  In the run-up to any major sports tournament, winning probabilities of
participants are publicized for engagement and betting purposes. These are
generally based on simulating the tournament tens of thousands of times by
sampling from single-match outcome models. We show that, by virtue of the
tournament schedule, exact computation of winning probabilties can be
substantially faster than their approximation through simulation. This notably
applies to the 2022 and 2023 FIFA World Cup Finals, and is independent of the
model used for individual match outcomes.
