Brain Teasers
World Series Gamble
The winner of the World Series is the first team to win four games, so the maximum number of games that could be played is 7. You want to place a $100 bet (even money) on your team to win the whole series. A bookie says he will not take bets on the whole series, but would be willing to let you bet on each individual game. Is there a betting strategy you could put in place to replicate your $100 bet?
Hint
Think back from game 7Answer
On games 1 and 2, bet $31.25. On game 3, bet $25.00 if your team is 2-0 or 0-2, and $37.50 if the record is 1-1. On game 4, bet $12.50 if the record is 3-0 or 0-3, and bet $37.50 if the record is 2-1 or 1-2. For game 5 (if you get to it), bet $25 if the record is 3-1 or 1-3, or $50 if the record is 2-2. If there is a game 6, bet $50 on it. If you get to a game 7 (so the record is 3-3), bet $100.Here is why this works. At game 7, you need to have had $0 profit or loss from the previous games, so you want to bet $100 to replicate your winner-take all bet. Taking a step back, this means that if your team was 3-2, you would have had to lose enough money to get to $0 profit, and win $100 if they won, so your bet would have had to be $50. (Same on the losing side, so you would lose $100 if your team lost and they were 2-3 coming in to the game, or gotten back to $0 if they won to get to 3-3.) The reverse induction works all the way back to the initial bet of $31.25.
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Comments
Wow!!!
Really unclear as to what it is you were talking about... but either way, you could bet $100 each time, and win/lose/win/lose/win/lose and then bet $100 the last game, too. ...whatever
If you bet $100 each time, you would lose $400 if your team went 0-4. The objective (maybe I should have been more clear) was to win or lose $100 if your team won or lost the entire series.
I didn't understand what the question was asking.
Surely the odds on each game would vary so that your winnings woudn't always be equal to what you bet.
Its too long and complicated for simple people like me
i agree w/ skybet
man it was way to easy
yeah, skybet. my brain hurts...
The teaser is flawed. It makes two undocumented assumption
1) All bets have even odds
2) It must take 7 games befoire a team wins the series. It may take anywhere between 4 and 7 in reality.
Would have been a good teaser if these assumptions were stated.
1) All bets have even odds
2) It must take 7 games befoire a team wins the series. It may take anywhere between 4 and 7 in reality.
Would have been a good teaser if these assumptions were stated.
The even money piece is stated parenthetically after the bet you want to make. And the beauty of this plan is that it does work if the series ends after 4 games. Or 5. Or 6. Or 7. That's actually what has to happen to replicate the even-money bet you want to make. If you want me to walk you through the entire betting tree, send me a PM. Thanks.
too complicated!!!!
Feb 24, 2005
I didn't think it was possible, but the solution shows it is so. Wow, you really opened my eyes on this one. That was a great one.
Mar 04, 2005
The flaw in your solution is exposed if your team loses the series 1-4. At 1-3, under your betting sheme, you would have $50.00, and if you bet $25 as you suggest, and lose, you would still have $25 and the series would be over. Even if you win, you would have $75 at 2-3. If you bet $25 on game 6, and win, you "could" enter game 7 with $100, but if you lose, the series would be over at 2-4, and you would have $50 left.
Oops -- should have said to bet $25, not $12.50, on game 3. Thanks for pointing out the error. I will correct the teaser.
you need to factor in the "juice" (which is a percentage that the bookie adds for a lost bet) which is usually 10% of the action. it was a fun teaser anywho!
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