Re: [Bug-gnubg] Errors in evaluation of races with backgammons

[Philippe Michel]

On Mon, 27 Feb 2012, Joseph Heled wrote:

> Using some python trickery it is possible to get the true backgammon
> figure. "true" here means that you always make the optimal move which
> minimises the probability of backgammon.  The number is 40615026 /
> (36^5) = 0.6716982730973429
>
> Now, nngnu gives those numbers for plies 0 to 5
>
> 0ply  0.6775242686271667
> 1      0.6775177717208862
> 2      0.6775177717208862
> 3      0.6775176525115967
> 4      0.6717002391815186
> 5      0.6716980934143066
>
> which I am happy about, but it seems that *there is* some problem in
> gnubg, which gives different numbers for different plies.

This is because the pruning phase in gnubg is using only the race pruning 
net output (plus basic sanity checking). Adding the backgammons 
post-processing leads to the same numbers :

        Win     W(g)    W(bg)   L(g)    L(bg)   Equity    Cubeful
static: 1.000000 1.000000 0.677524 0.000000 0.000000  +2.677524  +2.677524
 1 ply: 1.000000 1.000000 0.677518 0.000000 0.000000  +2.677518  +2.677518
 2 ply: 1.000000 1.000000 0.677518 0.000000 0.000000  +2.677518  +2.677517
 3 ply: 1.000000 1.000000 0.677518 0.000000 0.000000  +2.677518  +2.677517
 4 ply: 1.000000 1.000000 0.671700 0.000000 0.000000  +2.671700  +2.671701
 5 ply: 1.000000 1.000000 0.671698 0.000000 0.000000  +2.671698  +2.671699

I will commit the fix.