What's the average number of hsdir fetches before we get the hsdesc?

Hidden services publish their hsdesc to six hsdir relays, once an hour.

Then relays come and go, changing the set of six that clients will compute when deciding which relay to fetch from.

Also, both hidden services and clients only fetch a new consensus every 2-4 hours, so they will be perenially a few hours behind.

This could pretty easily result in a situation where (due to different knowledge on the hidden service's part) the hidden service doesn't publish to all six that it's "supposed" to, and (due to different knowledge on the client's part) the client doesn't pick from the same six that the hidden service published to, and (due to churn in the relays) the six that the hidden service published to might not remain the right six from a global perspective.

Realistically, do these skews matter?

We could imagine doing an experiment where we follow the client algorithm and find out the average number of fetches we do before we get an answer (or give up).