Betting on the world series

This Riddler classic puzzle is about placing bets on baseball:

You are a gambler and a Cubs fan. The Cubs are competing in a seven-game series against the Red Sox — first to four games wins. Your bookie agrees to take any even-odds bets on any of the individual games. Can you construct a series of bets such that the guaranteed outcomes are: You win \$100 if the Cubs wins the series and lose \$100 if the Red Sox win it?

The challenge here is that we don’t know ahead of time when the series will end. It could end in a four-game blowout, or it could last the full seven games. How should we construct our bets so that the result is the same regardless of series length? Here is my solution:
[Show Solution]

4 thoughts on “Betting on the world series”

  1. Is it more elegant to know that you have to be at a sum of zero if the series is tied at 3 each, at which time you’d need to bet $100? Then, if you have listed the sample space as a tree, you can just work backwards.

    1. If you want to eliminate some parameters you can just express it as (n C r) / 2^n, where n is the number of games left to play until the championship (aka M-1) and r is the number of games you still need to win. Yours is in the form of the table and obviously equivalent, though.

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