Author: Peter Fendrich
Date: 03:31:57 12/23/02
Go up one level in this thread
On December 22, 2002 at 07:48:37, Rémi Coulom wrote:
>This is what my program says:
>
>number of wins n1 = 4
>number of losses n0 = 6
>P(p1>p0) = 0.274414
>
>Below is what your own program says. 4 6 100 is only slightly different, but
>that is certainly related to the incaccuracies of the Monte Carlo method.
>
>Result Evaluator. Version 0.8
>by Jean-Peter Fendrich; peter@fendrich.net
>Enter 'Help' for more information
>
>
>Enter a match result in the form Wins Losses Draws or Q for quit. 4 6 0
>10 games. Result: 4.0-6.0
>Some different values of Pw and Pd:
>Pw Pd Trin cumTrin
>------ ------- ----------- ---------
>0.33 0.33 0.00355636844 0.05450558
>0.40 0.20 0.022020096 0.122454
>0.49 0.01 0.189157533 0.7482712
>0.37 0.26 0.0100980272 0.07425042
>0.33 0.35 0.00276091416 0.05424455
>0.01 0.99 2.05078125e-021 0.9980402
>0.80 0.10 8.6016e-005 0.6260984
>............................................................................
>Probability for A better than B is: 0.2745533
>
>Enter a match result in the form Wins Losses Draws or Q for quit. 4 6 1
>11 games. Result: 4.5-6.5
>Some different values of Pw and Pd:
>Pw Pd Trin cumTrin
>------ ------- ----------- ---------
>0.33 0.33 0.00118545615 0.03502741
>0.40 0.20 0.0044040192 0.0886891
>0.49 0.01 0.00189157533 0.6468857
>0.37 0.26 0.00262548707 0.05006582
>0.33 0.35 0.000966319957 0.03491507
>0.01 0.99 2.03027344e-021 0.9975906
>0.80 0.10 8.6016e-006 0.5771945
>............................................................................
>Probability for A better than B is: 0.2747703
>
>Enter a match result in the form Wins Losses Draws or Q for quit. 4 6 10
>20 games. Result: 9.0-11.0
>Some different values of Pw and Pd:
>Pw Pd Trin cumTrin
>------ ------- ----------- ---------
>0.33 0.33 9.56946654e-008 0.0008574022
>0.40 0.20 3.58271855e-009 0.01094223
>0.49 0.01 3.00550302e-021 0.6054174
>0.37 0.26 2.26497568e-008 0.002691502
>0.33 0.35 1.21011565e-007 0.0008517853
>0.01 0.99 2.94689602e-021 0.9916248
>0.80 0.10 1.36669867e-014 0.2530475
>............................................................................
>Probability for A better than B is: 0.274245
>
>Enter a match result in the form Wins Losses Draws or Q for quit. 4 6 100
>110 games. Result: 54.0-56.0
>Some different values of Pw and Pd:
>Pw Pd Trin cumTrin
>------ ------- ----------- ---------
>0.33 0.33 2.33563783e-045 1.125915e-019
>0.40 0.20 9.44803171e-067 1.700053e-011
>0.49 0.01 6.40245019e-196 0.1909135
>0.37 0.26 1.07422165e-055 3.536888e-015
>0.33 0.35 2.38440436e-043 2.734289e-019
>0.01 0.99 2.54074667e-016 0.8122032
>0.80 0.10 2.91139955e-099 2.06995e-005
>............................................................................
>Probability for A better than B is: 0.2773552
>
>Enter a match result in the form Wins Losses Draws or Q for quit. Q
>Result Evaluator ended
Remi,
I don't get the same results as you:
(all the sample values of Pw, Pd, Trin and cumTrin are the same)
Mine Yours
4 6 0 : 0.2745363 0.2745533
4 6 1 : 0.274543 0.2747703
4 6 10: 0.2740947 0.2773552
I'm not sure what's happening here but as you say, the Monte Carlo method
doesn't give exact values.
I thought that the program could be reliable to 3 decimals but maybe not...
However, if I'm right about draws, the prob would slowly move towards 0.5 when
the number of draws increases. I continued up to 500 draws and got the
following:
4 6 100: 0.2758096
4 6 200: 0.2820387
4 6 300: 0.2906555
4 6 400: 0.3076096
4 6 500: 0.3273436
The probability for A neatly grows with more draws.
OTOH I can't argue against your formulas. Give me some more time.
Could you please elaborate the first formula in section "3 Draws do nout Count".
How do explain 1 - p0 - p0.5 = 1 - u + up0.5 - p0.5?
I'm a bit interested in the term up0.5 that seems to be superfluous.
Maybe we should continue via email if no one else shows interest in the
discussions.
I don't know if Uri still follows it, if so shout...
/Peter
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