## Monday, October 16, 2017

### How much could you theoretically win on Jeopardy?

There was a recent puzzle question that asked what was the maximum amount of money a contestant could win in a single game of Jeopardy!  This presumes one single contestant rang in first on every single question and answered each one correctly. I will attempt to answer that question here, using my amazing powers of ciphering.

Caveat: I have never seen a Daily Double (1 in the first round, 2 in the second) come up on the topmost question (\$200 for first round, \$400 for second) but I am not aware if there is an actual rule for it. I'm going to assume for the sake of argument there is no rule, and it's possible a Daily Double could appear in a top level question for both rounds.

Here we go:

ROUND ONE

Six categories, each containing five questions. The questions are worth:

\$200
\$400
\$600
\$800
\$1000

I can calculate clearing a single category would award the player:

\$3000

Setting one category aside that contains the Daily Double, answering five categories correctly would net the player:

\$3000 x 5 = \$15,000

Assuming the Daily Double in the sixth category is under the \$200 answer, answering the other four questions would bring the total to:

\$15,000 + \$400 + \$600 + \$800 + \$1000 = \$17,800.

When the player chooses the last answer, the Daily Double, they will not receive the \$200 but instead have the option to make it a true Daily Double and double their money. Which, of course, they will do.

\$17,800 x 2 = \$35,600.

Thus they will end Round One with a comfortable lead of \$35,600. Let's set that sum aside for a moment.

ROUND TWO (Double Jeopardy!)

Dollar values are doubled in this round, so the questions are now worth:

\$400
\$800
\$1200
\$1600
\$2000

Clearing a single category would earn the player:

\$6,000

Setting two categories aside that contain the two Daily Doubles, answering four categories correctly would net the player:

\$6,000 x 4 = \$24,000

Assuming the two Daily Doubles in the sixth category are under the two remaining \$400 answers, answering the other four questions in the two remaining categories would bring the total to:

\$24,000 + \$800 + \$1200 + \$1600 + \$2000 + \$800 + \$1200 + \$1600 + \$2000 = \$35,200

At this point I will re-add the winnings from Round One to their Round Two total:

\$35,600 + \$35,200 = \$70,800

When the player chooses the first Daily Double under the first \$400 answer they will again make it a true Daily Double and double their money. Doubling their money with the first Daily Double would net them:

\$70,800 x 2 = \$141,600

Choosing the second Daily Double would double their money once again:

\$141,600 x 2 = \$283,200

They will end Double Jeopardy!

FINAL JEOPARDY!

This is a simple doubling of their previous total:

\$283,200 x 2 = \$566,400

So, theoretically, a contestant that buzzes in on every answer first, answers them correctly, saves the Daily Doubles for the very last answer(s) and makes each a true Daily Double, then doubles their bet in Final Jeopardy would win that contestant in one day:

\$566,400