Rollouts

 Settlement limit

 From: Kit Woolsey Address: kwoolsey@netcom.com Date: 16 December 1997 Subject: Re: Value of the cube? Forum: rec.games.backgammon Google: kwoolseyELAvuJ.AM5@netcom.com

```> I'm reading the JellyFish manual and it says......
> The cube is only used for cashing or settling games, so cubes are
> never accepted. This is done to reduce the random error of the
> results. The game is cashed when Jellyfish's estimated equity exceeds a
> predefined settlement limit, set by the user. The default value of the
> settlement limit is 0.55. In most positions cubes can be taken with a
> cubeless equity higher than this, because the cube has value in
> itself. For this reason the player with the advantage gets to cash
> some positions which are takeable. But on the other hand he will
> sometimes lose equity by not doubling when the equity is close to 0.5,
> which is often correct. The default value is chosen in the hope that
> these effects will cancel each other out.
>
> So is the above statement about these effects canceling each other out
> not valid then or have I misunderstood somewhere?

In pre-Jellyfish days, suppose you had a position which you were very
interested in what the equity was -- say, whether it was a pass or a take.
How would you go about determining it?  You would roll the position out a
couple of hundred times by hand, and see what the total results were.

Since the cube is part of the game, you would have to take it into
account.  So if during the rollout you thought the guy who owned the cube
had a double you would have him redouble to 4 (he owned the cube at 2
originally, since it was a pass/take question), and if you thought the
other guy had a take you would have him take and continue the rollout
with the cube on 4.

The problem with this approach is that there might be a couple of 8 or 16
cubes in the rollout.  While if you are playing the position as a
proposition for money these high cubes are definitely a part of the
action, for the rollout purposes one or two high cubes can distort the

The generally accepted practice is to decide whether it is the double or
the take which is the question (on the first redouble).  If you judge
that is is a marginal redouble, you just continue the rollout with the
redouble having not been made.  On the other hand, if you judge that it
is a clear redouble but a marginal take, you assume that it was a pass
and score it up as a 2-point win for the redoubler.  This way, you avoid
large cubes.  The idea is that sometimes you will fail to redouble when
you should, but other times you will pass a redouble you should take.
Hopefully, the equity swings from these decisions will cancel out in the
long run.

When Jellyfish does rollouts with the cube in play, it is doing exactly
the same thing.  No doubles up to a point, and above that point it is
scored as double and pass.

Where does the settlement figure of .55 come from?  Good old trial and
error.  In fact when Fredrik first came up with the idea of rollouts with
the cube he guessed at a .50 settlement figure, and sent me a
beta-version to test out.  Rollouts of "known" positions convinced us
that the .50 figure was too low, and after a lot of experimentation it
appeared that .55 gave the most accurate results for most positions.  Of
course the user can make the settlement number what he wishes.

I feel that since for Jellyfish rollouts we can do a few thousand if
necessary (as opposed to the couple of hundred if doing it by hand) we can
afford some moderately high cubes, since the sample size should be large
enough to cut down on the luck factor.  Perhaps the user should be able
to set the cube limit -- then in the rollout the program allows the cube
to go up to that limit, and uses the settlement approach to make sure it
doesn't get any higher.  But that is a matter for the next version of
Jellyfish.

Kit
```

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### Rollouts

Advice  (David Montgomery, Apr 1996)
Cautionary tale  (Kit Woolsey, Sept 1995)
Combining rollouts  (Gregg Cattanach+, Dec 2003)
Confidence intervals  (Bob Koca, Nov 2010)
Confidence intervals  (Timothy Chow, May 2010)
Confidence intervals  (Gerry Tesauro, Feb 1994)
Cubeless vs centered-cube rollouts  (Ron Karr, Dec 1997)
Duplicate dice  (David Montgomery, June 1998)
How reliable are rollouts?  (David Montgomery, Aug 1999)
Level-5 versus level-6 rollouts  (Michael J. Zehr, June 1998)
Level-5 versus level-6 rollouts  (Chuck Bower, Aug 1997)
Positions with inaccurate rollouts  (Douglas Zare, Oct 2002)
Reporting results of rollouts  (David Montgomery, June 1995)
Rollout settings  (Lokicol+, Apr 2010)
Settlement limit  (Michael J. Zehr, Apr 1998)
Settlement limit  (Kit Woolsey, Dec 1997)
Settlement limit in races  (Alexander Nitschke, Dec 1997)
Some guidelines  (Kit Woolsey, Apr 1996)
Standard error and JSD  (rambiz+, Feb 2011)
Standard error and JSD  (Stick+, Oct 2007)
Systematic error  (Chuck Bower, Oct 1996)
Tips for doing rollouts  (Douglas Zare, June 2002)
Truncated rollouts  (Gregg Cattanach, Oct 2002)
Truncated rollouts: pros and cons  (Jason Lee+, Jan 2006)
What is a rollout?  (Gregg Cattanach, Dec 1999)

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