Alex has decided to start a widget company with his $800 savings. He has put in an order for a widget machine that will be delivered next week and will cost him $800, to be paid on delivery. However, when he went back to check on his money he found out that last night, in a drunken stupor, he placed a $400 bet on Red in the upcoming Red vs. Blue Frungy tournament.
A Frungy tournament is a seven game tournament, one game played each day, and the first team to win 4 games wins the tournament. Red and Blue are equally skilled teams, and each game is 50-50 between them (and there are no ties in Frungy). Alex decided to go to the betting office to simply bet his remaining $400 on Blue so that they would cancel and he would be guaranteed to get back his $800 at the end of the week, but he has found out that that part of the betting is closed, now he can only bet on the individual games each morning.
Each morning, Alex may place as much money as he likes on an even bet for either Red or Blue. The bet is resolved that evening, and he will receive any winnings before the next day. Find a betting strategy that guarantees that Alex will end the week with at least $800 so he can make the payment for his widget machine.
Assuming that all made sense through the "theme", you basically have to guarantee that if Blue wins 4 games, you have made at least $800 from your bets. If Red wins 4 games, then your side bet kicks in and you are safe no matter what.
Alex would just like to bet all $400 on Blue in the first game, but Blue might lose the first game and then go on to win the tournament. Find a strategy that maximizes the probability of ending the week with at least $800.
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