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

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

[Dominik Csapak]

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@proxmox.com>
Signed-off-by: Dominik Csapak <d.csapak@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?

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

diff --git a/docs/technical-overview.rst b/docs/technical-overview.rst
index 6a76942f1..fdeb3a093 100644
--- a/docs/technical-overview.rst
+++ b/docs/technical-overview.rst
@@ -298,8 +298,8 @@ will see that the probability of a collision in that scenario is:
 
 For context, in a lottery game of guessing 6 numbers out of 45, the chance to
 correctly guess all 6 numbers is only :math:`1.2277 * 10^{-7}`. This means the
-chance of a collision is about the same as winning 13 such lottery games *in a
-row*.
+chance of a collision is lower than winning 8 such lottery games *in a row*:
+:math:`(1.2277 * 10^{-7})^{8} = 5.1623 * 10^{-56}`.
 
 In conclusion, it is extremely unlikely that such a collision would occur by
 accident in a normal datastore.
-- 
2.39.5



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[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@proxmox.com>
> Signed-off-by: Dominik Csapak <d.csapak@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!


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

[Dominik Csapak]

On 3/7/25 11:27, Thomas Lamprecht wrote:
> 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@proxmox.com>
>> Signed-off-by: Dominik Csapak <d.csapak@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.
> 

nice, have to look at this in the future. Currently, when doing calculations
with such big numbers, i still use wolframalpha.

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



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