[pbs-devel] applied: [PATCH proxmox-backup] docs: fix hash collision probability comparison

[Thomas Lamprecht]

On 07/03/2025 10:33, Dominik Csapak wrote:
> Commit:
>  efc09f63c (docs: tech overview: avoid 'we' and other small style fixes/additions)
> 
> introduced the comparison with 13 lottery games, but sadly without any
> mention how to arrive at that number.
> 
> When calculating I did arrive at 8-9 games (8 is more probable, 9 is
> less probable), so rewrite to 'chance is lower than 8 lottery games' and
> give the calculation directly inline as a reference.
> 
> Suggested-by: Dietmar Maurer <dietmar at proxmox.com>
> Signed-off-by: Dominik Csapak <d.csapak at proxmox.com>
> ---
> @Thomas: if you can remember how we arrived at the '13' all those years
> ago, we could check if that calculation makes more sense than what I'm
> doing here, and rererence it?

I remember that we discussed this a bit, but cannot  come up with anything
that'd would explain this number, as it seems rather obviously wrong.
My commit introducing this is also _far_ from ideal, so the mistake might
not even be directly in having chosen number, but possibly an oversight and
including some unfinished addition to the docs with a cleanup commit.


Anyhow, rechecked the math now and winning 8 lotto game of 6 out of 45 in
a row checks out, as:

(1 / binomial(45, 6))^8 ≈ 5.162329215E-56 << 3.1115E-61

and

(1 / binomial(45, 6))^9 ≈ 6.337987952E-63 >> 3.1115E-61


btw. liking `qalc`, a calculator with a good REPL CLI interface, more and
more, much more ergonomical than bc or the like but still lightweight and
tuned for math – unlike using a REPL of a interpreter like perl or python.

> 
>  docs/technical-overview.rst | 4 ++--
>  1 file changed, 2 insertions(+), 2 deletions(-)
> 
>

applied, thanks!