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Subject: Re: The law of diminishing returns

Author: Uri Blass

Date: 04:42:50 07/14/02

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On July 14, 2002 at 07:19:36, Rolf Tueschen wrote:

>On July 14, 2002 at 01:38:40, Uri Blass wrote:
>
>>On July 13, 2002 at 19:05:35, José Carlos wrote:
>>
>>>On July 13, 2002 at 17:16:05, Rolf Tueschen wrote:
>>>
>>>>On July 13, 2002 at 16:57:51, José Carlos wrote:
>>>>
>>>>>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.
>>>>
>>>>No reason to become so upset only because I told you not to insult Uri.
>>>>You have insulted him on his lack of intelligence
>>>
>>>  Uri knows I didn't. It seems _you_ are not capable to understand. I'm sorry,
>>>I'm not gonna explain _you_ what I said to Uri. He understood. That's enough.
>>>Please, stop defending him from nothing.
>>
>>You did not insult me for lack of intelligence but you said that you find it
>>strange that I disagree with Ed when Ed has a lot of experience about chess
>>programming and I am new in the task of chess programming.
>>
>>I think that the fact that I am new in chess programming was not relevant for
>>the discussion because I do not need to be a programmer to have an opinion about
>>data that everyone can see after hours of analyzing.
>>
>>I doubt if Ed has more experience than me in giving programs hours to analyze
>>and looking if the program changes it's mind.
>>
>>The data that Ed gave is from games and if programs can get depth 16
>>in games then the position is relatively simple so the program usually does not
>>change it's mind.
>
>Are you sure? I do not understand. Simple for the machines? Or from the chess?
>Please give us one or two examples out of your experience.
>
>Rolf Tueschen

Positions when programs can get depth 16 in games that are not correspondence
games are usualy simple positions(there is a forced line or it is an endgame).

machines tend to change their mind more often at big depth in complicated
positions in the middle game.

Uri



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