Zilch dude. Once in a trillion gazillion years. . .
. . . roughly a similar chance to accidentally replicating someone else's DNA.
. . . to brute force 256-85=171 bits at 1Tkey/s, it'd take some 94847369674933745800730934462790 years. . .
Doesn't it actually depend on the method you use for creating the BTC address? If you are using a brainwallet, or some non-random method of key generation, wouldn't you have an increased chance that someone else might use the same non-random method?
Most of the examples I see regarding key collision generally seem to refer to the chances of matching a pre-chosen address. ( If address YYYY has 5,000 BTC associated with it, what is the chance that someone can figure out the key and steal the coins?), but this question of any 2 random addresses resulting in a collision seems more like the birthday problem. Given a pool of people with randomly distributed birthdays, how many would have to be selected to have a reasonable chance that two of them will share a birthday? The number is certainly less than 365. It really comes down to how you define "reasonable chance", but if for the sake of the current discussion we choose 50% chance, the number is only 23, for a 99% chance of collision you only need to choose 57 people.
I really don't understand how the math for the birthday problem is calculated, but I have wondered sometimes how the numbers work out when applied to randomly generated BTC addresses. I suspect the odds are still beyond concern, but I also suspect that they are smaller than the typical answer.
