RE: [Bug-gnubg] Analysis of race rollouts

[David Montgomery]

> > 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.  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.

---

Hmmm, re-reading your remark, Joseph, I get the feeling I've missed
some important context for this discussion.  I'm talking about 
2-sided play using a 1-sided db, but perhaps you are talking about
something else.  I'll go back and read the archives.

David