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 From: Jim Segrave Subject: Re: [Bug-gnubg] Question About Rollout Date: Tue, 13 Nov 2007 22:51:14 +0100 User-agent: Mutt/1.5.13 (2006-08-11)

```On Tue 13 Nov 2007 (11:14 +0100), Massimiliano Maini wrote:
> 13/11/2007 09:53:12:
>
> > Hi Mochy,
> >
> > the winning chances reported by a rollout are in a sense cubeless. What
> > actually goes on is the following. If a game is played to the end the
> > actual result is recorded, i.e. 1 lost backgammon counts as one game in
> > that column. However, many games are truncated, either by using the race
> > database, or at cash point. In these cases the evaluation values at the
> > truncation point is added to the individual columns. For example,
> > suppose that you double out when winning 60% games and 40% gammons. Then
> >
> > 0.60 0.40 0.00 - 0.40 0.00 0.00
> >
>
> Hmmm I'm confused:
>
> 1- When you say "cubeless", do you mean that the game will be truncated
> right after the very first double decision, if any? I understand your
> example of a double/pass, but what about a double/take situation?

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)

> > > Rollout details:
> > > Centered 1-cube:
> > >   0.669 0.146 0.002 - 0.331 0.078 0.003 CL  +0.405 CF  +0.621
> > > Player player owns 2-cube:
> > >   0.670 0.152 0.001 - 0.330 0.077 0.003 CL  +0.854 CF  +0.574
>
> 3- Any idea why a simple "full cubefull rollout" approach is not
> implemented ?

> I mean letting gnubg play against himeself cubefull and record the
> outcome.

It does put the cube in play during rollouts

> I suspect this comes from the fact that its result would not be a W/G/BG%
> but more an equity (for money) or a MWC (for match), but hey, these
> are what matters ...
> Another reason is that the current method, truncating at double decisions,
> should/could "reduce the variance" (provided the evaluation is good).

If you set up a position where one player should have doubled and the
other should have dropped, the rollout goes very quickly, since for
all but the awful rolls, the stronger position doubles on the
following roll and, unless the position has noticably improved for the
trailing player, it's still a drop and that trial is completed.

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