Here are some recent situations I have seen on Jeopardy. The analysis really flows pretty easily after internalizing the principles I wrote about in part 1.
game 1. player A: 13,400; player B: 8,000; player C: 8,000
B & C bet the max, and A bet 2,600. They all got it right, for the first three-way tie in the history of Jeopardy. The question here is why did player A not bet the extra dollar?? The only possible rational reason for this is if Player A felt that playing again against the same two opponents gave him a better chance than playing against the next 2 players in line to come on the show.
However, at the start of the next day's show Alex mentioned that during the break beforee the final question the prior day some kid in the audience had shouted out "Has ther ever been a three-way tie". Apparently the leader then decided to set it up for the tie to make history!
game 2: Player A--22,500, betting 8,301
Player B--15,400, betting 7,701
Player C--6,400, betting 6,400
Plasyer B blunders on 2 counts here. First, he does not create the necessary "separation" between his bet and A's bet. Although they are not close with their starting amounts, B is close enough to A to still be able to create separation. He does this with a bet of less than $1,201. This ensures that he wins whenever he and A both get the question wrong.
The other reason B blunders is he doesn't take C's score into account. Based on C's score, he needs to bet less than 2,600, so that he still beats C when C bets everything and gets it right, but he (B) misses. So, the small bet is correct for B for 2 reasons here.
game 3: Player A--16,800, betting 9,201
Player B--13,000, betting 13,000
Player C--13,000, betting 5,000
Very nice bet by C here, as he will win whenever they all miss the question. If you run through the 8 possible outcomes here, you will see that A wins in 4 of those, and B and C win 2 each. You might think, therefore, that B and C's chances are equal; however, B's chances are dependent on his getting the questions and A's missing it. It is much more likely that each will either get the question or each will miss it, than that one will get it and the other won't. Consequently, C's bet is much preferable to B's.
game 4: Player A--16,100, betting 10,800
Player B--13,400, betting 3,000
Player C--4,000, betting 4,000
Player A gets lazy here and doesn't want to do the math to make the correct bet of 10,701. The reason you don't bet that extra 99 is that it makes it easier for B to create the separation he needs.
B's range of correct bets here is 0-5,399, ensuring separation from A while also ensuring he cannot lose to C no matter what.
game 5: Player A--20,200, betting 13,000
Player B--16,200, betting 15,000
Player C--9,800, betting 9,800
Again, we have a lazy A here. There is no reason in the world to bet more than the 12,201 needed to ensure victory whenever he gets the question right. All the extra 799 does is create additional scenarios under which B or C could sneak in with a win when A misses the question.
B's big bet is certainly odd. She must have liked the category of classical composers. In fact she won the game when she got it with Beethoven, and A missed with Mozart!
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