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Many will find this ludicrous... - another example

Posted By: Daniel Murphy
Date: Tuesday, 11 September 2012, at 2:31 p.m.

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

My post was based on the notion of rerolling whenever the RNG generated an unwanted doublet.

Right, and your numbers look fine, for a system which would produce 9.09% doublets.

finding that doublets appear only 60% as often as expected, and that non-doublets appear with the expected frequency.

That's impossible, so I think you (or he) mean that there didn't appear to be any bias for particular doublets or nondoublets or singlets; all doublets appeared to occur with about the same too low frequency, and all nondoublets with about the same too high frequency.

The method used in your initial post has non-doublets appearing more often than 30 times in 36.

Of course, as does your method and any that results in less than 16.66% doublets, overall. Reviewing some of the posts today, new and old, I did find a lot of estimates of the frequency of doublets in the red room:

"under 13%" in the small data set that prompted the investigation
"only 60% of what they should have been," which would be 10%.
9.4% -- The 27-9-2009 data, adjusted again to eliminate opening rolls
9.31% -- The 27-9-2009 data, incorrectly adjusted to eliminate opening rolls
9.22 -- Womack post 27-9-2009
"about 9.2%" -- Womack blog
9.192% - Petch, for a 630k dice test
"about 55%", which would equal 9.1666%
9.122% - Petch, for a ~84k dice test
"by about half", where exactly half would be 8.3333%
"60% fewer doubles," a misstatement, since that would only be 6.6666%

So, I used 8.33% because that's what I had seen in one post without reviewing the old discussion, and 9.22%, from the post that Michael recently linked to.

In 2009, there was speculation that the SHG was rerolling doublets sometimes, along the lines of your hypothesis. But after the SHG programmer popped in to acknowledge that there was a problem and it was being worked, I don't see where anyone ever explained exactly what the RNG was doing wrong.

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