How do i know if this is random enough?

Question

I wrote a program in java that rolls a die and records the total number of times each value 1-6 is rolled. I rolled 6 Million times. Here's the distribution:

#of 0's: 0
#of 1's: 1000068
#of 2's: 999375
#of 3's: 999525
#of 4's: 1001486
#of 5's: 1000059
#of 6's: 999487

(0 wasn't an option.)

Is this distribution consistant with random dice rolls? What objective statistical tests might confirm that the dice rolls are indeed random enough?

EDIT: questions have been raised over application: a game that i want to be as fair as can be reasonably achieved.

Answer 1

To test whether this particular distribution is consistent with the expected distribution of numbers rolled with a "fair" dive, you need to perform the Pearson's Chi-square test.

Note that this still will not prove that your algorithm is "fair", only that these particular results look "fair".

To test whether your algorithm is "fair" in general, use the Diehard tests, as others have mentioned.

Answer 2

If your random number generator passes the Diehard tests, that's the best you can do.

Even a physical die won't be perfect with 1/6 per face.

Increase the trials by an order of magnitude, then do it again. If you get 1/6 for each trial you'll be fine.