I'm right there with you, Dave. The logic is simple and most Jeopardy viewers and contestants know it. There's a strategy for first, second and third place players that make me shake my head when people blow it. For example:

1st place = $18000 2nd place = $9000 3rd place = $5000

Player #1 bets zero, player #2 bets everything and player #3 bets $4001. That way, player #2 can tie player #1 and player #3 can at least come in second if player #2 answers incorrectly.

1st place = $18000 2nd = $12000 3rd = $10000

Player #1 bets $6001, player #2 bets $8001, player #3 bets $8001. That way, player #1 can beat player #2 regardless of what player #2 bets. Player #2 can beat player #3 if they both answer correctly and player #1 answers incorrectly. And player #3 beats player #1 and #2 with a correct answer and an incorrect answers by the others. Bets should always be made knowing that players #2 and #3 can only win if the player[[s) ahead of them miss the final question.

Here's the tricky one [[and my logic may not serve for everybody here):

1st place = $18000 2nd place = $17000 3rd place = $15000

In this case, player #1 has to bet $16001 and player #2 has to bet everything. If I was player #3, I'd bet $0. You always want to leave with the most money possible but #3 only wins with missed answers by the other two. You could play it safe and bet as much as $13000 [[leaving you with $2000 with an incorrect answer while knowing that #1 would be left with $1999 with the most logical bet). Personally, I'd be fine with 15 grand.