You’ll want to watch Part Four before tackling this situation, which comes from September 27. Sarah, trailing by 100, has found a Daily Double on the last clue in Double Jeopardy!.
She’ll want to wager enough to put herself in first, surely – but what amount should she wager so that if she’s wrong, she’ll optimize her chances of returning the next day? Note: there might be more than one answer.
Hint: Remember the two wagertotie scenarios I suggested you memorize in Part Four:
evenlyspaced scores
first = second + third
Click here for my thoughts!
(Thanks to the J! Archive)
(click to view as a slideshow)


(1/8) Let’s return to the beginning.


(2/8) First vs. second. Rule #1: Kara locks out Russ.


(3/8) Rule #2: Russ stays above a Kara miss. Note that this means a maximum of zero.


(4/8) Rule #3: Kara wagers to stay above a zero wager by Russ.


(5/8) Since Russ can’t wager less than zero, and Kara has both a minimum and a maximum of 6,000, each must wager exactly that.


(6/8) Rule #4 opens up another possibility to Russ: wagering everything.


(7/8) Rule #1: Russ still has both options in play against DJ. (If DJ had more than half of Russ, Russ would need to wager everything, lest he get passed by third.)


(8/8) Kara threw in the extra dollar, but Russ’s wager was by far the bigger blunder. There’s no compromise – pick one or the other!
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Using your special scenarios, I think $6,700 would be good (end up third with evenlyspaced scores if wrong). I chose a wager of $6,400+ since that would put her above 1.5 times Neal’s total if right and thus force her opponents to get Final right to win. (As a sidenote, evenlyspaced scores as you described it applies only when 2nd is within 2/3 of the leader. If between 2/3 and 3/4 3rd will be in a “mustgetFinalright” position like Sarah would be on a Daily Double miss in your scenario. If at 3/4+ then 3rd is close enough to bet and stay above where his/her opponents would likely land on a miss.)