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

by wol (Hermit)
 on Jul 02, 2009 at 10:49 UTC ( #776697=note: print w/replies, xml ) Need Help??

An avenue for investigation...

If a player were to keep rolling the same number, where would they wind up?

As the board is a finite size, there's only two possible kinds of answer, they'd wind up going round in circles, or they'd get to the end and (as this is a game for one) win.

For example, if a player keeps rolling 1, then they'd get into a loop involving ladder 28=>84 and snake/chute 87=>24. (Caution: calculated using head, not Perl.)

So what are the results for rolling only 2s .. 6s? Is it possible to win the game? Which number results in the most convoluted loop? Which number carries on longest before it gets into a loop.

Grr - damn this paid employment lark! I have to stop before I can actually try any of this stuff out!

--
use JAPH;
print JAPH::asString();

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

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Re^2: Dial up some obscure stats for the Chutes and Ladders game
by toolic (Bishop) on Jul 03, 2009 at 23:26 UTC
Thanks for the ideas.

You reminded me that I wanted to do some more analysis. While you are interested in infinity, I am still obsessed with ending the game in the minimum number of spins (7).

In another sample of 1 million games, 1509 ended in 7 spins. Of those games, there were 421 unique sequences of 7 spins. Some sequences only occurred once (38 out of 421). Other sequences occurred multiple times, up to a maximum of 10 times.

```These 2 sequences occurred 10 times each:
4->3->6->5->6->5->5
1->4->4->5->5->4->4

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