user91517: I am running a test to see if I can obtain a successful bitcoin address collision after generating billions of addresses. I am not entirely sure how I would check them yet. Basically I have an extra 10TB hard drive and am running supervanitygen on my 32-core, 128gb ram linux work computer. It seems to be generating about 90,000,000 (90 million) addresses (address + private key pair) every 4 hours. 
Do you think it's possible or likely to run into an address collision this way? Or perhaps if everyone in the world did the same thing? Or what if I waited 10-20 years, and then checked the addresses?
This is all just a test to see if the bitcoin system is secure enough for big investment decision.

user51948: A very relevant answer can be found here: Is Each Bitcoin Address Unique?
This is a question of the birthday attack on the hashes. Bitcoin addresses (assuming the "normal" style starting with a 1) encode 160 bit hashes, so the output space has a possible 2^160 hashes. Because its a hash function, we assume all outputs have equal probability of being output.
At the rate you gave in the OP, you would generate 1.971 * 10^11 addresses in 1 year. Using the approximate birthday formula n^2 / 2H, the probability of a collision in 1 year is thus roughly on the order of 10^-26. That is, basically 0. In 20 years that probability becomes around the order of 10^-24. Still basically 0. If all 8 billion people in the world generated addresses at that rate for 20 years, in total 3.1536 * 10^22 addresses would be generated. Even then, the probability of a collision is only around 0.0003. And remember that a collision like this is completely different from a targeted attack to find the private key of a specific address. If there was a collision, chances are overwhelming that there would be no funds ever sent to the address anyway, making the attack useless.

user208: Because of the Birthday paradox, you only need 280 addresses (despite there existing 2160 different address combinations) before a collision becomes probable.
Thankfully, that is still an enormous number. At 90 million addresses per 4 hours, it will take about 445 times the age of the universe to reach that number.
It's also irrelevant. Even if anyone - or everyone - generates 90 million addresses per 4 hours, there aren't that many addresses receiving funds. Thus only actually used addresses matter.

91517: <p>I am running a test to see if I can obtain a successful bitcoin address collision after generating billions of addresses. I am not entirely sure how I would check them yet. Basically I have an extra 10TB hard drive and am running supervanitygen on my 32-core, 128gb ram linux work computer. It seems to be generating about 90,000,000 (90 million) addresses (address + private key pair) every 4 hours. </p>

<p>Do you think it's possible or likely to run into an address collision this way? Or perhaps if everyone in the world did the same thing? Or what if I waited 10-20 years, and then checked the addresses?</p>

<p>This is all just a test to see if the bitcoin system is secure enough for big investment decision.</p>
 51948: <p>A very relevant answer can be found here: <a href="https://bitcoin.stackexchange.com/q/8804/51948">Is Each Bitcoin Address Unique?</a></p>

<p>This is a question of the birthday attack on the hashes. Bitcoin addresses (assuming the "normal" style starting with a 1) encode 160 bit hashes, so the output space has a possible 2^160 hashes. Because its a hash function, we assume all outputs have equal probability of being output.</p>

<p>At the rate you gave in the OP, you would generate 1.971 * 10^11 addresses in 1 year. Using the approximate birthday formula <code>n^2 / 2H</code>, the probability of a collision in 1 year is thus roughly on the order of 10^-26. That is, basically 0. In 20 years that probability becomes around the order of 10^-24. Still basically 0. If all 8 billion people in the world generated addresses at that rate for 20 years, in total 3.1536 * 10^22 addresses would be generated. Even then, the probability of a collision is only around 0.0003. And remember that a collision like this is completely different from a targeted attack to find the private key of a specific address. If there was a collision, chances are overwhelming that there would be no funds ever sent to the address anyway, making the attack useless.</p>
 208: <p>Because of the <a href="https://en.wikipedia.org/wiki/Birthday_problem" rel="noreferrer">Birthday paradox</a>, you only need <em>2<sup>80</sup></em> addresses (despite there existing <em>2<sup>160</sup></em> different address combinations) before a collision becomes probable.</p>

<p>Thankfully, that is still an enormous number. At 90 million addresses per 4 hours, it will take about 445 times the age of the universe to reach that number.</p>

<p>It's also irrelevant. Even if anyone - or everyone - generates 90 million addresses per 4 hours, there aren't that many addresses receiving funds. Thus only actually used addresses matter.</p>
