The probability of casting a pivotal vote in an Instant Runoff Voting election

I derive the probability that a vote cast in an Instant Runoff Voting election will change the election winner. I phrase that probability in terms of the candidates' expected vote totals, and then I estimate its magnitude for different distributions of voter preferences. The result is very similar to the probability of casting a pivotal vote in a Single-Member District Plurality election, which suggests that Instant Runoff Voting does not actually increase or decrease voters' incentives to vote strategically. The derivation uncovers a counter-intuitive phenomenon that I call "indirect pivotality", in which a voter can cause one candidate to win by ranking some other candidate on their ballot