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I'm a newbie to Bitcoin, so I apologize if this seems like a "noob" question.

So, from what I've read: anyone can create a new Bitcoin wallet. Upon creation, a wallet address is automatically generated. The wallet address can be used by others to make transactions to that particular wallet.

Now, my question is, what guarantees that two automatically generated wallet addresses will be unique? If my friend and I created separate wallets on our own computers offline, then what is the guarantee that the two wallet addresses will be unique? What if the two randomly generated wallet addresses turned out to be the same?

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The probability is unfathomably small. In practice it will never happen. You can find one billion friends all keep generating trillions of addresses every second and there won't be any duplicate addresses til the end of the life of the sun.

Edit: this actually exaggerated a bit. By virtue of the Birthday Paradox you only need to generate 2^80 addresses (not 2^160) to likely get a pair of duplicate addresses among all the addresses generated. So this address generating party won't be able to run that long.

On the other hand if your billion friends all keep generating addresses in an attempt to get the same address as yours, then it does take forever to happen.

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I've seen this question several times, and us puny humans don't understand how HUGE! big numbers are. So, let me put it this way:

If there are a million people on the bitcoin network, and they each have a million accounts each, and if you can create 30 peta-accounts per second, generate the public key, and check if that public key has money (30 petahashes is approx the current bitcoin network hashrate, and you would need to hash each key).

In 1.5x10^9 millennia, you have about a 50% chance of getting the same wallet as someone else. Before then, there will be over 27,000 extinction level events - events which will kill over 50% of the life on earth - not counting man-made ones.

Also note that the Birthday paradox doesn't apply here; a collision is only relevant if one has money in it at some point now or in the future.

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  • Very nicely described. Thank you for your answer!
    – Vikram
    Mar 10, 2014 at 7:58
  • Our sun does not have enough fuel for anywhere near 1.5x10^9 millennia - in a few billion years it will become a red giant and all life on earth would be killed...
    – uminatsu
    Mar 10, 2014 at 18:37
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    I chose the extinction level events, because it's a probabilistic event; this is to counter people saying "well, it's just chance, isn't it? You MIGHT duplicate a wallet on the first try"; yes, and we MIGHT get 27,000 asteroids raining down in the next 5 minutes.
    – AMADANON Inc.
    Mar 10, 2014 at 19:29

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