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Two questions / challenges appropriate to this thread

Posted By: Chuck Bower
Date: Friday, 26 December 2014, at 4:39 p.m.

In Response To: Revised Baffle Box Rules--you know better (Phil Simborg)

1)

A) Roll a single precision die through a Simborg box (of your choice). Roll a second die through the box, dropping it vertically but at a random location (in terms of the rectangular box opening). Call P(U) the (Unintentional) probability of the second die changing the first die's value.

B) Begin as in A (rolling the first die) but then (still dropping vertically) choose an entrance point so as to maximize the chances of changing the first die. Call the expectation of this Intentional change P(I).

C) What value P(C) should one choose for a money-wagered 'Contest' such that a statistically significant result is 90% likely to be measured in a reasonable time between the two contestants? (Keep in mind that each is putting up his own \$ so the vig should be shared between them.) Let's set "reasonable amount of time" as 4 hours and "statistically significant result" as 90% confidence.

2) Start with a Simborg box and two non-precision dice with drilled out pips (but with rounded corners -- similar to what many cheapo sets of the last 40 years have as standard equipment). Drop the dice vertically into the box. Have an assistant record the results. Let's assume 4 seconds per diceroll, on average. How much actual data collection time do you estimate to reach 95% confidence that you get more than random expected 66 rolls?

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