On 5 October 2009 I was sat in a Wetherspoon's on Mile End Road with my good friend John Faben. John is a PhD maths student and the owner of this blog, and that night, as he so often does, he asked me a question to which I had no hope of giving an adequate answer. It played on my mind for a few days, then I forgot about it.
I saw John again last Sunday. Funnily enough, we were in a Wetherspoon's. I was reminded of his poser from eight months ago, and resolved to put it out to chess blog readers far and wide. The problem is as follows:
Imagine, if you will, a game of chess between a competent human and a computer. The former must start with just a bare king; the latter, perhaps somewhat unfairly, has all of its pieces intact. If, however, all of the computer's moves were generated at random, what are the chances of the game ending in a draw?
6 comments:
Interesting question. My guess would be the chance of draw would be close to 99%. I am 190 ECF player with a PhD in maths for what it's worth!
I'd also be interested in knowing the chance of a draw for two computers playing random moves from the normal starting position.
Is it assumed that the human plays the best moves, merely "competent" moves or is drunk?
I suspect that my chances of being able to follow the explanation when it comes are vanishingly small.
I'll venture to say that the human will secure his draw more often than not.
My proposed strategy: head for a1 or h1 and sit there waiting for stalemate. If it gets a little bit hot in one corner, then break out and try the other one.
To EJH: is there a concept of "best" moves when one has only a king versus an army?!
Thanks for the blog link. His blog is excellent and I have added it to my favourites.
I think it's pretty hard to imagine any position where you have, say, a 50% chance of delivering mate. And further, it's hard to imagine accidentally reaching a position where any move has a 50% chance of delivering mate. So if I had to place a bet, I'd bet on a draw.
I think the odds maybe slightly change if any promotion is automatically a queen. I do think promotion will be a crucial issue. Presumably piece selection on promotion is random.
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