A efficient binomial random number generator code in Java

Question

The relevant question is: Algorithm to generate Poisson and binomial random numbers?

I just take her description for the Binomial random number:

Answer 1

I could imagine one way to speed it up by a constant factor (e.g. 4).

After 4 throws you will toss a head 0,1,2,3 or 4.

The probabilities for it are something like [0.6561, 0.2916, 0.0486, 0.0036, 0.0001].

Now you can generate one number random number and simulate 4 original throws. If that's not clear how I can elaborate a little more.

This way after some original pre-calculation you can speedup the process almost 4 times. The only requirement for it to be precise is that the granularity of your random generator is at least p^4.