Originally posted by sonhouse
I saw this Jeopardy show the other day, at the end player #1 had 13,000,
player #2 had 10,200, and player #3 had 10,000.
Is there a betting strategy that would give anyone an edge? If #1 doubles, and misses, he is at zero, but if he wins he has more than anyone else but say if he bets zero, he has 13K at the end no matter what he answers so the other players knowing that, what is their best bet?
player #1, since he has the most money, MUST bet enough money to allow for himself to win if he gets the answer correct, but should generally only bet JUST enough to go above the next highest possible value (double player #2). in this case, player 1 would bet 7401. This gives him the best possible scenario in case everyone gets their response wrong as well.
differing strategies now present themselves for player #2 and #3, depending on whether they trust player #1 to bet the "correct" amount. that is, they should assume that player #1 will put himself in the best possible position to assure his victory if he gets the question right. the following ideas are based on that assumption, and may not work in practice, but are my personal takes that i can logically defend.
if player #3 were out of the picture (as is sometimes the case) i would, as player #2, bet just enough to go ahead of player #1 (this is dependent upon our relative scores). So I COULD bet 2801. This FORCES player #1 to get the right answer to beat me if i get the right answer, and assures my victory over him if we both get it wrong.
since player #3 is very much "in the fight" since his score is comparable to the other players... player #2 (in my opinion) MUST bet enough to go ahead of player 3's score doubled. this makes player #2's bet at a minimum 9801. But then you lose the "double wrong answer" victory over player #1, and so you might as well bet to double your money (as player #1 has already assumed you would do).
Now player #3 actually has the interesting choice, since player #2 must bet at least 9801 to play for a victory. if player 3 chooses to double his score, he gains little. his only chance to win is if the others get the answer wrong, and he gets it right. Instead, if player #3 bets 3001 (my preferred choice), he clearly wins if the others get it wrong and he gets it right, but he also wins if EVERYONE gets it wrong. he also wins if the other two make a strategic blunder and bet zero, (regardless of whether they get it right). So, if he gets it right, he is forcing the other players to ALSO get it right in order to reap the advantage they earned from the earlier rounds of play.
I think many would tell me in practice this isn't a great choice, but I think that depends on the quality of strategist you are playing against, and CERTAINLY depends on the relative scores of the three players. The easier method is definitely to just try and double your money to secure the highest possible dollar amount available to your score... but I think you throw away the very plausible "victory by default" if final jeopardy is a real stumper.
This is all based upon "optimal" choices, and clearly could fail if any of the players either make a miscalculation; or if they fail to "play for a victory," instead assume they will get it wrong, and try to position themselves in such a way that will benefit them if everyone gets it wrong.
any comments/other strategies? i always enjoy analyzing these things, and frankly am befuddled by players who make strategic blunders in final jeopardy. it happens far too often that the person who was in first place doesn't bet enough to win, and then there is an easy final jeopardy, so the person loses.