World Series Survival
The CIA asks you to infiltrate the North Korean leadership. After attempting to enter the country, you’re captured by Kim Jong-il. But it turns out he’s a fan of American baseball, and as the World Series is about to start, he chooses to give you a sporting chance to be freed.
The Yankees are playing the Red Sox and the 2 teams are perfectly, absolutely matched. Each game is a coin flip — the chances of a win for both are exactly 50%. The outcome of any previous games does not give you any information about who’ll win the next game.
The Dear Leader wants to bet a million bucks that the Yankees will win the entire series. He will front you the cash (i.e., he’ll give you $1 million up front, and you give him $2 million back if the Yankees win, and give him nothing if the Yankees lose).
If you decline the bet, he will kill you. If the Yankees win and you don’t have all $2 million to pay him, he will kill you. If the Yankees lose, and you have money left over, he will accuse you of stealing and kill you. You have no money, except for the money he’s given you, and maybe a couple hundreds in your pocket (for rounding errors).
There are bookies you can place bets with in Pyongyang, but unfortunately they will only accept bets for one game at a time, not for the whole series. Since each game is a coin flip and the outcome of previous games doesn’t change that fact, you can place whatever size bet you want on each game, at fair odds ($1 wagered wins $2 back), right before they occur (after any previous games have been played). Obviously you must have the money in your pocket to place the bet.
Remember, the World Series is a 7-game series where the first team to win 4 individual games is declared the winner.
How should you place your bets to guarantee you’ll have 2 million bucks for Kim Jong-il if the Yankees win the entire series, and $0 if they lose?