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 BackgammonBackgammon and variants. Backgammon Links You are not allowed to post messages to this board. Minimum level of membership required for posting on this board is Brain Pawn. Mode: Everyone can post
15. July 2010, 12:47:41 Subject: Re: Opening rolls for Brainking dice Modified by wetware (15. July 2010, 12:53:16)  [cross-posting from the "Feature requests" board, where a discussion developed recently] I wish the system made it easier to gather the data that would demonstrate the severity of this problem. As I've said elsewhere (I think), it could also help pinpoint when the problem began (or was it always this way?), which should help identify what changed to cause it. I also wish the problem occurred 100% of the time, which would make it impossible to dismiss. As it is, we have only the beginnings of statistical support for our claim, and gathering the aggregate data that would provide more solid support is a daunting task...for us the members. Fencer is quite correct about the groundless wailing over poker or dice cheats. There's plenty of that online; such complainers are easy to find, and the vast majority deserve our scorn and satire. But the genuine exceptions (in online poker especially) that have come to light should give one pause. Hats off to those who stood their ground in such cases, labored to gather the data, and revealed the truth at last. (added comment Wednesday evening / Thursday morning): I plan to make one last good-faith effort to present some useful data. I plan to examine all of my backgammon (but no variants) games stored here from 2009--that's 13 matches, and a total of 137 games in which at least 2 rolls took place. I have no reason to believe that that year is appreciably better or worse than any other year of mine. I'm sorely tempted to separately track the opening rolls that I "won" and "lost", but I don't plan to do so for this exercise. If I'm understanding the situation correctly (and there are good "numbers" people here who will be able to correct me if I'm wrong), the responder's roll should theoretically match the opener's roll 1 in 18 times (or 5.555_ %), on average. I'm also going to report the percentage of responder's rolls where both dice differ from the opener's roll. Theoretically, I think that should happen 4 times in 9 (or 44.444_%), on average. But I think the actual observed value is going to shock and convince even the most diehard skeptics here. Average expectation of opener's and responder's both dice exactly matching out of 137 played = 7.6111_ games. Observed number=38 games (27.737%) That's about 5 times the expected frequency! Average expectation of responder's dice both differing from opener's dice out of 137 played = 60.888_ games. Observed number=28 games (20.438%) That's less than half of what's expected. If I feel energetic, I'll analyze my 124 matches from 2008!  15. July 2010, 16:57:09 Subject: Re: Opening rolls for Brainking dice wetware: Good work. There certainly is a suspicious pattern. Your sample size is still quite small, however. What is needed now is a statistical analysis of the probability that this distribution could occur randomly. I.e., is it within a couple of standard deviations of the norm, or is it a one in a billion chance? 15. July 2010, 17:06:51 Subject: Re: Opening rolls for Brainking dice PS maybe I don't understand what you are tracking here. Can you describe exactly what you are looking for? As I understand it, you are comparing the two dice of the first roll of the game, i.e. of the first player to move, with the two dice on the next roll, i.e. the first roll of the second player to move. Are you counting situations in which the same dice occur, but in a different order, as a match or non-match? The probability of the same two dice occurring in the same order on the second roll is 1/36. However, the probability of the same two dice occurring in any order is 2/6 x 1/6 = 1/18, as you observe. 15. July 2010, 17:18:55 Subject: Re: Opening rolls for Brainking dice Modified by Resher (15. July 2010, 17:19:27) alanback: I don't think we can distinguish between the two situations (ie same order match v different order match) as the game records the order the dice were played rather than the order they were rolled. I've also downloaded my 2009 BG games and am working on the same stats as Wetware has produced, to increase the sample size. 15. July 2010, 17:57:27 Subject: Re: Opening rolls for Brainking dice Resher: Too bad, as it would probably be more meaningful to measure only the same order case. Still, based on your analysis, there does seem to be something odd going on here! 15. July 2010, 18:07:17 Subject: Re: Opening rolls for Brainking dice alanback: random.org has a great dice roll system... 15. July 2010, 18:12:00 Subject: Re: Opening rolls for Brainking dice Orlandu: Yes. Dailygammon.com uses random numbers from random.com 15. July 2010, 17:31:06 Subject: Re: Opening rolls for Brainking dice Modified by Resher (15. July 2010, 18:31:58) alanback: I've just tested Wetware's data against a Binomial distribution with n=137, p=1/18. I think getting 38 double matches is more than 11 standard deviations away from the expected number! #sd's = [38-np]/sqrt[np(1-p)] = 11.33 15. July 2010, 18:17:39 Subject: Re: Opening rolls for Brainking dice Resher and Alan: Thanks, guys! I am now planning to conduct a similar review of my 124 matches from 2008. Expected completion: some time this weekend. Alan: I didn't care about the order of the dice for these purposes. (I.e., I considered 52 and 25 to be a match.) Another oddity noticed during review, but not yet reported: the "misses" show a strong tendency to be "near-misses". For example, if an opening roll of 42 is not exactly matched by responder's roll, the responder's roll will show excessively high occurrences of 52, 43, 41, or 32. That is to say: even when you do manage to miss, you're too often "off by 1". The most extreme outlier was a match with Hrqls (Backgammon (Hrqls vs. wetware) ), in which 9 games out of 14 were exact matches, and the remaining 5 non-matches were all of the "off by 1" variety. Note: I'm inclined to consider 1 to be "next" to 6. I think it's reasonable, especially if some "remainder" function is at play in the dice generation routine(s), as is often the case. 15. July 2010, 18:29:09 Subject: Re: Opening rolls for Brainking dice Modified by Resher (15. July 2010, 18:30:28) wetware: Just finished looking through my first 100 BG games from 2009 and: Number of games where responder's first roll matches on both dice = 27 (expected number = 6, so more than 9 sd's away) Number of games where responder's first roll differs on both dice = 16 (expected number = 44, so more than 5 sd's away) 15. July 2010, 18:39:12 Subject: Re: Opening rolls for Brainking dice Resher: Thanks so much for the SD calculations! I knew that was critical for us to express just how extreme these results are, but I've forgotten too much of my statistics coursework and tools. FYI: my next data set (matches from 2008) will be ~10 times the size of the results I reported from 2009. |
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