"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.

(In reply to re: possible theory by brianjn)

This does not address my solution as such but does acknowledge the thought that Paul has put into this, and in the following I doubt that none of us could expect a closer result. (See my solution)


Paul
Using his fractions of 10/65 and 11/65 the run would theoretically require 65000 attempts to 'fairly' get a distribution of:

 10000  11000   11000  11000  11000  11000  (= 65000)

This amounts to  15.384% for "1" and 16.923% for the other faces.

brianjn
My sample was against 60000; I locked that in as a program constant, I can't retract that.

By proportion occurrences using Paul's figures are:
9230.769 for "1" and 10153.85 for the other faces.

In contrast I expect values of:
9166.667 for "1" and 10166.67 for the others.

Note that while our margin for #1 differs by about 60, and we differ by about 13 for the other values, across a range of 60000 (65000) who could properly quibble?

Posted by brianjn on 2008-07-30 09:20:28