Safe Harbor Games Dice
Posted By: W Womack
Date: Sunday, 27 September 2009, at 7:59 a.m.
In the thread "Grid Gammon Charging" Neil Robins made a comment regarding the number of doubles on SHG games he had analyzed. Since I play on SHG I was curious about this so I did a little analysis of my own. I took the files from the last 118 matches I have played on SHG and parsed the rolls from the mat files. This gave a data set consisting of 25,470 individual rolls.
Given the relatively large sample size I would expect that if the dice where essentially random that the frequencies would be very close to the expected values. To test this assumption I generated a set of 25,470 rolls using the integer generator at Random.org and performed the same calculations on these data as on the SHG data.
Following Neil's lead I looked at the double frequency. The expected frequency of doubles is 16.6667% (6/36). The SHG data set contained 2349 doubles, only 9.22%! The random.org data set contained 4234 doubles, 16.6235%. This low number of doubles is also reflected in the average pip count for the SHG data set which is 7.649 rather than the expected 8.1667 (Random.org set was 8.1654).
Looking at non double rolls is a little tricky given the double results. To do this I eliminated doubles from consideration. The mat files do not distinguish between the two dice, so 12 and 21 for example are the same roll. For the SHG set the most common non double roll occured 1598 times and the least common 1460 times. There were a totat of 23,121 non double rolls, therefore the most common non double had a frequency of 6.9115% and the least common 6.3146% vs the expected of 6.66667%. The same analysis on the random.org data gave a range from 7.1341% to 6.4278%. While a formal statistical test might reveal an issue here it appears that the data sets are comparable and when considered without doubles the SHG dice behave like true random dice.
Below are the roll tallies for the SHG data:
Roll Total 11 374 21 1510 22 424 31 1542 32 1535 33 371 41 1598 42 1544 43 1537 44 395 51 1460 52 1566 53 1580 54 1535 55 385 61 1586 62 1548 63 1481 64 1591 65 1508 66 400 Grand Total 25470
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