How many digits is enough to reference a Git commit?

Depends on the total number of commits. The probability $p$ can be approximated as

$$p\approx \frac{n^2}{2m}$$

• $n$ is the number of items
• $m$ is the number of possibilities for each item

The number of possibilities for a hex string is $(16^c)$

• where $(c)$ is the number of characters.

So for 8 characters and 30K commits (assuming 30K ≈ $(2^{15})$):

$$p\approx \frac{n^2}{2m}\approx \frac{(2^{15}{)}^2}{2\times 16^8}=\frac{2^{30}}{2^{33}}=2^{-3}$$

Increasing it to 12 characters:

$$p\approx \frac{n^2}{2m}\approx \frac{(2^{15}{)}^2}{2\times 16^{12}}=\frac{2^{30}}{2^{49}}=2^{-19}$$