I like to think of using all of the sun's energy to generate addresses. If you had a computer powered by the Sun, generating millions of addresses per second, statistically, the Sun would burn out before you generated an address used by some one else.
I can generate millions of addresses per second with my video card. Well like 8 million. It says it'll only take 10 years to find 1FAGABEEFE*
Apparently it'll take 10^48 years to find Avalon's address. I better get started.
I think of it like this:
You're about as likely to find Avalon's address in use as if Avalon stored their cash in a wallet buried in a landfill. By giving the public key, we know what the wallet looks like, but this is not very helpful. But - what are the odds of finding *a* wallet in any landfill with coins in it if we have highly-efficient garbage-sorting robots?
Let's say there are 500,000 wallets in landfills containing money. Let's say there are 100 "treasure hunters" with four garbage-sorting robots each, each sorting through 8m objects per second. In total, the treasure hunters are able to sort through a total of 3.2b objects per second out of a total of 2^160 objects. We know there are roughly 500k wallets in existence, effectively the wallet pool when trying to find *a* money-filled wallet to 2.92e+42 in our example, or 292,000,000,000,000,000,000,000,000,000,000,000,000,000 (+- a couple zeroes!), so our chance of finding a wallet-filled address at any second is 3,200,000,000/292,000,000,000,000,000,000,000,000,000,000,000,000,000, or ~1.095e-33(%).
Hooboy these numbers suck. Let's try monthly percentage. %/sec*60(to get to /min)*60(to get to /hr)*24(to get to /day)*30(to get to /month) = ~2.838e-27(%) or..... .000000000000000000000002838%/month (+- a couple zeroes, again).
Let's change our example up, though -- just for fun. Let's say miners have decided it might be worth more to start these kinds of "treasure hunting" pools once GPU-mining kicks the bucket for BTC. It gets REALLY popular, and there are now the equivalent of 10,000 treasure hunters with four 8m/sec garbage-sorting robots each. Bitcoin gets more popular, too, and there are currently 25,000,000 money-filled wallets in landfills.
(2.92e+42)/25,000,000=5.8460065493236116728147393308651e+40 (effective "landfill pool" [address pool] after factoring in # of cash-holding wallets)
5.8460065493236116728147393308651e+40/320000000000=5.4738221262688166832958186847263e-30 (%chance of pool finding address per second)
5.4738221262688166832958186847263e-30*60*60*24*30=1.4188146951288772843102762030811e-23 (%chance of pool finding address per month)
or..... ~.00000000000000000001419% (+- one zero), 0.00000000000000000017028%/year, 0.000000000000000008514%/50years, 0.000000000000008514%/500kyears
.... And all that math (none of which I'm sure of!) just goes to show..... shit's probably pretty safe... until dedicated ASIC address generators hit the market at 1/1,000 the price of what it'd currently cost to do the same work. Then it may only take a few billion years.
(someone should correct my math)