Pascal Georges wrote:
Hi!
>> Above all, I find very intriguing the new Monte Carlo search method,
>> even if I have a lot of doubts about it (if I have correctly
>> understood it).
>> I mean: trusting in statistical results can be very dangerous in chess
>> (especially in endgames), very often there can be only one winning line,
>> but it is enough to win the game, instead the Monte Carlo method could
>> consider it as a draw line.
>> Maybe, I'm missing something... maybe Monte Carlo search is only an
>> addition to the normal evaluation, not a replacement.
>
> Same thing for me. I don't get the point about playing thousands of
> bullet games, and draw any conclusion from this.
> It looks a bit like writing down the evaluation tree into several games,
> but with some selective lines calculated as far as the end of the game :
> what is the real difference with selective depth ?
> The only advantage I see is that winning/losing lines are calculated
> with statistics, and maybe the number of games compensates the fact that
> the moves were calculated in 1 second ?
I think this approach to explain it does not work as it does
not get the scaling right and I think scaling is the crucial
point here.
Maybe a sample form maths where I know it.
If you want to find the area of a circle you can take a
sheet of chequered paper and count the squares you need to
fill the circle. With the area of each square you get the
area of the circle immediately. If you want to improve your
measurement you need to use smaller squares and the ammount
scales I'd say quadratically. As does the time you need for
counting. Still you always get an error as the circle is
round and you can not really fill it with squares. You can
estimate the error though and it gets smaller for smaller
squares. This is all pretty obvious I think.
Now you forget all this and you take a bunch of needles. And
just throw the needles at the circle. You count the ones
that hit inside the circle and the ammount of hits compared
to the number you threw gives you a measurement of the area
of the circle as well. Its clear in this example: the larger
the circle, the easier you get a hit. Now, to increase
precision you have to increase the number of needles you
throw. But this has no direct connection to your measuring
device as in the case above with the chequered paper.
Hence, the scaling for this approach is entirely different
compared to the chequered sheet of paper. IMHO this is the
key to these things:
As a mathematician you'd now take an n dimensional "circle",
calculate the "scaling" for your "sheet" of paper and
compare it to the needles you need to throw.
Again you will find that the scaling for the paper method
gets worse as you increase the dimension of the problem
while the ammount of needles grows much slower.
Note here that in too few dimensions the MC method is _much_
slower than the paper method! In my fortran codes you easily
get a factor of 10 or more at 2D if you require the same
error bars. You only gain with the dimensionality of your
problem. Thats why I can imagine that it works with Chess or
Go.
If you want to look it up, there's a pretty good discussion
of these types of algorithms in the context of the
evaluation of integrals in the "Numerical Recipes". They
also explain the general idea of this sort of things in
pretty much details. I mean the real hardcover book not the
codes (they also offer codes in C, C++ and of course
Fortran). Should be available in the next university
library.
BTW: a pretty funny way to get the integral is to just cut
the circle out of the paper and use a balance. Together with
the density of the paper you can calculate the area. You get
astonishing precise results by that. (A classical example
from the physics excersises in the first semester :) Its yet
another, completely different approach to the same problem.
It just lacks the possibility to go into n dimensions for n
> 3 ;)
--
Kind regards, / War is Peace.
| Freedom is Slavery.
Alexander Wagner | Ignorance is Strength.
|
| Theory : G. Orwell, "1984"
/ In practice: USA, since 2001
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