Question

There is a game with two players. Both players place $1 in the pot to play. There are seven rounds and each round a fair coin is flipped. If the coin is heads, Player 1 wins the round. Otherwise, if it is tails, Player 2 wins the round. Whichever player wins four rounds first gets the $2 in the pot.

After four rounds, Player 1 has won 3 rounds and Player 2 has won 1 round, but they cannot finish the game. What is the fairest way to divide the pot of $2? In other words, what is the probability that player 1 would win if they were to continue and play the last three rounds? Likewise, what is the probability player 2 would win if they were to continue and play the last three rounds?

Answer #1

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