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## RE: [Bug-gnubg] new contact net

 From: Ian Shaw Subject: RE: [Bug-gnubg] new contact net Date: Tue, 10 Jun 2003 11:25:53 +0100

```
> -----Original Message-----
> From: Joern Thyssen
> Sent: 10 June 2003 09:49
> To: GNU Backgammon Bugs

> > > For 500000 7pt matches, the new net is 50.59% - 49.41% against the
> > > current one.
> > That's a lot of matches. Using our hard-won knowledge of
> yesterday, I
> > calculate the SD as 0.0001%, so the 99%CI is about 0.0003%. (I'd say
> > that's significant enough not to bother with the luck
> analysis, Jørn.)
>
> Hmm, I get a std.dev of 0.1% ( 0.5/sqrt(500,000) ), and a 95%
> CI of +/-0.2%.
>
Aargh! I thought I had this sussed.
I calculated SD = SQRT(0.5059 * 0.4941)/500000 = 0.0001
I missed out the root of n, so should have done: SD = SQRT(0.5059 *
0.4941/500000) = 0.0707

You have calculated SQRT(0.5059/500000) = 0.0010
But this gives a fractionally different result if we calculate using the
losses: SQRT(0.4941/500000) = 0.0099. This discrepancy would increase as the
score favours one side. Surely the SD should be the same if we are simply
looking at the same result from two viewpoints. It doesn't make sense to have a
narrower 95%CI for the loser than the winner.

--Ian

```