Possible issues with random number generators for calculator apps

[ttw]

The problem is that small samples do not look like large samples. Taking sequences of coin flips as an example, a string of 10 heads in a random sample of size 15 is rather remarkable; a sequence of 10 heads in a random sample of size 1500 is nearly certain. Long random strings contain lots of non-random-looking short strings. Good PRNGs easily generate this behavior. The problem is inherent in "random" behavior.

I posted (I think three) pretty good generators for the HP50g somewhere on this board. They consist of a Tausworthe (shift-register) generator combined with a long linear contruential generator. (Each generator "sees" the other as a non-linear sequences.)

I personally prefer to design each "random looking" simulation to have provably independent parts where necessary. It's a bit of work but the results are good. Of course, short runs don't look very random anyway.