Quote:
Originally Posted by vixticator
Somewhat unrelated... let's say you go into final jeopardy with only 2 players because one guy was eliminated by having less than zero (right?) and the other two players have $1,001 (p1) and $1,000 (p2)? If they both play perfectly and let's say they somehow know each have 50% chance of getting the answer right how much should they bet? I assume there is a right answer... or is there a huge continuum of best responses?
This is a good example, I don't know what you mean by "plays perfectly" but in a real life situation on national TV final Jeopardy here you can take it to the bank that player 1 is betting $1000 or $1001.
He pretty much has to since in his mind he has to believe that there is a good chance that player 2 is just gonna bet $1K, and he certainly would look like a shmohawk if he bet less than $1K, got it right, and still lost. Virtually no one in the world would risk this happening against a random person whom they know nothing about.
So, with that in mind, played 2 can pretty much bet anywhere from 0-$998 if all he cares about is winning/losing and he'll basically win everytime P1 gets it wrong. I haven't thought about this too hard but taking the actual $ into consideration it seems to make sense that he bet $998 when he believes there is a >50% chance he will get the final question right, and bet 0 if he believes there is a <50% chance he gets it right, from a strictly EV standpoint.
EDIT:
Quote:
OP is basically right, still, FJ wagering is a mixed strategy not an absolute one. if P2 knows P3 is betting small, then he can bet small and lock out P1.
-ChipsAhoya
Chips is 1000% correct here, but my position is that you can pretty much
never be sure that randoms on Jeopardy are going to be betting in such a manner, and a leader failing to bet enough to cover a 2nd place double up is far, far, far too risky to ever be practical imo. There are definitely counter examples that can be conjured up, but they will almost certainly rely on assumptions regarding knowledge of opponents, categories, or questions that are highly unrealistic.
EDIT 2: Like P3 is Chris Ferguson and he doesn't know that you know who he is.
Last edited by Brocktoon; 06-08-2009 at 11:31 PM.