Final Jeopardy! wagering analysis:
Tuesday, February 9, 2016 (College SF #2)
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I hate the middle semifinal in Jeopardy! tournaments, because it makes me think it’s Wednesday.
Tough board in the Double Jeopardy! round – that LEATHER category was brutal. Whenever I hear the term “patent leather” I think of Grease and nothing more recent.
|
Emily Bingham |
Sam Deutsch |
Hannah Norem |
| 5,100 | 12,800 | 9,100 |
| Wright State | USC | Augustana |
Tonight’s Final Jeopardy! category is:
| WORLD LITERATURE |
Everyone’s still alive, but Sam and Hannah could play some mind games.
First-order calculations
Emily’s in it, but she needs to get it right to have a shot. Sam could wager to stay above her.
| Emily |
Sam |
Hannah | |||
| 5,100 | 12,800 | 9,100 | |||
| FIRST-ORDER | SECOND-ORDER | COVER ZERO | |||
| min | max | min | max | min | max |
| 2,300* | 5,400 | 1,100 | 1,700 | ||
| 2,600 | |||||
Second-order calculations
If Hannah plays conservatively, Sam could wager to automatically win… but does he want to take the risk that Hannah goes big?
| Emily |
Sam |
Hannah | |||
| 5,100 | 12,800 | 9,100 | |||
| FIRST-ORDER | SECOND-ORDER | COVER ZERO | |||
| min | max | min | max | min | max |
| 2,300* | 5,400 | 1,100 | 1,700 | ||
| 2,000 | 5,700* | ||||
What actually happened
| Emily | Sam | Hannah | |||
| 5,100 | 12,800 | 9,100 | |||
| 4,001 | 5,401 | 9,100 | |||
| 9,101 | 18,201 | 18,200 | |||
| min | max | min | max | ||
| 5,100 | 5,401 | 1,101 | 1,699 | ||
| 1,999 | 9,100 | ||||
The contestants continue to impress me with their wagering skills. Congrats to Sam on advancing, and to both Emily and Hannah on a well-played pair of games for each of them.
One semifinal left… which of these wild cards will play for $100,000?
| Mon 2/8 |
Niki |
Gus |
Emily S. |
| UC Berkeley | Stanford | Columbia | |
| Tue 2/9 |
Emily B. |
Sam |
Hannah |
| Wright State | USC | Augustana (SD) | |
| Wed 2/10 |
Ziad |
Sarah |
Kate |
| NC State | Pitt | Northeastern |
The Final Jeopardy! clue
| WORLD LITERATURE |
| IT WAS ORIGINALLY PUBLISHED IN 1915 UNDER THE GERMAN TITLE “DIE VERWANDLUNG”, MEANING “THE TRANSFORMATION” |
[spoiler]What is The Metamorphosis by Franz Kafka?[/spoiler]
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Tonight’s game shed light on a question I have been pondering. In these semifinal games does it ever make sense for second or third to not bet it all? Here if Sam had gone for the lock and missed and Hannah had missed then Emily would have won. So there is some logic behind the wager she made. But she has to hit in order for her strategy to work. And betting it all would have also worked in this scenario. If either Sam or Hanna hits with the wagers they selected any strategy she could employ would fail. And if everyone misses this strategy fails as does betting it all. So I am having trouble coming up with a reason not to bet it all. There are some non-bet-it-all scenarios that succeed (Keith laid a couple of them out) but there are not many and they are low probability ones. It looks to me like second and third should both bet it all in almost all cases.
I apply the same logic to semifinal games as I do in regular play; I disregard the prizes for second and third. Given Sam’s wager, Hannah would have been better off wagering between 1,101 and 1,699, since the only way she has a chance at winning is if he misses.