Devise a strategy of betting on a seven-game series such that if team 1 wins the series you win $\$1000$ no matter what and if team 1 loses, you lose $\$1000$. You can think with a strategy for NBA final and you are not a fan of both teams.
Any idea is welcome！I am looking for a best expected winning pre-designed pattern of this game.
Observation 1: The bets on the first six games, if each team wins three, must land you at wining/losing zero (I call this winnings of $0$). If this is not the case, then no bet on the last game achieves $\pm1000$.
Observation 2: The bets on the first five games, if one team wins three of them, must land you at $\pm500$ ($+500$ if team 1 wins three, $-500$ if team 2 wins three). Then (and only then) you can bet \$500 on team 1 in game six and be assured of either immediately getting the proper result, or reaching a 3-3 tie at $0$ winnings.
Observation 3: The bets on the first four games, if each team wins two, must land you at $0$ (and you bet \$500 on team 1 in the next game).
Observation 4: The bets on the first four games, if one team team wins three, must land you at $\pm750$. Then you can bet \$250 on team 1 and either terminate in the proper winnings or arrive at 3-2 at the proper amount ahead or behind.
Observation 5: The bets on the first three games, if one team wins two, must land you at some value that allows you to reach either $\pm750$ or $0$ depending on the outcome of the fourth game. That implies that the wager in that situation must be \$375 and that the bets on the first three games, if one team wins two, must land you at $\pm375$.
Observation 6: The bets on the first three games, if one team wins all three, must land you at some value that allows your next result to be $\pm1000$ or $\pm750$ (see observation 4, which says in a 3-1 situation you need to be up or down by \$750). The value that allows this is $\pm875$ and the wager, of course, is \$125.
Observation 7: The bets on the first two games, if each team wins one, must land you even, and at that point you will bet \$375 (see observation 5).
Observation 8: The bets on the first two games, if one team wins both, must land you at some value that allows your next result to be $\pm875$ or $\pm375$, depending on the winner of game 3. Therefore, the bets on the first two games, if one team wins both, must land you at $\pm625$ and you will bet \$250.
Observation 9: The bet on the first game must land you mid-way between even and $\pm625$. Than means the first bet must be \$312.50.
So here is your strategy:
Bet \$312.50 on team 1 in the first game. Then bet \$312.50 on team 1 in the second game. At game three, if the teams are even, increase your bet for game three to \$375. But if either team is up 2-0, decrease your bet to \$250.
After three games, if one team has won all three you will be ahead or behind by \$875 and you will bet \$125 on the fourth game. But if either team is ahead 2-1, you will be ahead or behind by \$375 and you will bet \$375 on the fourth game.
After four games, if the series is not over, you will either be even and bet \$500 on game five, or ahead or behind by \$750, in which case you will bet on \$250.
After five games either the series will be over, or you will be ahead or behind by \$500, in which case you will bet \$500 on game six.
And of course if the teams are tied after six games, then you are even as well, and you bet the full \$1000 on the final game.