Quote:
Originally Posted by durkadurka33
OP's mistake is that if the values of people's 'stack' going into final jeopardy are different, then people have to get the answer 'right' regardless. So OP's argument doesn't work.
Stacks of 14000, 10000, and 8000.
Leader should wager 6001. Why do you think that this is irrational?
Because 2nd should risk 2000 or 0 and 3rd should risk 0. If 1st is wrong he will lose by 1 dollar. 6001 is literally the worst possible wager he could make, even 14,000 would be preferable. If he does the smart thing and bets 6000, he will win unless he is wrong AND second place is correct.
The argument for eliminating a strong opponent may be valid in theory but in practice you can almost never be certain enough that your opponent is in fact above average to justify the EV loss of risking losing by $1. The culprit is most often the leader who bids a dollar more than 2nd place can match. Unless 2nd was a champion of twice or more, the best case for knowing that 2nd place is well above average is if you and him both have really high scores (like ~17k+ without substantial help from double jeopardy) and even that could be because the categories were favorable or the third player just flat out sucked. The vast majority of the time there is insufficient evidence, due to sample size and variance issues, to assess how good your opponent is.
So it makes the most sense that the producers tell them to win by a dollar, which of course destroys the credibility of the show because it's not supposed to be, you know, rigged. Even if it was just tying that they didn't like, that still wouldn't explain the win-by-a-dollar strategy. Take rmoriar's example of 18k, 14k, 3k. If 1st is going to bet 10,001, he might as well bet 11,999, or at least 10,999, to beat 3rd place and undercut B's potential strategy to do the same (this is in the case that 3rd place is correct and the other two are wrong).
But of course nobody does that, so it must be that they are told to outbid by a dollar if they are in the lead. Doing it on their own would be abject stupidity. And Jeopardy is a difficult game that requires a lot of academic knowledge and good recall ability, which more often than not belong to intelligent people.