what are the chances of vanitygen address - private key pair collision? With no random number seed specified, assuming all vanitygen runs start with specific chunk for iteration, what are the possibilities of two different vanitygen runs to end up with the same address - private key pair?
Samr's vanitygen gets its initial private key from OpenSSL's random functions, which have been well vetted. Even if you specify a random seed (which is a good idea to add even more randomness) the entropy generation random libraries from the crypto is still used. It has equal randomness and strength as Bitcoin's address/key generator, with the exception that you are discarding millions of addresses that don't start with your vanity phrase.