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Subject: Re: Couple of chess programming questions

Author: Robert Hyatt

Date: 11:42:19 09/10/02

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On September 10, 2002 at 14:07:01, Dann Corbit wrote:

>On September 10, 2002 at 13:44:16, Robert Hyatt wrote:
>>On September 10, 2002 at 13:11:02, Dann Corbit wrote:
>>>On September 10, 2002 at 12:07:37, Vincent Diepeveen wrote:
>>>>>(3) Reading Aske Plaat's search & re-search paper, it really seems like mtd(f)
>>>>>is something of a magic bullet.  But I note it seems that more programs don't
>>>>>use it than do (for example Crafty).  What is wrong with mtd(f) which Plaat
>>>>>doesn't say?
>>>>There is nothing wrong with it. However a softwareprogram must have certain
>>>>conditions to let it work well (in hardware other issues play a role)
>>>>  a) it must be a static evaluation with a small granularity;
>>>>     if pawn=32 it will work great, if pawn=1000 like in DIEP it won't
>>>>     work at all, other things aren't interesting then.
>>>I have found this to be true also with experiments, and the reason is obvious.
>>>The MTD(f) algorithm basically does a binary search between two bounds (on
>>>average -- it might be faster or slower in individual cases).  If the interval
>>>varies from 3276700 to -327600 you have between 22 and 23 searches to resolve
>>>it.  If the interval varies from  3276 to -3276 you have between 12 and 13
>>>searches to resolve it.
>>>Therefore, you have a paradox.  The more accurately you search, the slower
>>>MTD(f) will become.  I can't see any solution to it, unless you use progressive
>>>accuracy to quickly narrow the search.  If you went to long double accuracy in
>>>your evaluation function, it will take a very long time to resolve the search
>>>with MTD(f), unless you double the accuracy with each iteration.  So for the
>>>first search, only (ugh) one significant digit is used.  Then two digits of
>>>accuracy, then 4, etc.
>>One issue with progressive bounds is to "bounce" _over_ the true value.
>>Searching from one side is faster than searching from the other, due to simple
>>math.  IE I tried several approaches that "died" until I started thinking about
>>what bouncing over the true score multiple times was doing to the shape of the
>One partial solution is to use a ceil() type idea for the upper bound and a
>floor() type idea for the lower bound {perhaps even with a small fuzz window}.
>But I still think PVS wins, in general.  At least I have not figured out how to
>make MTD(f) work as well.
>I do have a notion that if you have enough data you can improve the search a
>great deal.  MTD(f) is very sensitive to the initial guess and works best if you
>guess the true eval accurately.  However, even a perfect guess only halves the
>interval.  If you have a lot of data (perhaps by precomutation that has been
>stored in a database) you could search a narrow window around a central guess,
>and then switch to PVS when you run out of data.
>Suppose (for instance) that you have a 9 ply search for the position in question
>and you want to search to 14 plies.  You use your initial estimate (let's say it
>is +40 centipawns) and then your window is one full piece of 300 centipawns.  So
>you set the intial bounds at +190, -110 and search that interval.  Most of the
>time, the true value will be within a window of that size, and you will have
>saved a lot of time.  Only 8 searches will be needed if you have a resolution of
>1/100 pawn.  The deeper your inital search data is, the narrower your window can

Also it is sensitive to searching on the right side (upper side) of the
true score.  When you drop over the true value into the lower side of things,
failing high is much harder to prove than failing low, and efficiency goes
down the can.

I never took the time to try an approach that tried lowering the window in a
binary-way, but which would raise it even more quickly to get back on the right
side of the true score.  That might have a chance of helping significantly.

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