Backgammon Rollouts

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 results. So, what can we do about this? 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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