Doing further research rendered this question unsolvable due to the existence of “Schroedinger’s Vault” - where at any given time inbetween checks, it could be either up or down.

However, that doesn’t mean that we can’t estimate.

First of all, since the chunks are spread evenly, we can say that:

`chunk_section = num_of_farmers / (4 + {0,1,2})`

Depending on how full the Network is.

Take one vault out of there that has your piece: `1 / chunk_section`

Now that’s randomly selected. `1 / chunk_section`

is the probability that you will find your chunk in a random guess - or that a random node will go offline with your chunk.

Now in order to lose your chunk, that has to happen for all of the sections - and it has to be the one with the same chunk. So:

`P(lose_chunk) = (1/chunk_section) ^ (number_of_sections)`

Where the number of sections is at least four (2x primary chunk, 2x secondary chunk) and at most 6 (2x sacrificial chunk).

Now that’s at any given moment in time. Let’s use real numbers

So I think it’s *SAFE* to say that it’s **quite** smaller than 1%.

However this does not, nor cannot take into account time without further study and behavior analysis.

But the effects can be mitigated by placing the chunks strategically. Secondary chunks on vaults that have lower checking times, and primary chunks on vaults that have higher checking times.

That way you always have one vault that contains your piece that is checked closer to once every two minutes, than one that is checked once ever 20 hours.

Just my $.02