[kuboble]

> Then if the software has been around for one year, the expected value of p is 50%. But if the software has been around for ten years, the expected value of p jumps to 0.5^(1/10) ≈ 93.3%.

This reasoning is incorrect. You have to take the distribution of p into account.

In a world where almost every software has p=0.5 the software which has been around for 10 years is likely to have been lucky and not to have higher p.