Betting On A 7 Game Series
The Warriors are about to play a seven game series vs. the Trail Blazers. In a seven game series, teams continue to play games until one team has won four games. This team is announced the winner of the seven game series.
Being an avid fan, Ted wants to bet $100 that the Warriors will win the series. However, to his dismay, he discovers that he is only able to bet on one game at a time, and can bet up until that game starts.
With a bit of thought, he comes up with a strategy to place his bets for each game (based on results of previous games) so that the final outcome mimics betting on the series, IE he wins $100 if the Warriors win the series and loses $100 if they lose the series.
With this strategy, what is the dollar amount he should bet on the first game? e.g. If he should bet $12.34 on the first game, give your answer as 12.34.
Explicit Example: Consider a three game series, where the team that wins 2 games wins the series. Then, we if bet in the following manner, we see that no matter when the Warriors win (green lines), we get $100, and no matter when Trail Blazers win (pink lines), we get -$100.
This problem was presented to me some time back by my good friend, Matt Cushman.
The answer is 31.25.
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1 solution
It is likely easiest to figure out if you work backwards. i.e. Figure out what you would need to bet on whatever games could be the last ones and work backward from there.
Ted's strategy is as follows:
Therefore, the dollar amount he should bet on the first game should be $ 3 1 . 2 5 .