#1




series of escalating playoff bets  logic, help!
Del. Thank you.
Last edited by judigolders; 11132017 at 07:32 AM. 
#2




Wow, cool puzzle! I agree with your answer for part A, and it seems that the secret is starting with the last game and working backward. Using this method, I solved B:
B FIVE GAME SERIES? FIRST GAME BET _____ [$375] SECOND GAME BET ____ [$375] THIRD GAME BET IF A TEAM IS UP 2 GAMES TO NONE ____ [$250] THIRD GAME BET IF SERIES IS TIED 11 ____ [$500] FOURTH GAME BET (ASSUMES SERIES IS NOW 21) ____ [$500] FIFTH GAME BET (ASSUMES SERIES IS NOW 22) _____ [$1000]  Here's my logic: A: Solving for game 5: If the Indians win, you need to be at +$1000, and if the Indians lose, you need to be at $1000. This is a total of $2000 difference, so you need to bet half of that ($1000), and your current winnings before game 5 must be $0. B: Solving for game 4 if the Indians are up 21: If the Indians win, you need to be at $1000, and if they lose, you need to be at $0 (starting point for game 5). The total difference is $1000 so you need to bet half of that ($500), and your current winnings before game 5 must be +$500. B': Solving for game 4 if the Indians are down 12: Same logic before, just change pluses to minuses, etc. C: Solving for game 3 if the series is tied 11: If the Indians win, you need to be at +$500 (because you will be in state B), and if the Indians lose, you need to be at $500 (state B'). Total difference is $1000, so you need to bet half of that ($500), and your current winnings before this state must have been $0. D: Solving for game 3 if the Indians are up 20: If the Indians win, you need to be at $1000, and if they lose you need to be at $500 (state B). The total difference is $500, so you need to bet half of that ($250), and your current winnings before game 3 must be $750. D': Same as D, just reverse plus minuses, and consider state B' instead of B. E: Solving for games 1 and 2: If the Indians win games 1&2, you need to be at $750 (state D), and if they lose games 1&2, you need to be at $750 (state D'). So, the total bet for games 1&2 must be $750. If the Indians split games 1&2, you need to be at $0 (state C), so the amounts bet for games 1&2 must be equal. Half of $750 is $375. I haven't considered a 7game series yet, but I'm sure it can be solved using similar logic. Last edited by uigrad; 11102017 at 01:57 PM. 
#3




I just decided to do the 7game version, since no one else responded. Maybe I should have waited longer, haha!
CSEVEN GAME SERIES FIRST GAME BET _____ [$187.50] ($0 before) SECOND GAME BET ____ [$187.50](±$187.50 before) THIRD GAME BET IF A TEAM IS UP 2 GAMES TO NONE ____ [$250](±$375 before) THIRD GAME BET IF SERIES IS TIED 11 ____ [$125]($0 before) FOURTH GAME BET IF SERIES IS 30 ____ [$375](±$625 before) FOURTH GAME BET IF SERIES IS 21 ____ [$125](±$125 before) FIFTH GAME BET IF SERIES IS 31 _____ [$250](±$250 before) FIFTH GAME BET IF SERIES IS 22 ______ [$500]($0 before) SIXTH GAME BET (ASSUMES 32) _____ [$500](±$500 before) SEVENTH GAME BET (ASSUMES 33) ____ [$1000]($0 before) EDIT: If anyone wants to go a step further, imagine that you aren't concerned about what will happen if the Indians lose 4 straight (maybe your friend will pay off your debts if this happens, or maybe a time traveler from the future has ensured you that it's an impossibility. ) So, now, you want to change your odds so that if the Indians win the 7game series, you end up +$1024. If the Indians lose (but aren't swept in 4), you want to end up even ($0). What would be your strategy to make this work? How huge will be your debt if the unthinkable happens (Indians are swept in 4)? Note: I changed it to $1024 to make the math a bit easier. Last edited by uigrad; 11102017 at 02:55 PM. 
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