u/Shin_Cow

You play three tennis matches. You have a 70% chance of beating your teacher in any match and a 30% chance of beating a champion. Assume the results of all three matches are independent, and the win probabilities stay fixed.

Your goal is to win at least two consecutive matches. You can choose one of these orders:

Teacher — Champion — Teacher

Champion — Teacher — Champion

Which order gives the higher probability of achieving your goal, and why? Winning all three also counts as success.

Bonus: if the two win probabilities are any 0 < q < p < 1, is the same choice always better?

Creator disclosure: I run Think in Odds, a daily probability puzzle site. This is a released puzzle version; optional hints and a worked explanation are here: https://thinkinodds.com/puzzles/tennis?utm_source=reddit-mathriddles&utm_medium=reddit&utm_campaign=r_mathriddles_first_players_oct2026

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