World Series betting

You may bet only on individual games of a best-of-7 series (first to 4 wins). With $100, you want to net exactly +$100 if your team wins the series and −$100 if it loses, each game a 50/50. How much should you bet on the first game (in dollars)? (to 2 decimals)

Show hints (2)+
  1. Build the binomial tree of net payoffs from the end.
  2. The opening stake is half the difference of the two child values.

Answer

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31.25 (± 0.05)

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