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Statistical Analysis & Pattern Matching

If I have a set of random data, which could be the result of rolling a
6 sided die 1,000 times, and the die is favored to rolls 2 numbers more

often than the others, how do I analyze the data to determine which
numbers it favors without knowing in advance that it favors any of the

Considering I am looking at random data it is impossible to say if the
dice favors any number for sure, but I can assume that it favors a
number and check to see which numbers it would favor if it did.

That is an example of the type of problem I want to solve but I can
think of others.  How about an algorithm that generates random numbers
between 1 and 1,000,000.  Lets say I have a database of 10 million
numbers it has generated, and want to determine what numbers it favors.

 This is not the same question as asking if it is random data, because
for our purposes it is random.  This is just asking if it is more
likely to produce certain number.

Lets say for this example that the machine is programmed to never
produce the same number twice, until it has randomly generated every
other possible number.  Is there a way to predict this is happening by
looking at the data?  Normally the gamblers fallacy isn't a useful
idea, but in this case it would help you know in advance what the
machine will generate because that is how it is programmed.

How would I solve these problems using mathematica?

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