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Subject: Re: The law of diminishing returns

Author: José Carlos

Date: 13:57:51 07/13/02

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On July 13, 2002 at 15:09:18, Rolf Tueschen wrote:

>On July 13, 2002 at 08:02:09, José Carlos wrote:
>
>>On July 13, 2002 at 07:15:53, Rolf Tueschen wrote:
>>
>>>On July 13, 2002 at 07:09:02, José Carlos wrote:
>>>
>>>>On July 13, 2002 at 05:35:24, Uri Blass wrote:
>>>>
>>>>>On July 12, 2002 at 19:16:31, José Carlos wrote:
>>>>>
>>>>>>On July 12, 2002 at 14:56:11, Ed Schröder wrote:
>>>>>>
>>>>>>>Hi CCC,
>>>>>>>
>>>>>>>In Rebel I maintain a statistic file, on every iteration a counter is
>>>>>>>incremented with 1 (see column 2) representing the iteration depths Rebel has
>>>>>>>searched. When a new best move is found a second counter is incremented with 1
>>>>>>>(see column 3) representing how many times a new best move has been found on the
>>>>>>>given iteration depth, between brackets the percentage is calculated.
>>>>>>>
>>>>>>>As you can see the very first plies Rebel often changes to new best moves,
>>>>>>>however when the depth increases and increases the chance Rebel will change its
>>>>>>>mind drops and drops. From 16 plies on the chance a new better move is found is
>>>>>>>below 2%.
>>>>>>>
>>>>>>>I wonder what this all means, it is still said (and believed by many) that a
>>>>>>>doubling in computer speed gives 30-50-70 elo. That could be very well true for
>>>>>>>lower depths but the below statistic seem to imply something totally different,
>>>>>>>a sharp diminishing return on deeper depths.
>>>>>>>
>>>>>>>Interesting also is colum 4 (Big Score Changes), whenever a big score difference
>>>>>>>is measured (0.50 up or down) the percentage is calculated. This item seems to
>>>>>>>be less sensitive than the change in best move. However the maintained "Big
>>>>>>>Score Changes" statistic is not fully reliable as it also counts situations like
>>>>>>>being a rook or queen up (or down) in positions and naturally you get (too) many
>>>>>>>big score fluctuations. I have changed that and have limit the system to scores
>>>>>>>in the range of -2.50 / +2.50 but for the moment have too few games played to
>>>>>>>show the new statistic.
>>>>>>>
>>>>>>>Anyway the number of positions calculated seem to be more than sufficient (over
>>>>>>>100,000) to be reliable. The origin came from extensive testing the latest Rebel
>>>>>>>via self-play at various time controls.
>>>>>>
>>>>>>  Hi Ed, if I get this right, the second column (moves searched) is the number
>>>>>>of positions in which the program has reached the depth given by column 1. If it
>>>>>>was really "moves", there would be about 3x in depth 2 than in depth 1.
>>>>>>  Then the idea is that many more changes happen in low depths because the
>>>>>>program is there many more times, so I (ignoring "Big Changes") calculated a
>>>>>>couple of other numbers:
>>>>>>  The ratio moves changes / moves searched and the relative % of changes from
>>>>>>ply to ply:
>>>>>>
>>>>>>                 SEARCH OVERVIEW
>>>>>>                 ===============
>>>>>>
>>>>>>  (A)     (B)            (C)           (D)             (E)
>>>>>>Depth    Moves          Moves     Moves Changed /   rel % of changes from
>>>>>>       Searched        Changed    Moves Searched    ply n-1 to n
>>>>>>
>>>>>> 1     113768         0 =  0.0%        0
>>>>>> 2     113768     44241 = 38.9%    0.388870333
>>>>>> 3     113768     34262 = 30.1%    0.30115674        77.44%
>>>>>> 4     113194     32619 = 28.8%    0.288168984       95.69%
>>>>>> 5     113191     30697 = 27.1%    0.271196473       94.11%
>>>>>> 6     108633     28516 = 26.2%    0.262498504       96.79%
>>>>>> 7     108180     25437 = 23.5%    0.235135885       89.58%
>>>>>> 8     102782     22417 = 21.8%    0.218102391       92.76%
>>>>>> 9      82629     15400 = 18.6%    0.186375244       85.45%
>>>>>>10      59032      9144 = 15.5%    0.154899038       83.11%
>>>>>>11      39340      5183 = 13.2%    0.131748856       85.05%
>>>>>>12      23496      2350 = 10.0%    0.100017024       75.91%
>>>>>>13      12692       957 =  7.5%    0.075401828       75.39%
>>>>>>14       6911       396 =  5.7%    0.057299957       75.99%
>>>>>>15       4032       193 =  4.8%    0.047867063       83.54%
>>>>>>16       2471        72 =  2.9%    0.029138001       60.87%
>>>>>>17       1608        26 =  1.6%    0.016169154       55.49%
>>>>>>18       1138        17 =  1.5%    0.014938489       92.39%
>>>>>>19        921         6 =  0.7%    0.006514658       43.61%
>>>>>>20        795         7 =  0.9%    0.008805031      135.16%
>>>>>>21        711         1 =  0.1%    0.00140647        15.97%
>>>>>>22        636         2 =  0.3%    0.003144654      223.58%
>>>>>>23        574         5 =  0.9%    0.008710801      277.00%
>>>>>>24        507         1 =  0.2%    0.001972387       22.64%
>>>>>>25        451         3 =  0.7%    0.006651885      337.25%
>>>>>>26        394         1 =  0.3%    0.002538071       38.16%
>>>>>>27        343         2 =  0.6%    0.005830904      229.74%
>>>>>>28        296         2 =  0.7%    0.006756757      115.88%
>>>>>>29        269         0 =  0.0%    0                  0.00%
>>>>>>
>>>>>>  Column (D) means the probability at a certain position at a certain depth to
>>>>>>get a change, according to your data, for a random position (I assume you chose
>>>>>>random positions, because this data comes from real games).
>>>>>
>>>>>No
>>>>>
>>>>>I assume that the positions that was searched to big depthes like 16 are only
>>>>>positions that the program had enough time to search in the game to depth 16.
>>>>>
>>>>>These positions are not random positions from games.
>>>>>I expect in random positions from games to see at least 10% changes at depth 16.
>>>>>
>>>>>Uri
>>>>
>>>>  It's interesting that Ed, who has been doing chess programming for a lot of
>>>>years rely on statistical data, and you, absolute newbie to chess programming
>>>>can 'expect'. Quite amazing.
>>>>
>>>>  José C.
>>>
>>>Very telling about your lack of knowledge about interdisciplinary thinking.
>>>
>>>Rolf Tueschen
>>
>>  Well, you needed several hundred posts from Dann to understand the simple
>>concept of elo ratings. Lack of knowledge is easy to solve, while lack of
>>intelligence is a real problem.
>>  BTW, interdisciplinary thinking has nothing to do with validating intuitions
>>through experiments.
>>
>>  José C.
>
>Your habits are a bit strange for CCC. You want to insult people for their
>intelligence? Didn't you know that this is out of fashion?

  Did you feel insulted? Oh, sorry, I didn't insult you, really.

>Also you cannot prove
>your visions.

  Visions? I don't have visions. Maybe you take me for someone else ?!

>But I can prove where you lack of knowledge. Look at this:
>
>How do you know if or when I understood Elo system? Dann didn't
>explain anything to _me_,

  Don't feel bad because Dann had to explain that to you. It can happen to
everybody.

>He was the only one having the courage to give his verdict about SSDF
>Elo system - _with_ me! We two the only ones. And you were dreaming of his role
>as _my_ teacher? That's funny.

  I'm glad you enjoied Dann's lessons. Dann is very good at that. I also always
enjoy his posts.

>You do not  understand what validity means... ;-)

  Good argument!

>You have no idea of what interdisciplinary means too.

  Damn, you leave me without words!

>You are the typical expert
>with narrow views.

  Thanks for calling me expert... bah, just a little degree in computer science
and a few publications don't make me an expert...

>Do not insult Uri.

  I didn't. He knows it.
  BTW, do you feel the need to defend him? Don't you think he is capable to
defend himself? I think it's you who is insulting Uri.

>Because he knows a lot about chess.

  The first thing where we agree! Cheers!

>Know
>what I mean? Chess is the basis for computerchess. :)

  Words of wisdom...

>Only interdisciplinary help could enlighten you. If you have questions, please
>tell me, I'll try to do my best for you.
>
>Rolf Tueschen

  Thank you very much. I'll ask you anything I don't understand.

  José C.



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