Any analogy is going to be imperfect and incomplete.
There are 2
160 different Bitcoin addresses, which equals
1.46 * 1048 possibilities.
If someone is trying to attack the system, then the security is as if there are 2
128 distinct private keys, even though private keys are actually 256 bits long and pubkey-hashes are 160 bits long. Sometimes I say that there appear to be 2
256 lockers, but that many of them actually share their internal spaces with many others (via wormholes/magic).