Eric loses in Final Jeopardy by TWO dollars!
That was some interesting wagering.
Right! Eric did not have a runaway....so why did Megan not bet enough to pass his total going into Final Jeopardy? That made no sense....all Eric had to do was bet ZERO dollars and she would have lost regardless of whether he got the answer right or not. She's lucky he bet just enough to lose.
So...I finally got around to watching this episode last night. The scores going into Final J were:
Eric: $18,600
Megan: $10,000
Barry: $9,000
Eric had a runaway as against Barry but not as against Megan. Therefore, the logical wagers were as follows:
Eric: $1,401 (which was his actual wager). This wager assures Eric that, if he answers correctly, he'll win. Unfortunately, he could not guard against losing to Barry if he doubled his money and answered correctly. Therefore, there would have been no additional downside to wagering more than this amount. Wagering $0 was also a possibility but not a good one (see below).
Barry: $8,200. As noted, if Eric successfully responded to FJ, Barry couldn't catch him. Therefore, Barry had to wager for the possibility of Eric getting it wrong but also needed to take into account Megan's strategy, which is a bit complex as discussed below. Assuming Eric wagered logically, then Barry should have wagered enough to pass Eric. If Eric wagered $1,401 and missed, he'd be left with $17,199, so Barry should have wagered enough to surpass that number, which meant he should have wagered $8,200, which would have left him at $17,200. However, his best chance would have been to wager everything he had (see below). His actual wager of $8,000 made no sense at all.
Megan: Several options for Megan. Megan's first option was to double her money by wagering $10k. However, Eric could have easily countered that (and did), so her smarter move was to wager based on the premise that Eric would be incorrect. If Eric were incorrect and wagered $0, Megan should have wagered $8,601. However, wagering $0 would have been illogical for Eric because it takes the result out of his hand. Wagering $0 leaves it entirely up to Megan (who, as it turns out, was the only person to respond correctly). That leaves Megan's third, which was wagering what she did wager - $7,201. If Eric makes his most logical wager ($1,401) and responds incorrectly, then $7,201 wins (and actually did win) her the game. The $7,201 wager assumes Eric wagers logically and counts on him being incorrect. Since a correct response by Eric wins no matter the wager (unless Eric illogically wagers $0), Megan's wager was the almost right decision. The problem is that, had Barry responded correctly and made a more intelligent wager, he would have won. Therefore, Megan should have wagered $8,001.
I always wonder how much time they get to make their wagers. I assume it's more than the 2-minute commercial break, but I wonder if it's enough time to do all the necessary math. Hopefully, one of these days, I'll have the opportunity to find out.
P.S. Eric commented in a post-show interview that he completely overthought what I thought was a crazy obvious Watergate question. I kinda feel like when you see that the category is "1972," your first thought is either Watergate or the Munich Olympics. While they all gave Watergate-related responses, Nixon was really the obvious response.