## Question on bets!!

Discuss all those difficult questions here.

### Question on bets!!

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).
shankster78

Posts: 8
Joined: Tue Jun 24, 2008 7:44 pm

This is on the top ten list in our book!

Binomial trees!
mj

Posts: 1380
Joined: Fri Jul 27, 2007 7:21 am

Thanks a lot MJ. That cleared it up for me.
shankster78

Posts: 8
Joined: Tue Jun 24, 2008 7:44 pm

### Re: Question on bets!!

\$31.25, independent of how likely my team is to win any game.

To see this work back from \$100 as a boundary condition, with the further conditions
that anytime my uncle and I are tied the total I have won so far is \$0 net and that winning-
losing commute (ie. win-win-lose should be the same as win-lose-win).

This is enough to generate a solution, in which each current total is the average of its two
successors.
SpecialK

Posts: 1
Joined: Wed May 26, 2010 12:43 pm