perplexus.info :: Probability : 'Snake-Eyes ' Joe

'Snake-Eyes ' Joe (Posted on 2008-07-28)

"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.

Submitted by brianjn

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Solution: (Hide)

Javascript's pseudorandom generator was employed to run and collate 60,000 items of data at a time.

In a theoretically fair distribution one would expect the value to be 10,000 per face.

To create the bias the programming model has been designed to ignore every tenth value of "1" and regenerate it as a new number. Whatever that new number, it is then added to the count of the progressive tallies of each value.

Let 6X be the total of the data items.
The theoretical expectation per face is therefore X.
It would seem that the programming model depletes "1" by 10%, making the value of "1" equal to (X-X/10). And then, since the values representing the 10%, X/10, are redistributed, each value will receive X/60 making the theoretical model for this seemingly:
Face: 1 2 thru 6 Results: X - X/10 + (X/(10*6) X + (X/(10*6))
This would give values of approximately 9166.7 for "1" and 10166.7 for the other faces.

Note that Dej Mar copied the relevant code from the problem's page source.

Eigenray challenged the above as a solution. He went on to explain further. And then gives a theoretical statement as to why the value for 1 is as he stated.

Taking the random element out of the program structure (with which I had some inexplicable difficulty) I generated the following table of values which is consistent with what Paul was proposing, and Eigenray.
The result was: 1 2 3 4 5 6 Total 9231 10154 10154 10154 10154 10153 60000

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
looks like ....	Larry	2023-11-25 10:49:03
Solution modified	brianjn	2008-08-07 03:28:20
re: Let there be No Random	Eigenray	2008-08-02 05:07:29
Solution Change Requested	brianjn	2008-08-02 00:49:04
Let there be No Random	brianjn	2008-08-01 23:40:10
Recurrence	Eigenray	2008-08-01 22:16:07
re(2): error in solution - fallacy?	Eigenray	2008-08-01 20:56:51
re: error in solution - fallacy?	brianjn	2008-08-01 05:45:07
error in solution	Eigenray	2008-07-31 10:27:26
Solution	Dej Mar	2008-07-30 09:26:26
re(2): possible theory	brianjn	2008-07-30 09:20:28
re: possible theory	brianjn	2008-07-29 10:57:48
possible theory	Paul	2008-07-28 19:36:45
a solution	Charlie	2008-07-28 16:38:13

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