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Old 11-10-2017, 11:47 AM
judigolders judigolders is offline
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Lightbulb series of escalating playoff bets - logic, help!

Del. Thank you.

Last edited by judigolders; 11-13-2017 at 07:32 AM.
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Old 11-10-2017, 01:43 PM
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uigrad uigrad is offline
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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 1-1 ____ [$500]

FOURTH GAME BET (ASSUMES SERIES IS NOW 2-1) ____ [$500]

FIFTH GAME BET (ASSUMES SERIES IS NOW 2-2) _____ [$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 2-1: 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 1-2: Same logic before, just change pluses to minuses, etc.

C: Solving for game 3 if the series is tied 1-1: 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 2-0: 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 7-game series yet, but I'm sure it can be solved using similar logic.

Last edited by uigrad; 11-10-2017 at 01:57 PM.
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Old 11-10-2017, 02:25 PM
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uigrad uigrad is offline
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I just decided to do the 7-game version, since no one else responded. Maybe I should have waited longer, haha!


C--SEVEN 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 1-1 ____ [$125]($0 before)

FOURTH GAME BET IF SERIES IS 3-0 ____ [$375]($625 before)

FOURTH GAME BET IF SERIES IS 2-1 ____ [$125]($125 before)

FIFTH GAME BET IF SERIES IS 3-1 _____ [$250]($250 before)

FIFTH GAME BET IF SERIES IS 2-2 ______ [$500]($0 before)

SIXTH GAME BET (ASSUMES 3-2) _____ [$500]($500 before)

SEVENTH GAME BET (ASSUMES 3-3) ____ [$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 7-game 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; 11-10-2017 at 02:55 PM.
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