Volante wrote: ↑Tue Jan 11, 2022 1:15 pm
So let's talk strategy:
What should Amy have wagered for DD3 given scores of $16,200 / $4,200 / $12,800 ?
Definitely not an obvious answer here. Let's lay out some facts first. (I have not double checked the numbers, easily could have missed something, focusing more on the process for now)
Coryats to this point appear to be 16200/4200/8800. The 8800 assumes he answered DD2 worth 1600 correctly. 16k left on the board out of a possible 54k. So after DD3 the projected numbers would be 6800/1800/3800(rounded to the nearest possible number). So without taking DD3 into effect the numbers at the end of DJ would be 23000/6000/16800. Now, of course the projections can and will vary wildly because of sample size, etc., but it's still something to build around.
As of this writing, she is 80% on FJ and 87% on DD's. So if she wagers everything she wins 87% of the time. This is a 4th row DD so I might shave a few percentage points off that 87%, maybe 85%.
These totals don't give Amy a lock or a crush, so the min wager is probably out. So I'd want to find a number that very rarely puts her behind on a miss at the end of DJ. The difference above is 6200 but again with a lot of variation. If we do this she has a crush when she answers the DD correctly and is merely in the lead if she answers incorrectly. So 85% crush, 15% lead.
Final Jeopardy numbers, she answers correctly 80% of the time. Based on the various R/W numbers, let's estimate WR=8%, WW=12%. So she loses in the crush scenario 8% of the time, loses 20% of the time while in the lead. And the 20% number assumes 2nd place knows how to wager in this situation, which of course doesn't happen often enough.
So that leaves (.85)(.92)+(.15)(.80)=.902. This wager wins 90.2% of the time, significantly better than going all in on DD3 and winning 85% of the time.
Are these numbers perfect? Of course not. But they're close. And they give us a decent foundation on what to do.
So what's the wager? Again 6200 possible with lots of variance. In this situation I'm nearly positive you have to error on the low side, because with the 80% FJ get rate being in the lead is paramount. Without running more numbers I feel approximately 3000 on the low side, approximately 4000 on the high side. Category independent of course.
Now, all that said, naturally nobody can be expected to do all that in a few seconds on stage. But going through various scenarios like this in detail can help build a few platforms where you know how to wager in tricky situations. And this situation is one of the most tricky any contestant will face on the show. Most are simple, you either wager the min or the max. The nasty ones are the inbetweeners.
If I made a numbers mistake above then so be it. The concept is what's important.