Since I first started this blog, one of the great mysteries of the universe has been what exactly this is supposed to be about.  However, I have preferred not to make it about any one thing in particular, as I have mainly covered a certain range of topics within my areas of interest.  As a former math teacher and academic team coach several years ago, and also as a bit of a trivia fan, two of my areas of interest are math and the TV game show Jeopardy.  Here, I will combine these topics to present you with the following math problem:  What is the highest possible total you can get in a game of Jeopardy?

This question was originally inspired in my head in 2019 as Jeopardy contestant James Holzhauer became famous with one record-breaking performance after another as he won 32 games in a row.  Prior to James’s arrival on the show, the single-day record was $77,000, but he obliterated that record time after time with several results of over $100,000 each.  This led me to wonder what the highest possible single-day total was.  Suppose someone were to answer every single question correctly.  How much money would they earn in one game?  Let’s explore this question here.  If you’re the mathematically curious type, perhaps you’d like to see if you can figure this out for yourself before reading any further.  Or maybe you’d just like to read further.

The game is divided up into three rounds: Jeopardy, Double Jeopardy, and Final Jeopardy.  In the first round, six categories are available, with five questions each, for a total of 30 questions.  The questions range in value from $200 through $1,000.  One of the questions is a Daily Double, which allows the contestant who selected it to wager up to their current point value (or up to $1,000, whichever is greater).  Double Jeopardy has the same format, with two exceptions.  First, the point values are doubled, ranging from $400 through $2,000.  Secondly, there are two Daily Doubles in the round except for one.  Contestants may still wager up to their current point value (or up to $2,000, whichever is greater).  Final Jeopardy consists of one question, in which contestants write down their answers after having wagered a certain amount up to their current point total.  So, in order for a contestant to maximize their winnings, they must not only answer every question correctly, but they must also wager everything they have, every chance they get.  This would be a crazy strategy, but for the sake of argument, let’s suppose they do.

Incidentally, before we go any further, I realize that this game calls its clues answers, and the contestants have to come up with the question by starting their response with “Who is…” or “What is…”  With that in mind, I also realize that my use of the terms “question” and “answer” here are technically reversed, but I don’t care.  I’m just going to refer to these things the way everyone else does, with the clues as questions, and the responses as answers.  I also understand that Jeopardy is technically supposed to have an exclamation mark at the end and be spelled “Jeopardy!”, but the punctuation is messing me up when trying to write this, so I’m leaving out the exclamation mark.  Sorry if you care about things like that.

Anyway, to solve this problem, let’s first tackle the first round.  Each category’s questions are valued $200, $400, $600, $800, and $1,000.  Forgetting the possibility of the Daily Double for now, if a contestant runs the category, that’s a total of $3,000.  There are six categories, so (again leaving the Daily Double out of it for now), if a contestant answers each question correctly in the round, that comes to a total of $18,000.

Now the question becomes, what about the Daily Double?  Here’s where we run into two factors that the contestant doesn’t have control over: when they get the Daily Double, and the point value behind which the show’s producers have hidden it.  As far as when they get the Daily Double, take the game in which James finally lost.  His very first clue that he selected was for $1,000, and he hit the Daily Double right away.  Although he got the answer right to start off the game with $1,000, this little factor of luck ended up hurting him in the end.  Getting the Daily Double with the first question did him no good and may have cost him the game.  Getting a normal question correct would have still given him $1,000 to start, and he would have been able to get the Daily Double later and maximize his winnings.  Ideally, the hypothetical contestant who gets every question correct would want to hit the Daily Double with the very last question, so that they would have the most money earned up to that point.  So, while the contestant doesn’t necessarily control when they get the Daily Double, in order to get the maximum score possible, it would need to come up on the last question of the round.

The other factor to consider with the Daily Double is the point value behind which it is hidden.  Suppose the last question of the round in our scenario (the Daily Double) is for $1,000.  We have established that if it were not for the Daily Double being on the board, a contestant could earn up to $18,000 in the first round by answering every question.  So, going into this final question of the round, they have earned $17,000.  They wager everything and get the answer correct, bringing their first-round total to $34,000.  But is that the scenario with the highest possible score?

Suppose instead that the Daily Double is behind one of the $200 clues.  (I have actually never seen a Daily Double be on the top row of the board before, but it could happen if the show’s producers ever decided to put it there.)  Now suppose everything else is the same – our contestant has answered every question correct up to that point, leaving only the last $200 clue.  This means that their winnings at that time are $17,800.  They get the Daily Double on the final question, wager everything, and get the answer correct.  This means they have now earned $35,600 after the first round.  This would therefore be the highest possible first-round total.  So, getting the highest possible total depends on four factors:

1. Getting every question correct.
2. Wagering everything on Daily Doubles.
3. Getting the Daily Double on the final question of the round.
4. Having the Daily Double placed on the top row of the board.

Again, it should also be noted that while even the world’s smartest person has control over #1 and #2 above, they cannot control #3 or #4.  So, the winnings from a perfect game may vary, depending on when and where the Daily Doubles occur.  For our purposes, we are figuring out the highest total theoretically possible.

Of course, we have only figured out the highest possible total after one round so far.  Now we still need to move on to Double Jeopardy.  As previously mentioned, this round contains two Daily Doubles, and the point values range from $400 through $2,000.  This means that running an entire category in Double Jeopardy is worth $6,000, and the total point value from the entire board is $36,000.  Using the same logic from above, suppose we get every question correct in Double Jeopardy, but save both Daily Doubles for the last two questions of the round.  We need for both Daily Doubles to be behind $400 clues, which, since I have never seen the Daily Double appear on the top row before, I doubt we will ever see it placed there three times in the same game.  But suppose it happens.  Answering every question in the round up to that point leaves us with $35,200 so far in Double Jeopardy alone, going into the last two questions.  Adding in our $35,600 that we already earned before Double Jeopardy, this now brings our total to this point at $70,800.

With our current total at $70,800, we get the first of the two Daily Doubles.  Even though it would be crazy to wager it all, we do so and get the answer correct, bringing our total to $141,600.  Then, for the final question of the round, we get the second Daily Double.  Again, we wager it all, get the answer correct, and enter Final Jeopardy with a total of $283,200.

At this point, I would just like to point out how crazy it would be to actually wager it all on this question in this scenario.  Here you are, with $141,600 on the final question before Final Jeopardy, and both of your competitors have $0 (or negative amounts if they have buzzed in with incorrect answers).  They are already ineligible to compete in Final Jeopardy, and you have already won the game…that is, unless you wager it all and get the answer wrong.  Then you go down to $0, and nobody competes in Final Jeopardy.  Alex Trebek just says, “Well folks, it looks like we’re going to wrap up the show a little early today, so while I have this opportunity, I’d like to announce my retirement as the host of Jeopardy.”  And since we don’t want to see that happen, if you find yourself in this spot, at least knock off $1 from the wager to make sure that you still win the game and come back again the next day.  But at this point, I’m guessing your goal is to go for the perfect game, so you wager everything, get it correct (thankfully), and bring your total to $283,200.

Oh, but now we still have to play Final Jeopardy.  Of course, you are the only one still playing, so again, you could just knock off $1 from your wager to make sure you win the game and come back again the next day.  But no, you’ve come this far, and your ultimate goal is the perfect game.  So, you foolishly risk pulling a Cliff Clavin and wager everything on the Final Jeopardy question.  (For more context on pulling a Cliff Clavin, see the five-minute clip below, taken from the episode of Cheers when Cliff appears on Jeopardy.)  Thankfully, you do get the Final Jeopardy question correct, and you walk away with the perfect game!  Your final total: $566,400!

So, there you have it.  If you appear on Jeopardy, play as aggressively as possible, answer every question correctly, and the board happens to break in such a way as to maximize your earnings, you can theoretically walk away with $566,400 in one game.  Again, the circumstances to achieve that amount are extremely unlikely, not fully within the control of the contestant, and would partially be controlled by the producers’ placement of the Daily Doubles.  If we wanted to keep tackling Jeopardy-related math problems, this could lead us to other such questions like:

1. What is the highest possible score you can get on Jeopardy if the Daily Doubles are all on the bottom row?
2. What is the highest possible score you can get on Jeopardy if you hit all the Daily Doubles first?
3. What is the lowest possible score you can get on Jeopardy?

I’ll leave those questions for you to ponder on your own.  Or now that you know how much you can possibly win on Jeopardy, perhaps you’d like to go study, try to get on the show, and break the single-day record.  James currently holds the single-day record at $131,127.  Even though we’ve figured that a much higher total is theoretically possible, I imagine that record will be pretty hard to beat.  Good luck!

Incidentally, a new season of Jeopardy starts this Monday, September 14, with brand new episodes.  There’s my plug.  You’re welcome.