Thanks @kano, @a1 Hashrate LLC2022, @NotATether.

My intention was also to have a post that anyone googling mining difficulty can find.

I recommend these two articles that studied statistically the mining difficulty problem :

- https://www.zora.uzh.ch/id/eprint/173483/1/SSRN-id3399742-2.pdf
- https://doi.org/10.2139/ssrn.3399742

Conclusion is that the Hypergeometric Distribution is the correct model and not Poisson Distribution as commonly accepted (also assumed in Satochi's white paper).
Nevetheless, I agree that the way I stated the problem is incomplete. We should also do the calculation knowing that" there is competition with X hash power.

Overall, I agree that the ratio of own hash power to the network hash power can be a good approximation.