# 123 competition/games/jeopardy.p

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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