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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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Let there be No Random | Comment 10 of 13 |
I concede.

I rewrote the script so that there was no random element but which used the same program structure.

The result was:
    1         2            3           4          5         6       Total
 9231   10154     10154    10154   10154  10153   60000

This is the appropriate section of the non-random listing:

function deliver()
t=0;u=0;v=0;w=0;x=0;y=0;// Die face counts
tn=0;                   // counter for value of 1 up to 10
for (c=1;c<60000+1;c++)
     /* Following if reallocates values of 1 if count is 10 and initialises counter
    if (g==1 && tn==10)
    if (g==1){t++; tn++; } //tn is incremented here
    if (g==2){u++; }
    if (g==3){v++; }
    if (g==4){w++; }
    if (g==5){x++; }
    if (g==6){y++;g=0; }
sum=t+u+v+w+x+y; // this is the value of c=60000

I did attempt this exercise before posting the solution just to confirm my rationale but I couldn't get there unfortunately. I shall ask levik to modify the solution in his time.

(Eigenray, I trust others understood your last comment as it totally lost me; but thanks for the discussion, I'm sure it will benefit others.)

  Posted by brianjn on 2008-08-01 23:40:10
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