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arXiv · 2505.16842

First is the worst, second is the best? A Markov chain analysis of the basketball game knockout

Andrew Flatz·Michael C. Loper·Lezlie Weyer
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Abstract

The game of Knockout is a classic playground game played with two basketballs. This paper uses a Markov process to analyze each player's probability of winning the game given their starting position in line and shooting percentages, assuming all players are equally skilled. The two-player case is solved in general for any probability of a long shot and short shot shooting percentage and the n-player case with n > 2 is solved numerically. In doing so, this paper answers the question of whether or not the playground wisdom of ``first is the worst, second is best'' is true. We also examine the average number of rounds it takes before the game ends, analyze trends in the data to recommend tips to win at Knockout, and provide questions in the case of players not being equally skilled.

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Andrew Flatz, Michael C. Loper, Lezlie Weyer. 2025-05-22. First is the worst, second is the best? A Markov chain analysis of the basketball game knockout. https://arxiv.org/abs/2505.16842

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