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'Snake-Eyes ' Joe (Posted on 2008-07-28) Difficulty: 3 of 5
"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:

Scores 0 0 0 0 0 0 0

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

See The Solution Submitted by brianjn    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: possible theory | Comment 3 of 13 |
(In reply to possible theory by Paul)

I wondered about your choice of the fraction 11/66 to represent 1/6 but I now understand your reason.

In looking at your result I very much doubt that one could come much closer to my 'ideal', ie, the concept against which the simulated data was generated to 'mirror'.  It seems that, as a percentage, your model differs by about 0.107% on the value of "1" against mine.

In terms of your "NOTE:", your observations, as are those of Charlie, are consistent with mine as I developed this.  I have some exercise of control over the tally allocated to "1" but to a lesser degree for the other values.

And yes, a small margin of 2% might net casinos a tidy reward.

I have a serious thought before I release my "official solution".

  Posted by brianjn on 2008-07-29 10:57:48

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