Final Jeopardy! wagering analysis:
Monday, February 15, 2016
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We’re back to regular play… and, I’m happy to say, to the Aleve ad before Final Jeopardy!.
One dollar to anyone who can name our returning champion. Apparently I can’t even get his name right on the video. So sorry, Chris!
He lost the lead on the 21st and final clue(!!!!) of Double Jeopardy!. Hey, remember when people got mad at Niki for being “rude” to Alex?
|
Chris Becker (1x) |
Ramona Riddles |
Sarah Wright |
| 10,000 | 5,000 | 10,600 |
Tonight’s Final Jeopardy! category is:
| FAMOUS PHRASES |
When one player has exactly half another player’s total, things are going to get messy.
First-order calculations
Sarah can go either really big, or really small. Chris could sit tight.
| Chris |
Ramona |
Sarah | |||
| 10,000 | 5,000 | 10,600 | |||
| FIRST-ORDER | SECOND-ORDER | COVER ZERO | |||
| min | max | min | max | min | max |
| 8,800 | 3,800 | 9,400 | |||
| 0 | 5,000 | 600 | |||
Second-order calculations
Now we start to fill in the “tie” wagers…
| Chris |
Ramona |
Sarah | |||
| 10,000 | 5,000 | 10,600 | |||
| FIRST-ORDER | SECOND-ORDER | COVER ZERO | |||
| min | max | min | max | min | max |
| 8,800 | 3,800 | 3,800 | 9,400 | ||
| 0 | 5,000 | 600 | 600 | ||
| 1,200 | 1,200 | ||||
Zero wagers
Score differences:
Sarah and Chris: 600
Sarah and Ramona: 5,600
Chris and Ramona: 5,000
| Chris |
Ramona |
Sarah | |||
| 10,000 | 5,000 | 10,600 | |||
| FIRST-ORDER | SECOND-ORDER | COVER ZERO | |||
| min | max | min | max | min | max |
| 0 | 3,800 | 3,800 | 9,400 | ||
| 1,200 | 1,200 | 5,000 | 600 | 600 | |
| 5,000 | |||||
…and now everyone has the opportunity to wager for a tie. Or not.
What actually happened
| Chris | Ramona | Sarah | |||
| 10,000 | 5,000 | 10,600 | |||
| 601 | 5,000 | 5,000 | |||
| 9,399 | 0 | 5,600 | |||
| min | max | min | max | min | max |
| 1,200 ! | 5,000 ! | 9,400 | 9,401 | ||
| 0 | 1 | 3,800 | 3,801 | 599 | 600 |
| 4,999 | |||||
Well, only Ramona took that opportunity – and she’s the only one who made a good wager. Chris might as well wager 1,200 to cover that small range out of Sarah.
In any event, Chris has now won 2 games and $27,798 – and he’ll be back tomorrow.
The Final Jeopardy! clue
| FAMOUS PHRASES |
| IN ONE VERSION OF A 19th C. QUOTE, “THERE IS ROOM AND HEALTH…AWAY FROM THE CROWDS” SO YOU’RE URGED TO DO THESE 2 WORDS |
[spoiler]What is “go west”?[/spoiler]
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Why didn’t you like Sam / Chris’s wager?
I’d rate Sarah’s / Sarah’s incentive to wager $598 or $599 as much higher than normal. The $601 bet doesn’t cover that possibility with similar downside risk.
Okay, I can see that. But how many contestants in Sarah’s position would make such a wager? (Granted, more than would have before the advent of your site).
No idea how many players would wager small. I think you’re going about it backwards, though: you have to calculate the feasible ranges first, then decide which option is most likely to net you a victory.