How long would we have to use bitcoin before we *should* expect to see an address collision (two private bitcoin addresses both being assigned to the same person)? Well, hold onto your butts.

Our planet has approximately 7 billion people on it. But the population is growing.Eventually (and let's ignore the realities of communicating/synchronizing blocks across the vast distances involved in the cosmos) perhaps we will colonize other planets.So let's say we do.... instantly. In fact, let's colonize a billion planets in our galaxy right now, each with seven billion humans.But that's not good enough. What if we eventually colonize other galaxies too? So let's say we've also colonized one billion galaxies, and in each galaxy we've colonized one billion planets each with seven billion humans.That's a truly universal civilization. Good job, us!Now let's assume that starting this very second, all those people (our universal population of seven octillion) each begins to generate one thousand new bitcoin addresses every second."WHY ARE YOU GENERATING SO MANY FUCKING ADDRESSES! You're going to cause a bitcoin address collision!" yells the supreme universal bitcoin chancellor. "STOP IT!" ಠ_ಠLet's pretend everyone's in on the joke, and they all ignore him.( ͡° ͜ʖ ͡°)With this insane number of humans, all generating a thousand addresses every second it would still take about 150 billion years in order for there to be a 50/50 chance of a bitcoin address collision (I'm going off of the "Birthday Problem" distribution for this probability). For there to be approximately a 99% chance of a collision, the assholes would need to keep up this buffonery for about 400 billion years total.Looking ahead to what scientists think will be the timeline of our universe:50 billion years: If the Earth and Moon are not engulfed by the Sun, by this time they will become tidelocked, with each showing only one face to the other. Thereafter, the tidal action of the Sun will extract angular momentum from the system, causing the lunar orbit to decay and the Earth's spin to accelerate.100 billion years: The Universe's expansion causes all galaxies beyond the Milky Way's Local Group to disappear beyond the cosmic light horizon, removing them from the observable universe.150 billion years: The cosmic microwave background cools from its current temperature of ~2.7 K to 0.3 K, rendering it essentially undetectable with current technology.450 billion years: Median point by which the ~47 galaxies of the Local Group will coalesce into a single large galaxy.800 billion years: Expected time when the net light emission from the combined Milkomeda galaxy begins to decline as the red dwarf stars pass through their blue dwarf stage of peak luminosity.1012 (1 trillion) years: Low estimate for the time until star formation ends in galaxies as galaxies are depleted of the gas clouds they need to form stars.Summary: I'm pretty sure there will never be a bitcoin address collision. My math might not be perfect, but it shouldn't be off by more than an order of magnitude. You are welcome to fact check me and I'll correct it if necessary. via /r/Bitcoin http://bit.ly/1ICTNBc