Ugh.

that $11k wager is such an enormous $ev mistake, jesus. simply astounding.

don't bet $1401 here imo. alex called 'less than a minute to go' with 6 clues left. stall it up on the DD and do something else.

The more I think about it, the more I hate the "small" wager. If he gets it right he still has to get FJ correct to win. If he gets its wrong, then he needs the new leader to get it wrong (assuming level 1 wagering, but very good 1st order approximation).

Its an $800 clue in a category that he should be able to figure out from the clue itself. Got to be at least 60% there.

Going small and right he's only a little over 50% to win in FJ, if he's wrong he probably drops down to 30ish%, for a blended average somewhere around 40%.

from memory if he gets it wrong he will likely win on a single get double up in FJ (depending on what happens on the subsequent clues)

checked a few seasons on j-archive - $800 DDs are 70-75%

what on earth would he be thinking to bet 11k instead of shoving?

17,200-drops to 6,200
16,600
12,000

Ignoring the last $2000 in clues, his only path to victory is the lone get/doubleup. Best thing that can happen if he misses is for the 1st and 2nd place scores to tighten up and then maybe he can stand pat and hope for a double miss without needing to get FJ correct.

Even if he runs the 2,000 that gives him 8,200 which isnt enough to cover 16,600 likely FJ wager/miss.

If you bet it all and miss, you lose. A large (but not all-in) wager has the downside of not giving you a lock, but it has the upside (if you get it right) of winning a lot more money in scenarios where you get FJ! right, and also has the upside of keeping you alive if you miss the DD but manage a sole get in FJ! (since the new leader will have to bet big to guarantee himself a win).

Ignoring the remaining clues, if this was the last clue before FJ!, and you get the DD wrong with a large wager, you can expect the 16,600 guy to wager $7401 or more, meaning if he misses, he'll have $9199 or less. That creates a decent value in making sure that even if you miss the DD you still have at least $4600 of your own (which would mean a wager no larger than $12600, if you want to still have winning chances on a miss).

If the $16,600 runs the remaining clues and gets to $18,600, then he'd only have to wager $5401, and now you want at least $6,600 on hand to catch him if he misses, meaning a max wager of $10,600. Wagering $11,000 as he did is right in this vicinity. Risks getting shut out if you miss and the second place guy runs the table, but it does keep you alive when you miss the DD and he gets some but not all of the remaining clues.

Ultimately, it's better to shove. Assume you get the DD right 60% of the time, and everyone is 50% in FJ!, then shoving gives you a 60% chance to win and a 40% chance to lose (since there is only one winning path - you have no hope if you miss the DD but clinch if you get it).

$11,000 gives you three winning paths (DD right, FJ! right [30%] - OR DD right, FJ! wrong, but 2nd place misses FJ! too [15%] - OR DD wrong, FJ! right, and both other players miss FJ! [5%]) but only around a 50% chance of actually winning.

It helps though that $11,000 is enough that the third place player can't catch you in FJ! if you get the DD right and then wager enough in FJ! to lock out second place. With the $11,000 wager you win 75% of the time you get the DD right, and 12.5% of the time you get the DD wrong. If you really hate wordplay, $11,000 might be better than shoving if you think your DD odds are <33% (but still think all three players are 50% in FJ!).

Point is I don't think $11,000 was quite as bad as you guys are making it out to be, because of the backdoor potential. Which isn't to say it's optimal or anything...

You are overvaluing "not losing" over "winning". Big psychological impact on people to have "no chance to win", so big that people give up all kinds of equity to avoid "losing immediately"

You are giving up ~25% of your win equity when you get the DD correct and gaining ~10% of win equity when you get it right.

You are giving up way more probability than you are getting on the other side.

Sports analogy that sorta works?

Say you are on the 1 yard line with 30 seconds left in the game. Its 4th down. You are down by 4 points.

If you kick the field goal, there is still a chance that you can recover an onside kick, then drive and get a game winning 2nd field goal. But hey you are "still in it"

Or you can make it or break it 1 play from the 1 yard line which should be >50%. Of course if you miss it, you lose immediately.

11K is just horrible. Its better than 13K, but really bad compared to shoving.

All my analysis was about "winning" (which has significant value of course, since you get to come back and play again.) And I came to the same conclusion you did that all-in is better than $11,000... so I'm not sure what you're point is. The 25% vs. 10% part is why the odds of winning are better with an all-in *unless* you think your odds of answering the DD right are worse than 33%.

So what are you disagreeing with me about?

My point wasn't that it was a GOOD wager. It was bad. It obviously hurt his chance to win. All-in was better. My point was just that I don't think it was AS bad as posts were suggesting. You described it as "horrible". Yeti called it an "enormous mistake". And riverboatking implied he couldn't understand what possible thought process could even have gone into the wager.

To my mind, language like that should be reserved for mistakes that cost like $10k+ in expected value. I don't think this wager is such a mistake.

Is the disagreement in the terminology? Do you think a -$3k or -$4k EV error is "horrible"? Or is it in math (you agree with my terminology but think the error really was a $10k+ EV error)?

I might be underestimating the magnitude of the mistake, I'll run some more detailed numbers on exactly how much it probably cost him and then check back to see your thoughts.

i may have been overstating.

please use 75% for the DD being correct when you do the calculation.

Well, at 75% it looks like it was worse than I thought. I get about $13k in lost EV (assuming he bets "normally" rather than "optimally" in FJ! - although there's an interesting tangent there in the end... if he did something extremely unusual in FJ! then the DD wager on its own costs him less than $8k of EV versus all-in... still bad, but not "horrible" by my arbitrary $10k definition). All calculations do make the facile assumption that the remaining $2,000 in clues don't exist, because I don't want to work out the details of that component.

One major problem not mentioned in the previous discussion? At $11k, even getting it right (with no clues left) isn't enough to shut out 3rd place. He'd have to bet $5,001 to shut out second place, dropping him below $24k if he gets FJ! wrong. If he wanted to keep his backdoor chances alive he should have bet $11,401 on the DD (though I suppose with the $11k wager this is where those other clues come into play... he can still get those extra $500 he needs to shut third place out with a correct FJ!...) This inability to shut out third place after betting $11k causes about 30% of his lost EV as compared to all-in on the DD. If the $11k HAD been enough to shut 3rd place out on a missed FJ! then it becomes quite clearly a less than $10k EV error in the end.

Anyway, I assumed that the EV of "all future episodes" for a returning champ (aka the value of "winning" beyond this show's winnings) is $11,500 (estimated 40% chance of winning per episode, since a returning champ is presumably better than average, which translates to 2/3 expected wins, at a non-data-based estimated average of $15k per win [sidenote, anyone know the actual average value of a win?] for $10k in future winnings, plus an additional $1500 [$1k or $2k] in whatever future episode he eventually loses).

if he shoves all-in (and it's the last question) then he has $34,400 and it's a runaway. Assuming all contestants are 50% on FJ! [Aside #2, is this about right? I used to be obsessed with Jeopardy! years ago, but haven't followed it in a while. I think I remember 50% being the long term average, but might be wrong?] then his EV for this episode is $45,900 [$34,400 plus $11,500 in future winnings] when he gets the DD right, and $1,000 when he gets it wrong (doesn't get to participate in FJ!, obviously comes in third).

If he bets $11,000 and gets the DD right, I assume he wagers $5,001 to lock out second place. I also assume 2nd place wagers at least the $6600 needed to catch him on a miss, and 3rd place bets it all, so if he misses FJ! after a correct DD he needs it to be a triple stumper, so he gets FJ! right and wins 50% of the time, and he gets FJ! wrong but still wins 12.5% of the time. And if he gets the DD wrong, his backdoor chances allow him to win a smaller amount another 12.5% of the time. Net EV of all the scenarios: $27,438 when he gets the DD right, $3,862 when he misses it.

Lost EV assuming his FJ! wager in the $11k scenario is the "normal" $5,001, depending on his odds on the DD (it's definitely not "horrible" if he happens to genuinely suck at wordplay, and have 50% or less odds):
But then there's something else. If he goes all-in on the DD and gets it right, then he enters FJ! with a runaway lead. This means his net EV for the episode is equal to his score entering FJ! (no FJ! wager can improve his EV if he's 50% to get it right, and of course too big of a wager can hurt him badly if he gets it wrong by costing him the win.)

However if he bets $11k on the DD and gets it right... he still almost exclusively only wins on a correct FJ!... meaning his best strategy after betting $11k on the DD is to THEN go all-in on Final! And when this works (correct FJ!) this nets him by far the biggest pay day of any of the scenarios. If he made the $11k wager on the DD with an FJ! all-in in mind, it's still worse than just going all-in on the DD, but nowhere near as bad as the numbers above:
Of course noone who bets $11k on the DD in that spot is ever going to follow it up with an all-in FJ!, lol, because if they would consider all-in on FJ! they'd understand wagering well enough to know to go all-in on the DD instead, which IS still better.

TL;DR summary: It's borderline whether $11k was "horrible" or not... definitely bad though (but we all already knew that).

yes 50% for final is about right

triple stumpers are more like 15-20% though fyi (please don't waste more time redoing the math )

Yeah, 12.5% assumes fully independent probabilities for each contestant to get FJ! right, but obviously some questions are fundamentally harder than others, so there should be some correlation and it makes sense that triple stumpers would therefore be a bit more common.

Don't worry, I'm not redoing the math on exactly how bad the definitely bad $11k wager was

Lol all this over the word horrible. Semantics. Lots of love in places like j board and even thefinalwager over "gutsy" 11k wager cheesed me off and I used the term
Horrible in response.

Far from optimal=horrible in these parts.

bump

so nice when something you learn in high school (leni riefenstahl) finally comes up

Guy in the middle on Wed needs to just shove on the last DD whether he knows the category or not, anything less just doesn't make sense.

28k 12k 5k

With one 2k clue left

Yeah but why do that when you can wager a random, moronic, $4000

man it's bad to be on jeopardy and not know that DD. he would have won, sickening.

from jboard:

Pressure under the lights. If he wants to be around for final then hold back a dollar.

I really liked Alex's strategy. He's good with the buzzer and pretty knowledgeable too. I hope he'll do well in ToC. When is ToC?

My girlfriend hates him solely because of that jacket.

probably 10 months or so

Alligators are about 150 lbs

Komodo dragons are about 3 lbs