# Min and max winnings at Jeopardy?

sonhouse
Posers and Puzzles 04 Jan '10 13:15
1. sonhouse
Fast and Curious
04 Jan '10 13:15
Assuming the winner has response times twice as fast as anyone else, is able to click on every question and answers every question correctly, with the random nature of the doubles, I think from the third to the 5th level, what is the min and max winnings possible in one game?
2. PBE6
Bananarama
04 Jan '10 16:17
The maximum amount you can win on Jeopardy! is as follows:

The total dollar value on the board in the first round is 6*(\$200 + \$400 + \$600 + \$800 + \$1000) = \$18,000. For maximum winnings, the Daily Double clue must be hiding behind the least dollar value (\$200) and be picked last, so the maximum doubling total is \$18,000 - \$200 = \$17,800. Therefore, the maximum you can have at the end of the first round is 2*\$17,800 = \$35,600.

The total dollar value on the board in the second round is doubled to \$36,000. For maximum winnings, the 2 Daily Double clues must be hiding behind the least dollar value (\$400), and be picked last, so the maximum doubling total is \$35,600 + \$36,000 - 2*\$400 = \$70,800. Therefore, the maximum you can have at the end of the second round is 2*2*\$70,800 = \$283,200.

Final Jeopardy is simply a doubling stage, so the maximum you can win on Jeopardy! is 2*\$283,200 = \$566,400. Not too shabby! Next to impossible to achieve, but not too shabby at all.
3. uzless
The So Fist
04 Jan '10 19:432 edits
so to answer sonhouse's question, replace the -200 in the first section with -600 and in the second section replace -2*400 with -2*1200 to get the answer.

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4. 04 Jan '10 20:20
Minimum winnings would be \$0. Everyone bets the house on Final Jeopardy and loses.
5. PBE6
Bananarama
04 Jan '10 20:55
Originally posted by uzless
so to answer sonhouse's question, replace the -200 in the first section with -600 and in the second section replace -2*400 with -2*1200 to get the answer.

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sonhouse obviously asked the wrong question! ðŸ˜‰
6. sonhouse
Fast and Curious
04 Jan '10 21:041 edit
Originally posted by PBE6
sonhouse obviously asked the wrong question! ðŸ˜‰
I did specify every question answered correctly. Obviously if you flub them all you get zero.
So at the rate of 500,000 a day, Ken Jennings would have taken in 35 mil!
7. PBE6
Bananarama
04 Jan '10 21:07
Originally posted by sonhouse
I did specify every question answered correctly. Obviously if you flub them all you get zero.
I think he was referring to the fact that you assumed the Daily Doubles would appear in the 3rd, 4th or 5th rows, while I assumed they would appear in the 1st. Potato, tomato, taco, linguine, fettuccine, martini, bikini...
8. forkedknight
Defend the Universe
05 Jan '10 00:26
The minimum you could win by answering all questions correctly and wagering the max at all times would be to pick the daily doubles first and wager the max (1k for round 1 and 2k for round 2). This results in winnings exactly equal to the amount in prizes on the board.

Double your money on final Jeopardy, and you end up with 2 * (\$18,000 + \$36,000) = \$108,000