Possibility of collision

[TTBit]

The bitcoin vs the state thread got me thinking about how small of a chance we are talking about.

Please rank the following in the order of likeliness:

A: You thoroughly shuffle a deck of cards into its original order.

B: A normal 6 year old girl who never bowled before bowls a perfect game 10 times in a row.

C: A MLB baseball pitcher strikes out every batter he faces in a season.

D: Tiger Woods gets a hole in one for every par 3 he faces in a year.

E: A person wins 5 Powerball lotteries in a row (Say 80,000,000:1 against each)

F: A bitcoin address collision is discovered in the next 20 years using most modern technology.

If the 'atoms in the universe' rule is true, my guess:
A, D, B, C, E, F.

[FreeMoney]

A is 1 in 52! which makes it less likely than 5 power balls. I don't even know how to measure the others at all.

[nanotube]

A is 1 in 52! which makes it less likely than 5 power balls. I don't even know how to measure the others at all.

A is not 1 in 52. assuming that a "shuffling" produces a random ordering of the cards, you randomly produce 1 out of the 52! possible orderings of the 52 cards. that's 52 factorial, not "52 excited exclamation". which comes out to roughly 8.0658175170945e+67 - that's 8 with 67 zeros following it.

now, let's get back to our regularly scheduled programming.

EDIT: sorry, i completely missed the ! after /your/ 52 and thought you said "1 in 52". my bad. i must be getitng blind in my old age.

[nanotube]

oh and of the others, the only one that's easy to calculate without making a bunch of assumptions about the probabilities of the underlying events in the powerball lottery. if winning one is 1/80M, then winning 5, each of which has the same probability, is (1/80M)^5 == 3.0517578125e-40, which is roughly 10^27 times more likely than the 'random shuffling creating the exact same order of cards as before' bit.

[davux]

If the 'atoms in the universe' rule is true,

It's not. There are approximately 10^80 atoms in the universe. On the other hand, as said there, there are 2^160, or 1.46x10^48 possible addresses. So the number of atoms in the universe is nearly the number of bitcoin addresses multiplied by... the number of bitcoin addresses! Not quite the same, really.

I'm not saying a collision is more probable than the rest of your examples, though. It's just that people are starting to repeat this atom thing just because they read someone else repeating it in another thread.

[theymos]

If every person on Earth makes ten addresses per second for 20 years (2x10¹⁸ total addresses), then the probability that two of these addresses collide is about 1.57x10^-12.

I'm using the formula here:
http://en.wikipedia.org/wiki/UUID#Random_UUID_probability_of_duplicates