Most Money That Can Be Won?
The Theoretical Maximum for One Game of Jeopardy!
Here are the important parts of the analysis:
First and most obviously, the contestant must buzz in on every clue and get it right.
Second, on a Daily Double, the contestant must wager everything and get it right. The player also must hit each of the Daily Doubles; there is the slight chance that the player is not standing the leftmost podium and the player who chooses first hits the Daily Double off the bat. That blows it right there.
Third, note that Daily Doubles are really where the big scores come from because scoring becomes exponential.
Fourth, note that in order to maximize your earnings on the Daily Doubles, you need to have the most money possible before you land on them. For the purposes of this discussion, assume that a Daily Double can appear anywhere on the board. (When they're in the $100/$200 top row, the potential is greatest, but in reality they nearly always appear in the third row or lower.)
Finally, the strategies that apply to Daily Doubles also apply to Final Jeopardy! since you have the same potential to double your money there, too.
Taking all of that into account, the theoretical maximum would be obtained as follows.
1. Get $8900 in the Jeopardy! round by clearing all squares but the Daily Double, in the first row. Double up for a first round total of $17,800.
2. Do the same thing in Double Jeopardy!, leaving two Daily Doubles in the first row. That adds $17,600 to your score for a total of $35,400.
3. Double up twice to finish Double Jeopardy! with $141,600.
4. Be brave and double up again in Final Jeopardy! to finish with $283,200.
That means a five-time champion has the potential to walk away with over $1.4 million ; factor in the realistic locations of the Daily Doubles and the total is slightly smaller (exercise is left to the reader).