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BGonline.org Forums
Answering Paul Weaver: 7777 vs. 7776
Posted By: Jason Lee
Date: Saturday, 23 December 2023, at 4:08 p.m.
Paul Weaver asked: "would a rollout of 7777 trials be more accurate, on average, than a rollout of 7776?"
Answer #1: Yes... in theory. On average, more games in a rollout means more accurate results. A difference of one game is probably not measurable, so this is more theoretical than practical.
Answer #2 No... if we use GNUBG. This bot uses quasi-random dice to do rollouts. If the number of trials you ask for is a multiple of 1296, then GNUBG will ensure that each instance of the next two rolls is represented equally. For example, suppose we ask for 7776 = 36 * 36 * 6 trials. Then there will be 6 trials of the two-roll sequence 11, 11. There will be 12 trials of the two-roll sequence 44, 36. There will be 24 trials of the two-roll sequence 65, 53. If the number of trials is a multiple of 46656 = 36 * 36 * 36, then each three-roll sequence will be equally represented. We shall not talk about 1679616 = 36 * 36 * 36 * 36. If we ask for 7777 trials, some sequence will be overrepresented, introducing a bias.
Answer #3 Maybe... if we use XG. I looked in the XG documentation to see if it uses quasi-random dice in rollouts and couldn't tell. If quasi-random dice are not used, then my answer reverts back to #1.
JLee
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