My thoughts on this scenario.
P1 - 17,400
P2 - 9400
P3 - 12,400

Let's just say for argument's sake P1 makes exactly the shutout bet of $7401, and shows this bet to P2 and P3 before they wager.

Now P2 should say to himself, "Even if P1 gets it wrong, he will have 9999, which is more than I currently have. Therefore I must get this question right to win the game. Therefore I bet all 9400 to maximize the amount of money I get in the cases where I win the game."

Now P3 is caught in the middle. Given the leader (P1's) wager, P1 has to get it wrong for P3 to win. If P2 did not exist, P3 could bet such that he would be guaranteed to win every time P1 got it wrong. Unfortunately for P3, P2 does exist and is close enough that P2 cannot guarantee this.

Holding the fact that P1 gets it wrong constant, there are 4 cases:

P2 gets it right / P3 gets it right - P3 should bet it all

P2 gets it right / P3 gets it wrong - this case doesn't matter for winning the game because P3 is screwed because P2 went all in

P2 gets it wrong / P3 gets it right - this case doesn't matter for winning the game, P3 will win no matter what he wagered, to maximize winnings in this case you should bet it all

P2 gets it wrong / P3 gets it wrong - P3 should bet $0, he will remain above P1 if he does so



Basically P3 is caught between the other two. He cannot bet small enough to guarantee victory against P1 in the case of a P1 miss and at the same time large enough to shut out P2. P3 needs to decide which scenario is more likely:

Triple Stumper (aka all three miss) - he should bet $0 if this is more likely

P1 is the only one to miss - he should bet all $12,400 if this is more likely

Suzzer - How is your situation any different than everyone getting it wrong and you betting too much as the 1st place player thus allowing the 2nd place player to win the game even though he was wrong also?

"Here's the guy I was telling you about. He was in first place and everyone got the question wrong and he let the guy who bet $1 freaking beat him!!!"

You really can't see how that's different? If you get the question wrong you don't necessarily expect to win. If you're the points leader, get the question right, and don't win, that's something you're going to have to live with for the rest of your life. I mean if 2nd place tells you in the green room they're going to play rationally to lock out 3rd, and you somehow are 100% sure they're not gaming you, then yeah sure go for the best bet. But I just don't see any realistic situation where you know what 2nd is going to do with that much certainty.

Even if you somehow did, and 2nd was smart, they could always change their bet to take advantage of you using the shore strategy. I don't see how we can be so certain 2nd will play rationally vs. 3rd that we can deviate our bet from standard. But we are also equally sure that 2nd won't change their bet to exploit our shore strategy.

It just gets so messy. So much potential for overthinking and screwing yourself if you go down that road. This is starting to get like a pointless political or religious argument. So I will just say personally I just don't see any reason on earth to not just keep it simple and make sure you cover 2nd.

Suzzer,
Do you regularly watch Jeopardy?

I'm pretty sure if you're smart enough to be on Jeopardy you should have enoiugh self-confidence to deal with a yokel mocking your game theory decisions.

Tonight we had 2nd place and 3rd place each with (game theory/math/gambling) skillz

1st 16,700
2nd 15,600
3rd 3,000

All missed in FJ


3rd bet $0 which would have won except
2nd bet only $1111
1st bet $14,501

So 2nd scooped a nice $14489. Against like 95% of players, 3rd would have actually won.

Probably the hottest jeopardy cast of all time. The chic in the middle was probably top 1% and the chic on the end was probably top 5-10% of your normal female jeopardy contestant . Neither were anything special but the normal female jeopardy contestant is disgusting. I guess college week produces some hot lineups occassionally.

Wow this thread is amazing. It might be because i'm stoned, but just the idea that people analyze Jeopardy this thoroughly is awesome.

My strategy would be to get more questions right so i dont have to worry about hard math at the end imo

Ok , Jennings.

Not an idiotic wager but tonight started off College Week. In single jeopardy there was a category called "Time to Convert".

The $800 question read "Multiply your liters by 1.0567 to get your amount of these units"

Missouri State girl guesses gallons (wrong, ldo) then Ohio State girl guesses quarts and it counts.

Jeopardy FAIL

^^^

OK, I'll bite, why is this wrong?

I think they meant to say divide instead of multiply since 1 liter = 1.0567 quarts

Right, so 1 liter (multiplied by 1.0567) = 1.0567 of these units (quarts).

Color me confused. I guess the wording got me all twisted?

LondonBroil FAIL

I didn't know the answer to that, but gallons is such a terrible guess. People deal with 2 liter bottles of pop and 1 gallon jugs of milk every day, how can you think that a gallon is roughly half of a 2 liter bottle? Missouri State girl, you are dumb and I hate you.

This has been a very interesting thread (and I've started DVR-ing Jeopardy - which I can't believe I didn't think of before) but I find it funny how many people ITT are SOO confident in their answers on a topic that is pretty complex.

And here I was thinking I was the **** for thinking Jeopardy got a question wrong.

I just want to share with you the results of the first GIS page for "hot jeopardy contestant" so that we know what we're dealing with here:

In the kids' tourney last week, the Final Jeopardy answer was Anne Frank. All the kids got it right, but the chip leader going in wrote "Annie Frank", and they wouldn't give it to him, costing him the game.

I think the kid got hosed. If I ever ring in with Benny Franklin or Marty King Jr, and they give me any lip about it, I'll stick that magic pen up Trebek's nose.

to figure out the solution you need to know how much it's worth for them to win above and beyond the cash dollar value.
average win (aw) represents the average amount won by the winner in a single game.

if you give yourself pure chance odds at winning each time, your weighted return value (wrv) is:

[aw/3 + aw/3^2, + aw/3^3,... aw/3^n]
... blah blah blah
= 0.5(aw)


stacks...

P1: 4800
P2: 13800
P3: 12000

starting with the assumption that each person has a 50% chance of getting the question right, and using the bids suggested in this thread...


-------------------------------

-bid-
P1: $4,799
P2: $13,000
P3: $11,900

-expected gain-
P1: 1/8 *(9598+wrv)
P2: 1/2 * (26800+wrv) + 1/8 *(800+wrv)
P3: 1/4 * (23900+wrv)

for arguments sake, say aw = 20000 and therefor wrv = 10000
P1 wins 2449.75
P2 wins 18400 + 1350 = 19750
P3 wins 8475


-------------------------------

but that cant be the equilibrium if any one player can improve his EV by changing his bid.


P3 changing his bid to 2399 results in....

= 1/4 * (9601+wrv) + 1/4 * (14399+wrv) which is greater than 1/4 * (23900+wrv)

-bids-
P1: irrelevent
P2: 13000
P3: 2399


this redistributes the expected gains as follows (with the same aw and wrv values)

-expected gain-
P1 wins 0
P2 wins 1/2 * (26800+wrv) = 18400
P3 wins 1/4 * (9601+wrv) + 1/4 * (14399+wrv) = 4900.25 + 6099.75 = 11000

which shows that P3 made gains at the cost of P1 and P2.


--------------------------------


To test whether that's the final point of equilibrium, you need to see if either P1 or P2 can improve their EV by increasing or decreasing their bids.
P1 is basically ****ed in the current state, so it's up to P2.


With the given bids, 13800 is automatically better than 13000, but consider the other alternative... try out 4199...

and if he precisely bids 4199, there's a 1/4 chance that it would result in a draw (meaning both players come back and get the wrv).


so the new test bids are,

P1: irrelevent
P2: 4199
P3: 2399


with these new bids, the expectation is as follows...

P1: 0
P2: 1/2*(17999+wrv) + 1/4*({9601/2}+wrv) = 13999.5 + 3700.125 = 17699.625
P3: 1/4*(14399+wrv) + 1/4*({9601/2}+wrv) = 6099.75 + 3700.125 = 9799.875


two of those 1/4 outcomes obviously overlap and represent draw games.


which shows that it performs worse than the bid of 13000 (and therefor worse than 13800) with a wrv of 10,000. if you were to change the wrv to 20,000, it would be enough to change P2's optimal bid to 4199


--------------------------------


i think you can conclude that depending on the wrv,

p1 should always be ****ed
p2 should either bid 4199, or anywhere between 12001 and 13800
P3 should always bid anywhere between 0 and 2399.




finding the equilibrium bids is just a matter of plugging in all the numbers and the percentage estimates.
in extreme examples, it's important to adjust the wrv value based on how likely it is for you to win future days.
ie: for ken jennings, wrv was extremely high both because of a higher aw and a higher chance at winning each game (represented by the denominator of the series at the beginning).

he should've cited the mr. show sketch where they refer to her as annie frank.

nah if you add a syllable to a word in final jeopardy you're done.

Trebek has been slipping a bit lateley. Last night, twice. "HP"..."I'm sorry, that is incorrect. WAIT! Yes, you are correct." Then she hit the daily double, and before making her wager, Alex said "Choose your next category".

yeah two days running before he delivered the final jeop clue he apologised for some bs rambling he had done just before the commercial break.