Re: [Bug-gnubg] new contact net

[Joern Thyssen]

On Tue, Jun 10, 2003 at 11:25:53AM +0100, Ian Shaw wrote
> 
> 
> > -----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

No, I calculated:

sqrt( p * (1-p) / n )

In an earlier mail in yeserdays correspondance I derived the p*(1-p)
formula.  This formula is symmetric in p and (1-p) as you would expect
(the same SD for both winner and loser).

Since p ~= (1-p), we get sqrt(p^2/n) = p sqrt(1/n) ~= 0.5 * sqrt(1/n).

Jørn