I've asked the same question on Mathematics Stack Exchange meta, as my experience explained below was on the MathSE site. It seemed that the situation is something network-wide, and therefore I tried asking about it here.
Yesterday, I did more than forty reviews in different queues on the main MathSE site. Strangely, more than ten of them (more that 25%) were audits, which was something that hadn't happened to me before. More strangely, in the "Late answers" queue, I got two audits, one usual task after them and one more audit after that (which I think had never happened to me before; the "Late answers" cases have always been rare, audit or usual). It made me think about the algorithm responsible for choosing when to show an audit. I tried to make some guesses, but I think I ended up having more questions than good guesses. I ask some of them here, along with my guesses in the form of "is it because ..." questions, so that I make clear what I mean when I ask "how often" audits appear. I suppose they can be answered all at once by someone who knows about the algorithm.
- How often do audits appear?
- Yesterday was the first day that the queues "First answers" and "First questions" were active. Is there something related to that?
- Is the number of audits appearing in a day related to the number of reviews done by the user that day? Is it related to the number of reviews done by all users that day?
- Is the type of reviews done by the user related to the type of audits appearing? (I suppose not; as I got two audits in the "Late answers" queue, where I hadn't done any reviews in a very long time.)
- Is the choice of the user in the previous reviews (for example to reopen a post or leave it closed) and its similarity with the choice of other reviewers a factor? What about failing or succeeding in the previous audits?
- Is the algorithm different (or with different weightings of parameters) for different communities, or is it the same for all the Overflow and Stack Exchange sites?
- Is the fact that I haven't ever got an audit on MathSE meta because any of the above factors (or any other factor that affects the frequency of appearing of audits) is very low there, or is it because audits are only designed to appear on the main site?
- Is the number of audits one encounters related to the number of audits the algorithm can generate at that time, due to the number of available post qualified for it? (See here for the criteria.)