[EMAIL PROTECTED] wrote on
04/08/2008 03:14:19:
> 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 | | | |
> | |BAR| |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 intuitive (IMHO).
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.
MaX.
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