Quite often I worry about git hash collisions. I know the probability is as small as it can get. But what is the probability that out of all the git users so far, any one out of all had a git collision? (This is not the same as the previous prob)
Secondly hypothetically if I combine all the git repositories ever created in this world into one giant git repo, will I see any collisions?
A basic estimate is that the probability of collision is (n^2 / 2) / 2^160, where n is the number of hashes that have been generated. For example, if you've generated 2^64 hashes, you have a 1/2^33 chance of collision. This works pretty well until you get too close to 2^80, and larger.
Edit: That formula actually is a shorthand for (n * (n-1)/2) / 2^160, you get it because on your first hash, you have 0/2^160 chance of collision, and on your second hash, you have 1/2^160 chance of collision, and on your third, you have 2/2^160 chance of collision, and on your nth, you have (n-1)/2^160 chance of collision (assuming you haven't had any collisions already). So you can add up those probabilities to get (n * (n-1)/2)/2^160 -- you can just add the probabilities because the chance of having _two_ collisions is super unlikely (until it is no longer super unlikely, around 2^80 or so). (Really it's 1 - (1 - 1 / 2^160)^k and we're approximating that with k * (1 / 2^160.)
> 983.544.651.006.435.431.129.340.665.918.456.708.968.598.498.835
or 9.8 * 10^47 combinations are possible. Although this doesn't give the complete picture, this shows how big the sha1 space is.
983 billion, billion, billion, billion, billion
If every human that ever lived had made a thousand git commits every second of their lives to the same git repository, we would still expect no collisions.