Owa Tagee Kiam
Posted by bozino 10 years ago
I watched Jeopardy last nite, and it was an interesting finish. All three players were in it, but one had no way of winning. So I'm going to focus on the other two.  
Player 1 (P1) has 16,600, P2 has 11,400.  
P1 bets 6201, which makes sense. If P2 bets it all, he ends up with 22,800. So P1 needs to have 22,801 to win, hence the 6201 bet.  
P1 bet 1000. Hmm. That seems odd. Until they both got the question wrong.  
So, P1 ends up with (16,600-6201) = 10,399.  
P2 ends up with 10,400, and the win. He bet that both players would get the answer wrong, and won. I don't recall ever seeing that before, but I don't watch all the time, so maybe it happens a lot.  
Anyway, I knew there had to some math to explain this, and I just had to figure it out. So, here's the math:  
Pn = Player n amount left before final jeopardy  
Pnb = Player n bet  
Pnf = Player n final amount  
PnG = Player n goal amount  
P1b = (2P2 - P1) + 1  
in this case: 2*11400 - 16,600 + 1 = 6201  
If P1 wins, P1f = P1 + P1b = P1 + (2P2 - P1) + 1 = 2P2 + 1  
If P1 loses, P1f = P1 - P1b = P1 - ((2P2 - P1) + 1) = 2(P1 - P2) - 1  
in this case: 2(16,600-11,400) - 1 = 10,399  
P2g = P1f + 1 (i.e. P2 needs one dollar more than what P1 ends up with)  
from above, P1f = 2(P1 - P2) - 1, so  
P2g = 2(P1-P2)  
P2b = P2 - (2(P1 - P2)) = 3P2 - 2P1  
in this case: 3(11,400) - 2(16,600) = 34,200 - 33,200 = 1000  
This only works, however, if 3P2 >= 2P1. And, of course you have to assume P1 is going to bet the minimum to win, and both answers have to be wrong.  
Now, maybe this is some well known Jeopardy thing, but I thought it took serious balls for that guy to bet they'd both get it wrong. And, he knew how to bet properly for it. And he was able to the the math - I would have forgotten to carry a 3 or something.  
This is what I was doing until 11:30 last night (DVR'd the show, watched it at 10:30).  
For the record, the "answer" was something about this country allows US hurricane hunters into it's airspace. The three answers were: North Korea, China and Iran.  
The correct questionanswer (which I got): What is Cuba.
MrsBot: Dude, you turned a game show into a math problem. Nerd much?
I couldn't believe they all failed on that question.
FoolProof: It was super easy.  
They bidding wasn't really a mystery. It was a well played gamble on the part of the eventual winner. (Who was behind at the time.)
fabulon7: I also couldn't believe they ALL got it wrong. It was easy.
FoolProof: We are totally better at Jeopardy than the people on Jeopardy.
Schauspieler: "I lost on Jeopardy, Baby"
Make this into a paper
SpearmintFur: And you will get it published in a major paper.  
I know a guy got a paper on game theory in "Deal or No Deal?" got in the American Economic Review.