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

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