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Subject: Re: Mathematical question regarding chess

Author: Adam Oellermann

Date: 01:27:02 08/01/01

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On July 31, 2001 at 19:18:36, Roy Eassa wrote:

>On July 31, 2001 at 15:26:08, Ed Panek wrote:
>
>>On July 31, 2001 at 15:24:48, Roy Eassa wrote:
>>
>>>On July 31, 2001 at 15:21:17, Ed Panek wrote:
>>>
>>>>Lets say I have a move generator that selects a random move every time it is its
>>>>turn. What are the odds against it drawing/winning a game? Is it less likely
>>>>than winning a game of Keno with all the correct numbers picked?
>>>>
>>>
>>>Is the opponent Kramnik or Deeper Blue?  Or a human rated 400?  Or another such
>>>"random" program?  I think this matters.
>>
>>Lets try a random opponent first...and then Kramnik
>>
>>Ed
>
>
>Obviously, the chance of beating another random-playing program is 50% (not
>counting draws).
>
>The chance of beating Kramnik or another top-notch grandmaster is so small as to
>be essentially zero.  Perhaps one in (ten to the power of 40).
>
>What might be most interesting is estimating the chance of beating an extremely
>weak human player -- I don't know how low ratings go, but say USCF 400.  (I have
>a friend with a 4-year-old daughter who knows the rules of chess but not much
>more.)  Then the question becomes: how much better (or worse?!) than random are
>that player's moves?

When I got started with my chess program, I wanted to test my move generation
and so I implemented exactly that;  a program which would play chess by randomly
picking a move. It played a few games against my wife, who is in the category of
"knows the moves but hardly ever plays"; it never survived a middle game. I
would suspect that even a four-year-old who knows that "it's good to eat the
pieces" would win well over 99% of games, although obviously I don't have much
in the way of stats.

Some quick calculations in order to make this seem scientific...
- Branching factor is (say) 20 for the first 20 ply. I know, it may be more.
- Nothing reduces branching factor, because there is no eval/search
- Assume that to have a decent position in the middlegame against a novice, you
need to pick one of the top 4 moves in a perfectly-ordered move list.
- after 20 ply, the odds of having a decent position are 0.2^10 (you're only
playing alternate moves), which means the odds are 0.0000001024; or you'll get
one decent middlegame in about 10,000,000.

After that it gets worse; there are fewer good moves and potentially much more
branching in the middlegame. I therefore can state with some confidence that the
random-mover will never beat the 4-year-old. Implication: 4-year old is at least
750 elo points ahead of the random mover; which means the random-mover is
probably negative Elo (if such a thing is possible).

Puts me in mind of a big heap of monkeys, a big heap of typewriters, and
Shakespeare.

Cheers
Adam





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