Backgammon Rollouts

Rollouts

Tips for doing rollouts

From:   Douglas Zare
Address:   zare@math.columbia.edu
Date:   26 June 2002
Subject:   Re: rollout tips please
Forum:   rec.games.backgammon
Google:   3D1A3598.A4AED0C1@math.columbia.edu

The errors of a rollout come from four things: First, the bot may misplay unequally from the different sides. Second, if the rollout is truncated, the evaluations used at the point of truncation may be wrong. Third, there is still luck involved in the rollout, since variance reduction is not perfect. Fourth, the results may be misinterpreted. If you believe that the position is easy to play, 2-ply may even be overkill. On the other hand, some positions are tricky to play from one side and easy to play from the other. You need a very high level of play to get an accurate rollout in a position of one-sided errors. 2-ply might be sufficient, and it might not, but it should be reasonable if your own play is comparable to 2-ply's play. Some positions are easy to evaluate, and some are strange enough to warrant rollouts. If you don't trust the evaluations of positions with early primes, and are doing rollouts, truncation might be accurate if you trust the evaluations of the likely positions after a few rolls: Prime versus prime, crashed positions, position with several primed checkers, etc. Would you trust the evaluations then? I'm not sure, so I would tend to avoid using truncated rollouts then. On the other hand, in some stages of a holding game, you may know that either a shot has been hit or the game has turned into a race after a few moves. Then you may be able to trust truncated rollouts. Some versions of gnu have had inaccurate error estimates. Snowie apparently does in match play and when the cube is higher than 1. However, these bugs aside, you should look at the error estimates and compare them with the difference between the best action and the second best action. You should also compare the error estimates with the size of what you consider an acceptable mistake. For example, I really don't mind if I make a 0.050 take/pass error. If the best plays are too close to distinguish, then if the confidence interval is wide you should do more rollouts, but if the confidence interval is small you should accept that there is not a big difference between the plays, and move on. Finally, the results of the rollout may be interpreted by applying something like Janowski's formula. This might give an accurate assessment of cubeful equity given the cubeless bg/g/w breakdown, but it might be systematically inaccurate when you have a position with unusually good or bad opportunities to recube efficiently. In those situations, cubeful rollouts might be best, assuming that you trust the cube actions during the rollout... but there are simple positions in which Snowie rollouts reach the wrong conclusion no matter what settings are used. Also, I am highly sceptical of Janowski's formula when the position may be too good to double. Anyway, remember that rollouts tell you how the bot plays against itself, not how you play against your opponent, and not how perfect play does against itself. Douglas Zare

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