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 recent FIFA World Cups and is independent of the model used for individual match outcomes.
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