Jeopardy Math: What’s the most money that a contestant can win on one show?

You don’t need to be a Jeopardy fan to solve this math problem.  Try it!


Last night, Jeopardy stated running a special tournament head-to-head matching former super-champs Ken Jennings (longest winning streak – 74 games), Brad Rutter (most winnings including special tournaments) and James Holzhauer.

James Holzhauer – a professional gambler –  won $2,714,416 in his 33 appearances. His $82,255 average daily winnings uber-eclipsed other Jeopardy contestants.

See our prior post How a “professional sports gambler” is disrupting Jeopardy for a recap of his strategy

I was chatting with a friend who is a Jeopardy fan and former insurance industry exec.  The question on the table was whether Jeopardy has an insurance policy to cover a runaway daily winner like Holzhauer.  If yes, what’s the insurance risk?

Analytically, that led to today’s math problem: What’s the most that a contestant can win on one show?

For reference, Holzhauer won more than $100,000 five times  … his best day ($131,127) is an all time Jeopardy record. A typical Jeopardy winner hauls in about $25,000 per show.

Today, I’ll set-up the problem.  Again, you don’t have to be a Jeopardy fan or know the rules.  I’ll tell you all that you need to know to solve the problem.


What you need to know

The Jeopardy game has 3 rounds: The Jeopardy round, a Double Jeopardy round and a Final Jeopardy Round.

The Gameboard: In the Jeopardy and Double Jeopardy rounds, the gameboard has 6 topical categories, each with 5 questions.  The questions are sequenced from easiest to hardest,  The harder the question, the higher its dollar value.


Note: There is a complicator called “Daily Doubles” that I’ll explain later.


The Game: After the MC reads a  question’s clue, a contestant must buzz in before the other contestants and answer the question.

If the answer is correct, the contestant gets the assigned dollar value of the question and gets to select the next question’s category and dollar value.


Daily Doubles:  Hidden on the Jeopardy round’s gameboard is a square marked “Daily Double”.

Note: It’s not clear to me whether the show’s producer’s place the Daily Double randomly or strategically, e.g. tending towards more difficult questions.

If a contestant selects the square that has the hidden Daily Double, he can wager all or part of the winnings that he has amassed up to that point in the game.


Double Jeopardy: The basic rules and game play is the same in the Double Jeopardy round except that the question values are doubled, the questions are slightly harder and there are 2 Daily Double squares hidden on the gameboard.



Final Jeopardy

In the final round, all contestants have to answer the same question.  They are forewarned of the category and — before seeing the question — they can wager all or part of the winnings that they’ve amassed up to that point in the game.

That’s it.

Got it?


The Question: What is the most that a contestant can win on one Jeopardy show?


Hints: Assume that a player buzzes in first on all questions, answers all questions correctly, selects questions strategically … and that the Daily Double squares are placed beneficially (for the contestant).

Note: This is more of a logic problem than a number-crunching math problem.

Worksheet: For doodling and calculating ease, click for worksheet that displays the gameboards for the Jeopardy and Double Jeopardy rounds.

Now, get crackin’


Follow on Twitter @KenHoma

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