Alkatran: If you mean plurality instead of majority, you are correct. A total of seven is expected to occur 1/6 of the time, which is more often than any other total when using two standard casino dice.

If a process is truly random, the data generated by it should become closer and closer to the expected values as the number of experiments grows without bound.

The VB pseudo random number generator does a fair job of simulating standard Casino Craps. An application I wrote indicates that it becomes accurate to about 3-5 decimal digits after a few million dice throws, but does not seem to ever get more accurate. This suggests the generator is not the best possible for this purpose. It does a worse job of simulating the overall house percentage than it does in simulating the numbers on each individual die and the totals for two dice. This indicates that the simulated sequence of numbers on each die is not quite the true sequence expected.

Kedaman: I wonder if there is a pseudo random number generator or a random process which results in a minus infinity to plus infinity range of numbers. I doubt that there is.

Given a uniform distribution over a finite range, I am pretty sure that the mean is predictable, and that this is true for many other probability distributions. The VB generator is supposed to simulate a uniform distribution of numbers between zero and one. I am not sure if it is possible for the limit value (zero/one) to occur. The expected mean is ½, which seems intuitively obvious, but might be difficult to prove. The following is a reasonable argument, but not really a proof.

By definition of a uniform distribution, every possible number has the same probability of occurring. Every group of n numbers in small range (EG: .40000 to .40002) should be matched by a similar group of n numbers symmetric to ½ (EG: .59998 to .60000). Thus, each small group of numbers is matched by another group such that the average of the two groups is ½ or close to it.