Re: [Bug-gnubg] Analysis of race rollouts

[Joern Thyssen]

On Thu, Oct 31, 2002 at 10:47:02AM -0800, David Montgomery wrote
> > > But one-sided racing databases with the probability distribution
> > > of rolls to bear off *can and do* make desperation plays, if you
> > > choose plays by convolving the two distributions.
> > > 
> > 
> > But I am computing the probability distribution by playing out each side 
> > seperatly, ignoring desperation. After that it is too late.
> 
> Here's an example:
> 
> O has single checker on 6-point.
> X has one on the 1, three on the 4, and one on the 6.
> X is on roll with a 21.
> 
> I don't have a db handy, but I assume that the mean roll minimizing
> move is 1/off 4/2. 

Yes, you're right:

After 1/off 4/2:
Average: 2.792 (std.dev. 0.628)

After 1/off 6/4:
Average: 2.861 (std.dev. 0.771)

> Nonetheless, the single sided db can figure out
> that 1/off 6/4 (the "desperation" play) is the right move.
> 
> The relevant probabilities:
> 
> O off in 1: .75
> O off in 2: .25
> 
> 1/off 4/2 off in 1: 1/36
> 1/off 6/4 off in 1: 3/36
> 
> So 1/off 4/2 wins 1/144 and 1/off 6/4 wins 3/144, and 1/off 6/4
> is the right play, determined using only single-side probabilities.

Good example :-)

Jørn

-- 
Joern Thyssen, PhD
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