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BGonline.org Forums
Safe Harbor Games Dice
Posted By: Jim Borror In Response To: Safe Harbor Games Dice (W Womack)
Date: Monday, 28 September 2009, at 12:40 a.m.
First, let me commend you on your volunteering to do this analysis.
I would point out though, that in statistics, the context under which the data is collected is an extremely important piece of information which evalulating the validity of the data. In particular, was there any bias in which matches were used for the data?, Was the sample size of the matches sufficiently larget to give a more accurate distribution?
From your statement, you said you took all the matches you player over a certain period, so I think that satisfies that the matches were not chosen in a biased manner.
But, the length of the matches is a very important factor in measuring distribution. For instance, very short matches (1pt) tend to be way off the distribution curve because the number of rolls is so small. Much longer matches ( and thus more rolls) give a more effective sampling of the dice rolls. I'm estimating at this point, since I don't have all the data, but 118 matches comprising 25,470 rolls means approximately 109 turns per Match. This strongly suggest matches of about 3 to 4 games, which I believed you verified elsewhere, which suggest relative short matches of 3 to 4 pts max.
Since that is the average, what we don't know is how many matches were less than 3 points and how many were more 4 points. As I mentioned above, much longer matches - 200 to 400 matches - would give clearer representation of the data. If the majority of the matches you played were on the shorter side - then my experience has been that the results are less representative than if you had captured longer matches. Only you know what the length of the matches were, so I certainly would be interested in that information.
Also, taking into account that you are actually measuring smaller snapshots many different RNG implementations (each different player would be at the different point in the random cycle), then I think a larger sampling size would be warranated, than just measuring a single players 25,000 rolls.
My personal preference for sampling is a 100,000 rolls or more, and since I can do it, I have modified the backgammon code on SHG and placed a copy in the Test lobby, that will generate 100,000 rolls of two die using the same algorithm we use for dice rolls. For anyone sitting on the left side of the table, once they start a game, it will trigger the code to generate a file - randomdice.txt under the c:\program files\safeharborgames.net\shg installation\savfiles directory. Please feel free to take advantage of this if you like, and run an analysis on that file.
Jim
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