[Bug-gnubg] Problems with stopping rollouts when STDs are small enough

[Philippe Michel]

One of the available criteria to end a rollout is when standard deviations 
are small enough. For instance, it could be :

Stop rollout when STD's are small enough
After 1296 games, rollouts will stop if the STDs are small enough.
Rollouts can stop when the ratio |STD/value| is less than 0.0040 for every 
value (win/gammon/backgammon/...equity)

I think there are two problems with the way this is curently implemented :

- the "ratio ... for every value" works poorly when one of the values, 
usually backgammons for one of the players, is small but not zero. All 
other STD/value ratios are roughly identical but that of this irrelevant 
(equity-wise) term can be 10 or 20 or 30 times larger and cause the 
rollout to take much more time.

I'd suggest we check only the equity. If it is accurate, the single 
win/gammon/backgammon numbers will be as well if they are any significant.

- if one doesn't care for the individual kind of outcomes, the STD/value 
ratio doesn't seem pertinent. Do we really want to know equities around 
0.2 with an accuracy five times higher than those around 1 for instance ?

The simple STD on a 1-cube, whatever the equity, seems a better criterion.