This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.

What are the highest, lowest, and most different scores contestants

can achieve during a single game of Jeopardy?

competition/games/jeopardy.s

highest: $283,200.00, lowest: -$29,000.00, biggest difference: $281,600.00

(1) Our theoretical contestant has an itchy trigger finger, and rings in with

an answer before either of his/her opponents.

(2) The daily doubles (1 in the Jeopardy! round, 2 in the Double Jeopardy!

round) all appear under an answer in the $100 or $200 rows.

(3) All answers given by our contestant are (will be?) correct.

Therefore:

Round 1 (Jeopardy!): Max. score per category: $1500.

For 6 categories - $100 for the DD, that's $8900.

Our hero bets the farm and wins - score: $17,800.

Round 2 (Double Jeopardy!):

Max. score per category: $3000.

Assume that the DDs are found last, in order.

For 6 categories - $400 for both DDs, that's $17,600.

Added to his/her winnings in Round 1, that's $35,400.

After the 1st DD, where the whole thing is wagered,

the contestant's score is $70,800. Then the whole

amount is wagered again, yielding a total of $141,600.

Round 3 (Final Jeopardy!):

Our (very greedy! :) hero now bets the whole thing, to

see just how much s/he can actually win. Assuming that

his/her answer is right, the final amount would be

$283,200.

But the contestant can only take home $100,000; the rest is donated to

charity.

To calculate the lowest possible socre:

-1500 x 6 = -9000 + 100 = -8900.

On the Daily Double that appears in the 100 slot, you bet the maximum

allowed, 500, and lose. So after the first round, you are at -9400.

-3000 x 6 = -18000 + 400 = -17600

On the two Daily Doubles in the 200 slots, bet the maximum allowed, 1000. So

after the second round you are at -9400 + -19600 = -29000. This is the

lowest score you can achieve in Jeopardy before the Final Jeopardy round.

The caveat here is that you *must* be the person sitting in the left-most

seat (either a returning champion or the luckiest of the three people who

come in after a five-time champion "retires") at the beginning of the game,

because otherwise you will not have control of the board when the first

Daily Double comes along.

The scenario for the maximum difference is the same as the highest

score, except that on every question that isn't a daily double, the

worst contestant rings in ahead of the best one, and makes a wrong

guess, after which the best contestant rings in and gets it right.

However, since contestants with negative scores are disqualified before

Final Jeopardy!, it is arguable that the negative score ceases to exist

at that point. This also applies to zero scores. In that case,

someone else would have to qualify for Final Jeopardy! for the maximum

difference to exist, taking one $100 or $200 question away from the

best player. In that case the best player would score 8*$200 lower, so

the maximum difference would be $281,600.00.

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