> Hi folks, >
> GNU Backgammon Position ID: 7wAAALZzhgUAAA >
Match ID : cIlmAAAAAAAA > +24-23-22-21-20-19------18-17-16-15-14-13-+
O: xxx > OO | O O
X | 0 points > OO | O O
| > OO | O O
| > O | O
| > O |
| > |
|v 3 point match (Cube: 1) > |
| > |
| > | X
X | |
| > | X X X
X | | X
X | Rolled 51 > | X X X
X | | X
X | 0 points > +-1--2--3--4--5--6-------7--8--9-10-11-12-+
X: yyy >
> 1. Rollout 12/6
Eq.: -2.018 > 0.000 0.000 0.000
- 1.000 0.671 0.000 CL -2.018 CF -2.018 > [0.000 0.000 0.000 - 0.000
0.002 0.000 CL 0.004 CF 0.004] > Truncated cubeful
rollout (depth 8) with var.redn. > 216 games, Mersenne
Twister dice gen. with seed 834643698
> and quasi-random dice > Play: world class
2-ply cubeful prune [world class] > keep the first 0
0-ply moves and up to 8 more moves within equity 0.16 > Skip pruning for
1-ply moves. > Cube: 2-ply cubeful
prune [world class] >
> How can the equity be more than -2?
It's a normalized equity (EMG), this kind of quirks
can appear ...
J.Bagai has once proposed a new way of normalizing
equities that can be more coherent, but it's way too complicate and not
I proposed my own one (don't use a linear extrapolation
between loss and win, but take a polyline with points BGloss,Gloss,loss,win,Gwin,BGwin).
Much simpler and intuitive, but with a minor drawback, linearity:
at the same score, a 1%MWC error has a normalized equity which may not be the
double of the one of a 0.5%MWC error. But hey, after all, this stuff is not supposed
to be linear.
I think D.Zare has proposed the most interesting method
(as often ?): normalize with respect to the magnitude of the error
of playing an opening 31 (at this score) as 65 63. This is very interesting
for the evaluation of the magnitude of an error, but is unrelated to the notion
of absolute equity.
I would say that D.Zare method is best to compute
error's equities (from errors MWC), while my one is best for absolute equities (from MWC).
BTW, my method would soulve your issue (i.e. having
something < than 2 as normalized equity, as expected).
I can send you a small excel file with a drawing and
the formula for your example.