Question on bets!!

[gsjayaraman]

Hey guys,
Having a bit of trouble with this question. Any help appreciated.

Your favorite baseball team is playing against your uncle's favorite team in the
World Series. At the beginning of each game, you and your uncle bet on the game's outcome.
Your uncle, being wealthy and carefree, always lets you choose the amount of the bet. If
you bet b dollars and your team wins the game, your uncle gives you an IOU for b dollars.
But if they lose the game, you give him an IOU for b dollars. When the series is over, all
outstanding IOUs are settled in cash. You would like to walk away with $100 in cash if your
team wins the series, and lose $100 if your team loses the series. How much should you bet
on the opening game? (For non-baseball fans, the first team to win a total of four games
wins the series).

 

[doug reich]

I was actually asked an equivalent question on a job interview.

Work backwards. (i.e., Suppose the score is 3-3; what should my current P/L and bet size be to have the required output? What about 3-2 based on that knowledge? How about 2-3, 3-1, 1-3, 2-2, 1-1, 1-0, 0-1, in that order, I believe?)

EDIT: This is called dynamic programming.

 

[gsjayaraman]

Hey Doug,
Thanks a lot for the tip. I managed to work it out using binomial trees.
CHeers.
Sankar.