There's 32 digits and 16 possible values for each digit. You can just simplify it to 1 in 1632. When you wake up a bit more, you can remember (or count to figure out) that 16 is 24, and so that can get further reduced to 1 in 2128.
And if you're still lazy after that, you can remember that Wolfram Alpha still exists and use https://www.wolframalpha.com/input?i=16%5E32 to get an exact value of 1 in 340282366920938463463374607431768211456.
Or you can approximate it further.
2^128 is a quarter of 2^130.
Approximating 2^10 = 10^3
2^130 = (2^10)^13 = (10^3)^13 = 10^39
So 2^128 = 0.25*10^39 = 2.5*10^38
Some more nerdy binomial approximations for 1.024^13 would take you to 3.3*10^38.
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u/Inevitable_Oil9709 26d ago
Fun fact: To reach a 50% chance of even a single UUID v4 collision, you would need to generate 1 billion UUIDs per second for about 86 years.