arimaa >> General Discussion >> Endgame Puzzle 1
        
(Message started by: jdb on Jul 27^th, 2008, 6:46am)

Title: Endgame Puzzle 1
Post by jdb on Jul 27^th, 2008, 6:46am

How can silver save the day?

1w Ca1 Rd2
1b ra5
2w pass

Link to planning window:
http://arimaa.com/arimaa/games/planGame.cgi

Title: Re: Endgame Puzzle 1
Post by aaaa on Jul 27^th, 2008, 7:03am

Here's my attempt:

2b ra5e rb5s rb4e rc4e
3w Ca1e Cb1e Cc1e Rd2e
3b rd4e re4e rf4e
4w Cd1e Ce1e Cf1n Cf2e
4b rg4w rf4w re4w rd4w and wins

[EDIT]
Alternate defense:

3w Ca1e Cb1e Cc1e Cd1e
3b rd4w rc4w
4w Ce1w Cd1w Cc1n Cc2w
4b rb4e rc4e rd4e re4e and wins
[/EDIT]

Title: Re: Endgame Puzzle 1
Post by Fritzlein on Jul 27^th, 2008, 7:48am

Elmo and I agree with your solution. However, there is an interesting footnote. If Gold deviates with

2b ra5e rb5s rb4e rc4e
3w Ca1e Cb1e Cc1e Cd1e

then Silver can make a winning position symmetrical to the one you made with

3b rd4w rc4w

winning in the same total number of moves. When Elmo and I were satisfied with our solution, we checked it with Bomb. The position is small enough that Bomb can find a forced win in four in less than a second. However, Bomb considers the initial position a forced loss for Silver!

We dug a bit deeper and discovered why Bomb gets the wrong answer. When it is building its search tree, it allows a pass only on the fourth step, i.e. it can only make three-step or four-step moves. Why didn't Fotland allow two-step moves? Well, my guess is that he supposed one could make a four-step move into a two-step move by burning two of the steps with, say, a forward-and-back shuffle, so allowing four-step moves effectively allows two-step moves. However, in this position, Gold has no piece to shuffle except the rabbit. Once it starts stepping west on 3b, it can't step back east without hitting the hash table, which I am guessing effectively disallows that step.

This is just a warning to anyone out there who is composing "Goal in X" puzzles with the help of Bomb. In the endgame it is often necessary and correct to lose a step or two, and Bomb apparently can't do that quite correctly.

[EDIT]
I see your edit anticipated the alternate defense while I was typing my reply :P