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Subject: Re: Artificial Intelligence in Computer Chess - *DETAILS* as promised

Author: martin fierz

Date: 08:05:17 03/29/04

Go up one level in this thread


On March 29, 2004 at 10:27:19, Anthony Cozzie wrote:

>On March 29, 2004 at 10:01:55, martin fierz wrote:
>
>>On March 29, 2004 at 09:46:48, Uri Blass wrote:
>>
>>>On March 29, 2004 at 08:54:09, martin fierz wrote:
>>>
>>>>On March 29, 2004 at 07:04:13, Uri Blass wrote:
>>>>
>>>>>On March 29, 2004 at 06:25:28, martin fierz wrote:
>>>>>
>>>>>>On March 28, 2004 at 18:55:53, Artem Pyatakov wrote:
>>>>>>
>>>>>>hi artem,
>>>>>>
>>>>>>[snip]
>>>>>>
>>>>>>>>>On the other hand, I think a lot of researchers have been overly ambitious and
>>>>>>>>>have tried to replace Alpha-Beta & tricks with a neural network or some totally
>>>>>>>>>different approach. I think that with the current state of AI tools, these
>>>>>>>>>efforts are bound to fail.
>>>>>>>>
>>>>>>>>A lot of researchers?  Other than myself, I don't know of any other workers who
>>>>>>>>are attempting a complete and competitive chess playing program that doesn't
>>>>>>>>tread the oft traveled A/B bag-of-tricks road.
>>>>>>>
>>>>>>>That's good a point (will probably include in paper) - not many are working on a
>>>>>>>complete chess program, since most just address a particular section, like the
>>>>>>>evaluation function. But one old effort - MORPH - comes to mind, and I think I
>>>>>>>noticed a couple of other failed Neural Net efforts (don't have references
>>>>>>>handy, but I can look).
>>>>>>
>>>>>>steven is doing a completely radical departure from A/B. but many others are
>>>>>>applying more gradual changes to the A/B-model, with reasonable success
>>>>>>(smarthink, kaissa, gothmog come to mind, and probably most commercial engines
>>>>>>too). at least these engines make considerably larger attempts to shape their
>>>>>>game tree than a "classic" A/B searcher like crafty does.
>>>>>>
>>>>>>[snip]
>>>>>>
>>>>>>>As I mentioned before, I decided to concentrate my research on move ordering for
>>>>>>>a couple of reasons:
>>>>>>>1) Move ordering promises big payoffs if done right.
>>>>>>
>>>>>>how much deeper can you search if you reach 95% move ordering success (defined
>>>>>>as cutoff @ 1st / all cutoffs) instead of ~90% that most get today? how much if
>>>>>>you reach 100%?
>>>>>
>>>>>I cannot answer the 95% question but I can answer the 100%.
>>>>>
>>>>>If you reach 100% then always choosing the first move is enough because if the
>>>>>first move does not generate a cutoff no move is going to generate a cutoff so
>>>>>you can finish to search to the end of the game very quickly because you search
>>>>>only one move in every ply.
>>>>>
>>>>>Uri
>>>>
>>>>you do not answer the question here - and what you answer is wrong too :-)
>>>>always choosing the best move first to search means you search sqrt(N) moves per
>>>>ply on average, not 1 move per ply.
>>>
>>>No
>>>
>>>In that case you do not need to search the other moves because you know that
>>>they are worse.
>>>
>>>If you always start from the best move than the pruning strategy of not
>>>searching moves except the first move is simply correct and I see no reason not
>>>to use it.
>>>
>>>Uri
>>
>>come on uri, this is ridiculous. of course you can use that shortcut IF you know
>>that your move ordering is 100% perfect. in that case you need no search at all
>>either. obviously this is an academic question and has nothing to do with
>>reality, and is not what i'm asking... the question remains: in the extremely
>>unlikely case that you have 100% perfect move ordering (by accident), what do
>>you gain compared to 90% perfect (in the usual sense of move ordering %age)?
>>
>>cheers
>>  martin
>
>It would be possible to determine this experimentally - just keep track of each
>position and the best move at each ply on the hard disk.  It wouldn't be
>practical for use but it would be pretty interesting.
>
>anthony

if i had to do this i would produce a mock A/B program which first randomly
decides whether the node is a fail-high node (~50% of all cases i guess), and
then again randomly decides whether it fails high on the first move (~90% of all
cases), and finally decides to fail high somewhere in between move 2...N if not
on the first move (perhaps with equal probability, or with decreasing
probability from move 2...N). by playing around with the probabilites of these
random decisions, you can easily determine the numbers i'm looking for, and see
how they depend on the quality of your move ordering.

i disagree though that this is not practical: for example, if you find that
going from 90% to 91% move ordering (= fail high at first/total fail highs) you
need to search 50% less nodes on a typical search depth your engine reaches,
then you definitely know you should work on your move ordering. if you find that
you need to search 0.1% less nodes, you know that working on MO is a waste of
time from now on. the true value will probably lie somewhere in between, but in
any case, it gives you an idea of what you might gain with more expensive MO
schemes.

i can imagine some kind of formula just by doing some assumptions, which may be
completely wrong...:

the totally wrong-ordered case goes as
nodes(depth) ~ (N*N)^D/2

the totally ordered case goes as
nodes(depth) ~(1*N)^D/2

this formula stems from the fact that you search exactly 1 move at player A's
moves, and all N at player B's moves AFAIK, so for going 2 ply deeper i need 1*N
nodes. so let me assume random move ordering for player A, meaning i get the
best move right on average at move N/2, which gives me

nodes(depth) ~ (N*N/2)^D/2.

perhaps that should read (N*sqrt(N))^D/2, because it might be the geometric
instead of the arithmetic mean?!

in any case, you can now assume that you find the best move 1st in the fraction
F (~0.9), and in the remaining case at random, this leads to

nodes(depth) ~ (N*(1*F+(N/2*(1-F)))^D/2.

plugging in some numbers like N=20 (reduce from 40, trying to account for
nullmove?!), D=10, F=0.90 and 0.91 i get

nodes(10, F=0.90) = 79 million
nodes(10, F=0.91) = 62 million

so for 1% better move ordering i get 22% less nodes?! seems rather excessive.
let me try again using sqrt(N) instead of N/2 - that still gets a 12% reduction.

hmm, either my formulas are crap or i really have to work on my move
ordering ;-)

cheers
  martin



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