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## Re: [Bug-gnubg] Alternative weights files

**From**: |
Joseph Heled |

**Subject**: |
Re: [Bug-gnubg] Alternative weights files |

**Date**: |
Thu, 20 Sep 2012 11:05:20 +1200 |

You are right, I was slightly off. It is 1/2 and not 2/3.
The single experiment is two matches (with reversed dice).
The possible outcomes are XX, (X wins both), OO and XO (which is the same as OX.
I assign a +1 for XX, zero for XO and -1 for OO
That way, under the null hypothesis P(XX) = 1/4, P(OO) = 1/4, P(XO) =
1/2 the mean is zero and the variance is 1/4*1^2 + 1/4*(-1)^2 = 1/2.
The variance of N matches is N* (1/2) and so the std is (N/2)^0.5
-Joseph
On 20 September 2012 08:35, Philippe Michel <address@hidden> wrote:
>* On Wed, 19 Sep 2012, Joseph Heled wrote:*
>
>*> your test statistic is 117*-1 + 262*0 + 121*1 = 4*
>*> the standard deviation is (500 * (2/3))^0.5 = 18.25*
>
>
>* This doesn't seem right (why 2/3 ?) and this is more than the*
>* (1000 * 0.5 * (1 - 0.5))^0.5 = 15.8*
>* from the dumb rollout.*
>
>* On a second look I think it is :*
>
>* E(x) = (close to) 0*
>* E(x^2) = 121 + 117*
>
>* for a standard deviation of 15.4 or a little less.*
>
>* Duplicated dice would then be only a small improvement (at least in this*
>* example).*

**Re: [Bug-gnubg] Alternative weights files**, *(continued)*
**Re: [Bug-gnubg] Alternative weights files**, *Thomas A. Moulton*, `2012/09/18`
**Re: [Bug-gnubg] Alternative weights files**, *Guido Flohr*, `2012/09/19`
**Re: [Bug-gnubg] Alternative weights files**, *Michael Petch*, `2012/09/19`
**Re: [Bug-gnubg] Alternative weights files**, *Philippe Michel*, `2012/09/18`
**Re: [Bug-gnubg] Alternative weights files**, *Joseph Heled*, `2012/09/18`
**Re: [Bug-gnubg] Alternative weights files**, *Philippe Michel*, `2012/09/18`
**Re: [Bug-gnubg] Alternative weights files**, *Joseph Heled*, `2012/09/18`
**Re: [Bug-gnubg] Alternative weights files**, *Philippe Michel*, `2012/09/19`
**Re: [Bug-gnubg] Alternative weights files**, *Joseph Heled*, `2012/09/19`
**Re: [Bug-gnubg] Alternative weights files**, *Philippe Michel*, `2012/09/19`
**Re: [Bug-gnubg] Alternative weights files**,
*Joseph Heled* **<=**