Rollouts

 Level-5 versus level-6 rollouts

 From: Michael J. Zehr Address: michaelz@michaelz.com Date: 12 June 1998 Subject: Re: Rollouts for double/no-double when JF misevaluates equity Forum: rec.games.backgammon Google: 3581422A.ECF96A91@michaelz.com

```> Suppose one wants to look if X has a double in the following position :
>
>   +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
>   | X              O |   |    O           X |
>   | X              O |   |    O           X |
>   |                O |   |    O           X |
>   |                O |   |    O           X |
>   |                O |   |                X |
>   |                  |   |                  |64
>   |                  |   |                  |
>   |                  |   |                  |
>   |                  |   |                O |
>   |                  |   |                O |
>   |    O     X  X  X |   |    X           O |
>   |    O     X  X  X |   |    X           O |
>   +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
>
>   X on roll
>
> 12960 JellyFish level 5 rollouts give :
>
> centered cube :    equity = 0.68
> O holds a 2 cube : equity = 0.37*2
>
> This looks like a double, but according to the rollouts, X cubeless
> equity is 0.48 and according to the level 5 evaluation 0.37 only.
>
> So, is it possible that the rollouts underestimate the value of cube
> access for X, since he is only 0.07 away from a cash instead of 0.18 ?
>
> A rollout with a cash point of 0.44 instead of 0.55 (and the same seed
> than before) to try to take care of this gives a centered cube equity
> of 0.79, so it would no be a double (0.79 -> 2*0.37 ; the equity with
> O holding the cube should be the one with the normal cash point, since he
> won't be able to redouble before the position has changed substantially).
>
> Should one really take care of these errors in JF static evaluation
> in double/no-double rollouts ?
> What would be the appropriate cash point ? 0.55 ? 0.55 + L5 evaluation
> - rollouts' cubeless  equity ? something inbetween ?
> Should one check if the evaluation is more or less wrong for the market
> losers vs. the more sterile rolls ?

The double/no-double question is one of the hardest ones to answer in
backgammon today.  This problem is a subset of the class of problems in
which you have a decision to make this turn, and if you choose not to
take a particular action, you have the same decision to make next turn.
(Running off an anchor is another such category of problems.)

If you do your analysis by hand then you can try different strategies
(don't double until contact is broken, or don't run off the anchor until
either forced or a double is rolled) and compare them.  However the best
strategy is likely to be between the two extremes.

When using a computer to do the analysis it gets tricky for exactly the
reasons that Philippe mentions -- you can set up a position in which
you've forced the computer to make a particular decision on this turn,
but you can't easily force the computer to make the decision you're
trying to analyze on the second turn.

This is how I would analyze such a position using Jellyfish:

I always like to start with a level 6 rollout.  There's just too big of
a difference between level 5 and level 6 for me to want to start with
just a level 5 rollout.  The number of games to pick depends on how
patient you are and how fast your computer is. <grin>  It also depends
on how close the decision is.  A 1296 rollout usually gives you a
standard deviation of about .01 in equity, equivalent to about .5% in
winning chances.

With the rollout equity you can sometimes answer the double/no-double
question without doing much more analysis. 216 level 6 rollouts (seed 1)
gives an equity of .508 with a standard deviation of .023.  This is
quite a bit better than the level 7 evaluation of .400.  Level 7
evaluation also gives a volatility of .164.  If the equity plus the
volatility is over a certain amount (in the .60 range) then it's almost
certainly a double.

If a close answer were acceptable, I'd call it a double/take at this
point.  If a more accurate answer were needed, there are a number of
next steps one could take.

One option is a L5 rollout with the cube.  Before checking the cube
numbers, compare the cubeless equity against the L6 rollout.  Philippe
indicates that L5 gets a cubeless result of .48 which is consistent with
the L6 numbers (given the standard deviations) so L5 is probably playing
the checkers properly.

Next we might try to see if L5 is handling the cube properly in the
short term.  Give X and O various rolls, check the evaluation, then do a
rollout.  In this position JF might correctly evaluate the position
after X closes the bar point, but might incorrectly evaluate the
position before there are builders threatening the bar point.  If the L5
evaluation and the rollout are close next turn, then we can have some
confidence in the L5 cube equities from this position.  If they aren't
close, we might have to adjust the settlement limit.

I wouldn't suggest the settlement limit by the full amount of the
evaluation and rollout equity difference, however.  Sometimes X rolls
poorly to start and will be cashing some turns in the future where we
don't know if JF is under or over evaluating X's position.  Perhaps
adjusting the settlement limit by about half the difference will give an
accurate answer.  (How certain are you that the .55 settlement limit is
right to begin with?)

Finally you need to take into account the human aspects.  Has your
opponent dropped a similar position in the past?  How accurately do you
think he or she will play the position?  (I expect there's more skill
required to play O's side of this game than X's.  O has to carefully
balance leaving shots with bringing down builders to make points.)

The double/no-double decision is close here, but I'll agree with the
first L5 rollout -- double/take.

-Michael J. Zehr
```

### Rollouts

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)