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Re: Dial up some obscure stats for the Chutes and Ladders game

by dsheroh (Prior)
on Jun 30, 2009 at 10:09 UTC ( #775965=note: print w/replies, xml ) Need Help??


in reply to Dial up some obscure stats for the Chutes and Ladders game

The maximum number of moves seems to be infinite. In a sample of 1 million games, the maximum number of moves was 399; after 2 million, it was 437. Maybe there's an asymptote, I don't know. In any case, I think it is practically impossible to be that unlucky.

The maximum number of moves is infinite, provided sufficiently poor luck.

Proof: Starting on square 6, it is possible to spin an infinite sequence of fives, causing you to slide down the 16 -> 6 chute an infinite number of times and resulting in an infinite number of moves.

There are also several other infinite loops possible, due to the various chutes and the multiple sequences of spins that can take you from the bottom of any given chute to its top, but the 6-11-16 loop is the simplest to lay out.

(Disclaimer: I do not have a copy of the board readily available, so I have inferred the board topology from the posted source code. If there is no 16 -> 6 chute, or if there is a chute/ladder on 11, the specific example used will not work, but the general principle remains.)

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Re^2: Dial up some obscure stats for the Chutes and Ladders game
by toolic (Bishop) on Jun 30, 2009 at 17:18 UTC
    Thanks for the clear explanation. I updated the OP with a link to your reply.
    I do not have a copy of the board readily available
    The wiki link in the OP includes a photograph of the board.

    Update: The wiki photo differs slightly from my game board at home (and the code posted in the OP): the wiki board has a chute that starts on square 47 and ends on 26; the chute in the code is 48-26.

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