Jim Segrave <address@hidden> wrote on 13/11/2007
22:51:14:
> The game is played out with the cube on 2, sometimes that leads to
a
> redouble/take with the cube on 4. Gnubg plays both sides optimally
> (from gnubg's point of view) and terminates a rollout of a game when:
>
> one side wins outright
>
> or
>
> one side doubles and the response is drop
>
> or
>
> the preset maximum number of moves has been rolled out, in which case
> the evaluation of win/lose gammon/backgammon is used to assign a
> result other than plus or minus 1/2/4/8 or whatever cube value might
> apply
>
>
> > 2- At the end of the trials, the computed "cubeless"
figures will
> > lead to a "cubeless" equity that will be translated
into a cubefull
> > equity via the janowski formula, right? In Mochy's example, the
W/G/BG%
> > are the "cubeless" results of the rollout, the CL is
the "cubeless"
> > equity and CF is comuted via Janowski formula?
>
> Yes, but during the rollout the cube value can change, so the
> approximated equity is multiplied by the current cube value (with
> allowances for a cube which is greater than the value needed to win
a
> match for non-money games)
Hi Jim, I think it just doesn't work like this. I give you
an example:
let's say I'm playing a money session and I do a full
cubefull rollout (no truncation whatsoever). Let's say that in 90%
of the trials, player 1 wins 1 point while in 10% of the trials, player
2 wins 1 points. In terms of w/g/bg - l/g/bg this makes 0.9/0/0.0 -
0.1/0.0/0.0. But what happens if, in the same situation, all the
10% of player 2 simple wins happens with the cube at 16 because of a series
of double/take happened in these trials ? I suspect it will still produce 0.9/0/0.0 - 0.1/0.0/0.0,
but a totally differest (estimated) cubeful equity (much more favorable
to player 2).
I've found this post on the list archive (look at the entire thread):
- a cubefull rollout directly estimates the cubeful
equity, the janowski formula is not used.
- w/g/bg - l/g/bg are computed using actual results
(number of simlpe, gammon and backgammon wins and losses), independently
from the cube value (at the monent of the win/loss). When the rollout
is truncated (db position or double/pass or max number of plies),
the cubeless eval result (w/g/bg - l/g/bg) is used as result for this
trial.
- the only meaningful figure to look at after a cubeful
rollout (and probably also after a cubeful evaluation) is the cubeful
equity. w/g/bg - l/g/bg may be more or less meaningless (and
the cubeless equity deduced from them too).
I don't know if I agree with Joern when he says that
w/g/bg - l/g/bg could even be removed from the output of any cubeful
rollout/eval.
For sure we should make it very clear that w/g/bg
- l/g/bg are not really reliable in cubeful rollouts and in cubeful
evals, when the position may lead to cube action, since they do
not tale into account the cbe value.
MaX.
P.S. According to Christian's and Joern comments, in case
of a double/drop, the eval w/g/bg - l/g/bg (cubeless) will be used as
result of the trial in order to compute the overall (cubeless, in a certain
sense) figures for w/g/bg - l/g/bg. But the cubeful equity of this
trial (used to compute the overall cubeful equity) would be +1, right
?