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#1
11-10-2017, 11:47 AM
 judigolders Junior Member Join Date: Nov 2017 Location: Hawkins, Indiana Posts: 1
series of escalating playoff bets - logic, help!

Del. Thank you.

Last edited by judigolders; 11-13-2017 at 07:32 AM.
#2
11-10-2017, 01:43 PM
 uigrad Member Join Date: Jan 2014 Posts: 99

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.
#3
11-10-2017, 02:25 PM
 uigrad Member Join Date: Jan 2014 Posts: 99

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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