drudman
12-01-2004, 06:32 PM
The lady who beat Jennings I think made a big mistake in her final wager. She wagered just enough to go ahead of Ken by 1 dollar at his current total. Before she makes her wager, let's say she has three options. Bet it all, bet none, or bet somewhere in between.
She can't control what he bets or what he wagers. If she has a good read on Ken, she knows that he gets most Final questions right. Clearly, betting none is foolish because she needs him to a) lose and b) bet enough to put himself below where she is.
That leaves her with bet it all, or bet less than it all, but not nothing. In the second case, she must bet at least enough to tie him to avoid the pitfall of needing him to get the question wrong that eliminated option 1. I think it would be prudent for her to assume that he will not get the question wrong, based on our knowledge of his history. In which case, every dollar above going for a tie that she bets creates one possible case where they can both be right, and she wins. Which means betting it all creates the maximum number of scenarios in which she wins.
What she did is basically limit the number of scenarios in which they both are right and she wins to 2, when Ken bets 0, she wins, and when Ken bets 1, she ties (as good as a win in Jeopardy, but not when it means you will just have to face Ken again the next day).
For these reasons, I think that betting it all is clearly maximizing +EV.
In any case, she got lucky and Ken blew what I thought was an easy one.
She can't control what he bets or what he wagers. If she has a good read on Ken, she knows that he gets most Final questions right. Clearly, betting none is foolish because she needs him to a) lose and b) bet enough to put himself below where she is.
That leaves her with bet it all, or bet less than it all, but not nothing. In the second case, she must bet at least enough to tie him to avoid the pitfall of needing him to get the question wrong that eliminated option 1. I think it would be prudent for her to assume that he will not get the question wrong, based on our knowledge of his history. In which case, every dollar above going for a tie that she bets creates one possible case where they can both be right, and she wins. Which means betting it all creates the maximum number of scenarios in which she wins.
What she did is basically limit the number of scenarios in which they both are right and she wins to 2, when Ken bets 0, she wins, and when Ken bets 1, she ties (as good as a win in Jeopardy, but not when it means you will just have to face Ken again the next day).
For these reasons, I think that betting it all is clearly maximizing +EV.
In any case, she got lucky and Ken blew what I thought was an easy one.