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Subject: Re: Perfect game / Maximum Elo

Author: Christoph Fieberg

Date: 11:56:11 06/17/99

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FM <dankang@usa.net> wrote in article
<7k6a4l$jb7$1@pampascat.middlebury.edu>...
> Christoph Fieberg wrote:
>
> >The rating 10024 for the perfect machine means that Kasparov would score
> >just 0.5 points in 1,152,921,504 billion games! And that is with a
(high)
> >50% chance of picking a move that will not lose and a (low) expected
> >average game of 60 moves.
>
> Kasparov probably has 90%+ chance of picking a perfect move in most game
> situations.

Think of the fully analysed endgames. Humans thought some positions are
NEVER a draw and computers showed it is possible. However in these
particular positions only one weird move out of 20+ moves draws and that
for several moves onwards.

In such a position Kasparov would think a draw is impossible and would give
up. But lets assume he continues to play then his chances to find the
correct move would be very poor because he would have to "guess". Perhaps
his chance is at best 1:10 for every move then.

Now lets assume that the game is fully analysed and the computer plays 1.e4
and that the ONLY answer that draws the game is 1.-e5. The chance that
Kasparov would play the correct move are probably 1:2 because he thinks
that 1.-c5 would also draw.

Later he would often consider 2 or 3 moves playable, but only ONE of them
might be the correct answer (chance 1:2 [50%], 1:3 [33%]). Or worse - he
considers 2 or 3 moves playable but the answer is a totally different one.
In such a situation were a STRANGE move is the ONLY answer his chance to
find it would diminish 1:10 [10%] or 1:20 [5%].

Of course it might be possible that in the opening 3 or 4 different moves
would draw and that Kasparov would have a 100% chance to play 10 moves were
he is in a difficult position but still not lost. But then the number of
moves that draw would decline rapidly and it would become much and much
harder to find these moves. He would face that his chances would go down
rapidly.

If Kasparov makes 60 moves and has the following chances to find the
correct move

15 moves	1:1	100%
30 moves	1:2	50%
5   moves	1:3	33%
5   moves	1:4	25%
3   moves	1:5	20%
2   moves	1:10	10%

then on AVERAGE his chance is 50%.

I think that is a very good chance.

Christoph





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