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Subject: Re: In chess we will reach diminishing returns just like in Checckers 1994

Author: Tony Werten

Date: 04:55:09 10/30/03

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On October 29, 2003 at 03:15:23, Jorge Pichard wrote:

>"Experiments in Chinook show that there comes a point where increased search
>depth provides diminishing returns."
>
>From a mathematical game theory point of view, checkers is a simpler game than
>chess. There are only 5x1020 positions (5 with 20 zeros after it) in checkers,
>whereas chess has at least 1040 positions. Knowing this how long it will take to
>reach diminishing returns in chess?
>
>http://www.chessbase.com/newsdetail.asp?newsid=1270

It's still very questionable if there are diminishing returns. It depends on how
you define it.

If two programs play with 5 vs 6 ply search, the second engine has a 20% depth
advantage. With 10 vs 11 it's only 10%. So ofcoarse the difference in wins is
smaller.

My car drives 10 km/h faster than yours. If you drive 50 km/h our difference in
arrival time is 20 %, if you drive 100, it's only 10%. Is that diminishing
returns ?


Diminishing returns are only proven (IMO) if 6 vs 5 wins more games than 12 vs
10 because only then are you comparing something linear and you give a linear
advantage.

Compare it with a germ colony that gets 3x as big with every timeunit. Colony 2
get's one time unit extra. Now the play a game. A random number is choosen
between the amount of timeunits. Same story 6 vs 5 will win 20% more, 11 vs 10
will win 10%. But colony 2 is 3x as big in size !! Not important. Give a
constant sizeadvantage there will be diminishing returns. Given a percentile
timeunit advantage, there won't be.

Now replace timeunit with searchdepth and size with searchtime :)

Tony



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