In this note, we consider a form of competition in which two contestants face separate sequences of independent trials. The contestant with the longer sequence of successful trials wins. However, since the trials are independent, there may be a form of paradox whereby the loser is able to pass all of the trials in the winner’s sequence, whereas the winner could not have overcome two or more trials in the loser’s sequence. We refer to this as the spelling bee paradox and explore its likelihood in simple settings.
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