What's the probability of vanity pools causing RIPEMD-160 (public key hash) collisions? As Bitcoin vanity pools become more popular, the possibility of using that power to derive another person's Base58 public key hash becomes slightly more likely.

I'd like to know if anyone has done the math calculating probability of guessing a public key hash vs keys generated per hour.

In particular this information would be useful to defenders (and attackers) of accounts with large balances... Namely it may make sense from a risk avoidance strategy to keep large balances spread among several accounts for this reason


So the question is, what is the horsepower required needed to crack someone else's key hash and what are the mitigating circumstances such as ASIC or FPGA availability? 


If someone wants to take this a step further what is the maximum balance that should be held in an account based on those previous statistics
Bitcoin addresses are 160-bit numbers. Hence, randomly finding a private key corresponding to an address takes on average 2^160 attempts.

If 4 billion computers work on cracking a key doing 1 billion calculations per second for 15 billion years, they will find a total of 1.8*10^36 keys, so their chance to hit a right one is

(1.8*10^36)/(2^160) = 1.23 * 10^(-12)

which is one in a trillion. And this is only if they intentionally try to crack keys. If they just run normal vanity calculations, it doesn't matter how many keys they go over, as they'll eventually report just one key.

In the future (when the above figures may be slightly less ridicuolous), we might move on to longer key hashes.

So no, there's no risk.