Need for predictable random generator

Question

I\'m a web-game developer and I got a problem with random numbers. Let\'s say that a player has 20% chance to get a critical hit with his sword. That means, 1 out of 5 hits

Answer 1

The top few answers are great explanations, so I'll just focus on an algorithm that gives you control over the probability of "bad streaks" while never becoming deterministic. Here's what I think you should do:

Instead of specifying p, the parameter of a Bernoulli distribution, which is your probability of a critical hit, specify a and b, the parameters of the beta distribution, the "conjugate prior" of the Bernoulli distribution. You need to keep track of A and B, the number of critical and non-critical hits so far.

Now, to specify a and b, ensure that a/(a+b) = p, the chance of a critical hit. The neat thing is that (a+b) quantifies how close you want the A/(A+B) to be to p in general.

You do your sampling like this:

let p(x) be the probability density function of the beta distribution. It is available in many places, but you can find it in the GSL as gsl_ran_beta_pdf.

S = A+B+1
p_1 = p((A+1)/S)
p_2 = p(A/S)

Choose a critical hit by sampling from a bernoulli distribution with probability p_1 / (p_1 + p_2)

If you find that the random numbers have too many "bad streaks", scale up a and b, but in the limit, as a and b go to infinity, you will have the shuffle bag approach previously described.

If you implement this, please let me know how it goes!