Newhausen wrote: ↑
Fri Apr 23, 2021 11:01 pm
danspartan wrote: ↑
Fri Apr 23, 2021 10:46 pm
opusthepenguin wrote: ↑
Fri Apr 23, 2021 8:21 pm
Kelly lucked out here. He shouldn't have bet that dollar, leaving Dan a clear path to victory with no tiebreaker necessary.
$1 is a rational wager here. He is about 55% to win outright (leaders are favorites to get FJ correct).
Of the four 1st/2nd combinations
If leader bets $1
If leader bets $0
RR ties- 50% buzzer race
WR ties- 50% buzzer race
So if all possibilities were equal it’s a tie. 3/4 net wins.
However RR happens more frequently than WR.
So he is giving up half of ~33% (-16.5) and gaining half of about 18% (+10) for a net of -6.5% for wagering $0 vs $1.
Now if our leader thinks that 2nd is more likely to get FJ correct, then the math flips. But on average, leaders get more correct than trailing players.
(I am using leader is 55% to be correct and 2nd is 60/40 to correlate with 1st.)
RR=.55 x .6=33%
RW=.55 x .4=22%
WW=.45 x .6=27%
WR= .45 x .4 =18%
I feel like the person who has exactly double the other player's score going in to Final has a slightly better than 50% chance to win a buzzer race, almost by definition.
Not necessarily. On 5/18/2020, the first game taped without an audience, going in to FJ, Megan Elliott had $18,800 , exactly double Ben Scripps' score $9,400.
https://thejeopardyfan.com/2020/05/fina ... -2020.html
Ben was first on the buzzer 36.84% of the time, while Megan was first on the buzzer 29.82% of the time. The explanation was the Ben missed two daily doubles and several other questions while Megan answered all of her questions correctly.
OK, maybe that was unusual, but a leader should consider his/her individual situation carefully.
And, really, there is a psychological element to consider. For me, and I would assume for many, it would be much more painful to know FJ (even if you pretend not to) and then still lose, than to lose due to not knowing FJ. Look what happened to Roey Hadar:
Roey has to live with knowing FOR SURE he would have won if he had wagered, while Megan knows she could have easily lost anyway.
I liked both Roey and Megan and their losses both made me wish ties were still allowed. But, if I had to choose, I would much rather lose Megan's way.