Author: Erik Bergren
Date: 09:31:06 08/14/03
Go up one level in this thread
On August 14, 2003 at 07:41:32, Tim Foden wrote:
>On August 13, 2003 at 15:40:00, Erik Bergren wrote:
>
>>Here is the Theoretical and experimental data produced by
>>the programs above:
>>
>>
>> (After 10,000,000 matches):
>> (With Probability Ratio of .6237 for White to win.)
>>Number of White Theoretical Experimental Experimental
>>Wins per outcome outcome outcome
>>each match(="n"): for "n": for "100-n": for "n"
>>==========================================================================
>>50 821699 (823153) 823153
>>51 804525 805157 803365
>>52 755117 753009 756603
>>53 679385 680519 678344
>>54 585885 587044 585463
>>55 484234 482899 484001
>>56 383517 383030 383595
>>57 291021 291419 290359
>>58 211537 211395 211549
>>59 147254 146946 147571
>>60 98140 98336 98541
>>61 62601 63001 63208
>>62 38206 38150 38069
>>63 22301 22647 22274
>>64 12444 12388 12268
>>65 6635 6534 6614
>>66 3378 3295 3392
>>67 1642 1662 1607
>>68 761 757 735
>>69 336 336 334
>>70 142 153 129
>>71 57 51 52
>>72 22 16 21
>>73 8 11 8
>>74 3 1 1
>>75 1 0 1
>>76 0 0 0
>>(76 to 100 are all zero)
>
>Sorry, but this distribution looks almost exactly what you would expect for a
>50% outcome, not a 62.37% one.
>
>For 62.37% I would expect something like this:
>
> n tot n tot 100-n
>--- ---------- ----------
> 50 34116 34116
> 51 54610 20120
> 52 85326 11447
> 53 128900 6196
> 54 185092 3220
> 55 258427 1686
> 56 343477 808
> 57 439408 394
> 58 539885 161
> 59 637399 68
> 60 721291 33
> 61 783080 16
> 62 816871 5
> 63 818126 1
> 64 782431 1
> 65 719842 0
> 66 631379 1
> 67 531070 0
> 68 426372 0
> 69 328604 0
> 70 240963 0
> 71 169194 0
> 72 113084 0
> 73 71670 0
> 74 43304 0
> 75 25126 0
> 76 13580 0
> 77 7066 0
> 78 3411 0
> 79 1591 0
> 80 685 0
> 81 280 0
> 82 126 0
> 83 46 0
> 84 9 0
> 85 2 0
> 86 0 0
> 87 0 0
> 88 0 0
> 89 0 0
> 90 0 0
> 91 0 0
> 92 0 0
> 93 0 0
> 94 0 0
> 95 0 0
> 96 0 0
> 97 0 0
> 98 0 0
> 99 0 0
>100 0 0
>total 10000000
>
>Cheers, Tim.
No, you >>>>>>>missed a step<<<<<< in the experiment:
each opponent gets to play with the
White pieces an equal amount ( such
as by switching side after each game,
or switching sides mid match.)
Your data has its maximum around
.6237*10,000,000. That implies you
gave one opponent an advantage over
the other (I guess one opponent had
the white pieces for all the match)
( my experiment was perfectly
>>>>symmetric<<<<<, both opponents
had equal chances and that implies
that the most probable match result
>>>>must be 50 to 50<<<<<, thus you data is
not applicable since its maximum is at 63).
If switching sides is not accounted for
then the equations are (relatively) easy:
r^x*(1-r)^(100-x)*100!/((x!*(100-x)!))
I assume that is the equation that
produced your data.
These subtleties are easy to
overlook, thanks for taking a shot
at correcting me though.
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