Lesson 15

Agreeing to play such a game is really not worth it, and here's why. The tree in the previous step is drawn under the assumption that each player guesses how the coin lands with a probability of \(1/2\). But can we be sure that these events are independent? It turns out they are not! For example, if the second and third players agree to always bet differently, they gain an advantage against the first player: for instance, no matter how the coin lands, one of them will definitely guess correctly, causing the first player to lose the opportunity to take the entire pot. The tree below shows that under such a strategy (of the second and third players), the average winnings of the first player equal minus one euro!