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Many will find this ludicrous... - another example

Posted By: Taper_Mike
Date: Tuesday, 11 September 2012, at 9:25 a.m.

In Response To: Many will find this ludicrous... - another example (Daniel Murphy)

–

I don’t know that much about it. My post was based on the notion of rerolling whenever the RNG generated an unwanted doublet.

Michael’s post reports finding that doublets appear only 60% as often as expected, and that non-doublets appear with the expected freqeuncy. I do not know how to interpret this other that meaning non-doublets appear 30 times in 36. This forces me into the reroll assumption, because doublets cannot be allowed to appear the other 6 times in 36. Doublets should appear in 60% of the remaining 6, and the remainder are rerolled.

My initial post used 50% instead of 60%. Recalculating with 60% does not give the 9.22% figure you report for doublets.

100% Base

Non-doublet: 30/36 = 5/6
Wanted doublet: 60% of 6/36 = (6/10) * (6/36) = 1/10
Unwanted doublet (reroll): 40% of 6/36 = (4/10) * (6/36) = 1/15

93% Base = 14/15 (with the 15th roll a discarded doublet)

Effective odds of doublet = (1/10) / (14/15) = 15/140 = 10.7%
Effective odds of a non-doublet = (5/6) / (14/15) = 89.3%

Since this does not give 9.22% as the effective rate for doublets, my initial assumption concerning discarded rolls must be wrong.

The method used in your initial post has non-doublets appearing more often than 30 times in 36. One way to achieve your result is to assume that when an unwanted doublet appears, the dice are rerolled until a non-doublet comes up.

Perhaps that is how they do it.

Mike

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