Ranked-choice voting (RCV), also known as instant runoff voting or the plurality elimination rule, has experienced a significant rise in popularity in the United States over the last twenty years. Several US cities have adopted RCV to elect mayors and city councilors, and the states of Alaska and Maine have used the method to elect their US Senators and House representatives. RCV has many benefits which perhaps justify its increased use, but the method is also known to have defects. In the social choice literature, RCV is famously susceptible to many voting paradoxes, the most well-known of which are so-called monotonicity paradoxes. These paradoxes occur when the RCV winner could be made into a loser by gaining electoral support, or when one of the losers could be made into a winner by losing electoral support. For example, in the first RCV election which occurred in Alaska, the winner Mary Peltola would have lost if she had convinced 6000 of her opponent’s supporters to vote for her instead. That is, Peltola won because her campaign wasn’t good enough for her to lose. In this talk we explore the kinds of paradoxes which can be exhibited by RCV, providing empirical and theoretical probabilities that the method exhibits a particular paradox. Theoretical work suggests that RCV exhibits some paradoxes with high frequency, but the empirical probabilities tend to be much lower.