Okay, I actually did some really bad math on my last formula. Like Brock pointed out, I forgot to add the sum from Single Jeopardy to the two Double Jeopardy Daily Double calculations. I also thought that there were only 5 categories for some reason. So, here's my new, fixed, and correct formula. It's a little less confusing than Brock's crazy bracket bombardment.
(((6000+4800+3600+2400+1000)*2+(12000+9600+7200+4800+1600))*4)*2
=((17800*2+35200)*4)*2
=((35600+35200)*4)*2
=(70800*4)*2
=283200*2
=566400
So, I have found that Brock's sum was correct, and the REAL max possible total for a perfect game of Jeopardy is $566,400.
Ken Jennings won $2,522,700, so,
2522700/566400=4.4539194915254237288135593220339.
So, it would take roughly 4 and a half perfect games to match, well, actually beat, Ken Jennings' winnings. Take that, Ken!
Oh, and a 5 time champ (the old cut off was 5 games) could win:
$2,832,000
Eventually, I'll get around to figuring out the odds of that happening, but the placement of the Daily Doubles would make it astronomically unlikely (assuming that they're random). I'm guessing somewhere in the 5 billion to 1 range.
I just realized that I have way too much time on my hands!
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