"Snake-Eyes" Joe introduced a die of his own into a game of chance.

He was subsequently challenged that the die was biased.

Very rigorously test to see if there are grounds to substantiate this claim; don't accept just two or three trial runs. Are you able to offer a theoretical model consistent with your findings?

Test "Snake-Eyes" Joe's Die with this simulator which has a run of 60,000 at a time:

No:	1	2	3	4	5	6	Total
Scores	0	0	0	0	0	0	0

Note: the data changes with each subsequent mouse-over visitation to the link.

Based on the empirical evidence, but without a formal "proof", I'd suggest the following explanation:

 

Unlike a regular 6-sided die where the probability of each side is 1/6 (= 11/66), "Snake-Eyes" Joe's die has a probability of 11/65 for each of the numbers 2-6 and 10/65 for a 1 to appear. This reduces the chance of a 1 by only around 2%, but look what casinos can earn dollar-wise with a similar "small" advantage!

 

NOTE:  my experience of the trials is consistent with Charlie's. Over 20 60K trials uniformly showed a 1 as the least likely, whereas the other 5 all were highest sometimes and 2nd lowest other times and in the middle the rest of the time.

Posted by Paul on 2008-07-28 19:36:45