Re: [Bug-gnubg] More cube analysis oddities

[Joern Thyssen]

On Fri, Mar 21, 2003 at 01:44:47PM -0300, Albert Silver wrote
> I downloaded the latest build of March 20th and redid the rollouts
> exactly as the last time with 1296 trials, full rollout, 0-ply checker
> play, and 1-ply cube decisions, Jacoby on). The results were not really
> better, but Douglas Zare may have pointed out the problem. I can't post
> the detailed results as none of the export functions will carry the Hint
> window's contents, nor does the Copy button work. Basically it says:

> Cubeless rollout equity: +0.875
> 
> Cubeful equities:
> 
> 1. Double, take               +0.944
> 57.8% 37.9% 10.2% - 42.2%
> 
> 2. Double, pass               +1.000  +0.56
> 3. No double          +0.888  -0.55 (a rounding off problem I guess)
> 65.4% 46.7% 10.0% - 34.6%
> 
> Proper Cube action: Double, take

Can you post the position and match ID, please?

Disclaimer: I'm not an expert on rollouts, but I did program large parts
of the rollout code, so here's my view (feel free to post it on
gammonline):

Playing with Jacoby rule may destroy no-double part of the rollout
because gnubg may play some arbitrary move on the backgame side because
it thinks that no matter how it play, it's "double, pass" on the next
roll. 

Note the huge difference between the "double, take" and "no double" game
winning percentages: this is a major indication of the problem I
describe above. You can even see this problem in gnubg's 2-ply
evaluations where you can get ridicolous wins and gammon percentages as
gnubg selects some arbitrary move because it think it's "double, pass"
anyway.

If you compare with the rollout with Jacoby off you'll see that the
gwc's are much closer, because now many positions that were "double,
pass" are now "too good", so the game continues.

Try doing a cubeful rollout with *cubeless* chequerplay. This could give
better moves in the Jacoby "no double" rollout (yes, you can actually do
that... although I'm a bit afraid that the variance reduction may cause
problems, since gnubg will force cubeful evaluations for the variance
reduction part (since they're needed to reduce variance of the cubeful
equities), and these will of course display the same problem as I
describe).

The cubeless equity is calculated without Jacoby rule using the
percentages from the "no double" rollout:

2* 0.654 - 1 + (0.467 - 0 ) + (0.100-0) = 0.875

If you do the same with the "double, take" gwc's you get 0.635. This
gives a marginal take using Chuck's number (+0.64) based on Janowski's
formulae.  This also makes sense as gnubg's formulaes are based on
Janowski's formulae! Chuck's calculation is what I would call a "0-ply"
cubeful evaluation, so the rollout will of course give a different
result since market losers and market gainers are taken into account.
But the two numbers are not very far. A cubeful "double, take" equity of
+0.944 is what I, at my intermediate level, would call a close take.

If you want the "true" cubeless equity you should do a cubeless rollout
with cubeless chequerplay.

I hope this helps!

Jørn