Probability of 64bit Hash Code Collisions

Question

The book Numerical Recipes offers a method to calculate 64bit hash codes in order to reduce the number of collisions.

The algorithm is shown at http://www.javamex.com/tu

Answer 1

I'll provide a rough approximation to the exact formulas provided in the other answers; the approximation may be able to help you answer #3. The rough approximation is that the probability of a collision occurring with k keys and n possible hash values with a good hashing algorithm is approximately (k^2)/2n, for k << n. For 100,000 keys with a 64 bit hash, that's 10^10 / 32x10^18 or about 1 in 3 billion.

However, I suspect that if you go with not checking the actual key values on collision, there is a larger chance you'll find out the hashing algorithm is not "good" enough, after all.