Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

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ACW
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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by ACW » Tue Mar 22, 2016 5:58 am

Why play for a win-but a possible loss-when you can get a lock tie?

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by nserven » Tue Mar 22, 2016 9:29 am

The Ho-->Vietnam connection seems obvious in retrospect, but I looked at the 2011 date, wondered if it was somehow tied to the dissolution of the junta, and said Burma.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by opusthepenguin » Tue Mar 22, 2016 9:38 am

DadofTwins wrote:Using data from the last 1,000 3-player FJ's, a 0 bet wins outright 51.7% of the time. The rest go to a tiebreaker, where on an average clue an average leader is a 57.5% favorite against an average trailer. This puts the win expectation of a 0 bet at 79.4%.

A $1 wager wins outright 80.9% of the time, and loses 19.1% of the time assuming the trailer doubles up.

If the leader thinks the trailer will try to get cute with her wager and not double up, the 0 play is favored. Otherwise, out of every 200 lock-ties, a $1 wager will produce 3 more wins for the leader than a 0.

The difference in win probability is small enough, though, that I don't have a problem with whichever way a leader wants to go.
As you say, that's only if the trailer ALWAYS doubles up. Any wagering advice based on that assumption strikes me as pointless.

If I'm understanding your stats, here's the question to ask. Do I think the second place player has a greater than 1.5% chance of not betting everything? If so, the odds favor the $0 bet. Do I think 98.5% of second place players will understand their situation and make the right bet? Not. Even. Close. The $0 bet is the CLEAR winner here. The $1 bet is for suckers who believe in frictionless surfaces and spherical cows.

Or, as I say, maybe I'm misunderstanding your statistics?

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by davey » Tue Mar 22, 2016 10:08 am

I guess E.E.Cummings was being critical of English in pointing out the upper-case I.
I assumed the quote was celebratory, and who more likely to celebrate the large I but Walt Whitman?... :roll:
In any case, while he called himself a "small eye poet", Cummings did not consistently use lower-case for his own name...

http://faculty.gvsu.edu/websterm/cummings/caps.htm

http://faculty.gvsu.edu/websterm/cummings/caps2.html

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by opusthepenguin » Tue Mar 22, 2016 10:23 am

davey wrote:I guess E.E.Cummings was being critical of English in pointing out the upper-case I.
I assumed the quote was celebratory, and who more likely to celebrate the large I but Walt Whitman?... :roll:
Whitman was my first thought and I liked it a lot. But then I thought of Cummings and realized that was more likely for a J! clue that drew attention to upper- vs lower-case letters.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by danspartan » Tue Mar 22, 2016 10:36 am

First off, writing it as EE Cummings would offend ee cummings.


Do we know how often 2nd does not bet it all?

GTO is clearly to wager >0.

Practical concerns of win % if tied and % of time 2nd doesn't bet it all need some favorable assumptions to negate what is a a relative 10% advantage.

57.5% seems like a huge edge to predict a tie-break. Extrapolating from regular play doesn't account for folks getting on category and buzzer timing runs which likely inflate the edge of a one-off ring-in and category.

Want to see solid stats on 2nd under betting.

When under betting does occur it seems likely to be by a small value "everything but a buck", so I'd max a wager at $1.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by davey » Tue Mar 22, 2016 10:48 am

danspartan wrote:First off, writing it as EE Cummings would offend ee cummings.

First off, you didn't pay attention to my post or the links I posted with it.
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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by opusthepenguin » Tue Mar 22, 2016 11:00 am

danspartan wrote:Do we know how often 2nd does not bet it all?

GTO is clearly to wager >0.
I take it game theory requires rational bettors in both first and second place? If so, GTO is as useful for Jeopardy! purposes as postulating a frictionless environment when modeling how a velcro-encased hockey puck travels over hot tar. JTO is clearly to wager 0.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by danspartan » Tue Mar 22, 2016 11:47 am

davey wrote:
danspartan wrote:First off, writing it as EE Cummings would offend ee cummings.

First off, you didn't pay attention to my post or the links I posted with it.
What we believe to be true isn't always.
Did not read thread correctly , made an attempted to be funny. Apologies.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by danspartan » Tue Mar 22, 2016 11:54 am

opusthepenguin wrote:
danspartan wrote:Do we know how often 2nd does not bet it all?

GTO is clearly to wager >0.
I take it game theory requires rational bettors in both first and second place? If so, GTO is as useful for Jeopardy! purposes as postulating a frictionless environment when modeling how a velcro-encased hockey puck travels over hot tar. JTO is clearly to wager 0.
Keith just did some digging.

On the one hand, a shocking number don't bet it all from 2nd.

On the other hand, when 2nd answers FJ correctly, 1st gets it right also at 63%.

These two adjustments push in opposite directions starting from GTO. I don't think we can be all that certain about JTO (which is awesome BTW).

Think I'll go with $1 if we like the category and $0 if we don't. Not going to fault anyone on either option.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by GoodStrategy » Tue Mar 22, 2016 12:20 pm

Also the choice between $0 and $1 if second underwagers is relevant only if that bad wager is everything but a dollar - anything less and opusthepenguin's point doesn't apply (plus the leader would still get a tiebreaker shot if wrong and second is right with that all-but-a-dollar wager from second).

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by Golf » Tue Mar 22, 2016 12:42 pm

Based on:

RR-34%
RW-19%
WR-19%
WW-28%

and leader 52.5% to win the buzzer race
and trailer wagering everything 67% of the time

If leader feels >=2% better than average on the FJ category they should wager $1, otherwise wager $0.

So it's real close, the decision should be based on FJ category factoring in both what the leader knows about the category and what the trailer knows about the category if that can be determined. I would assume that most of the time the leader will wager $1 regardless of category, which is a mistake. But it's so close I don't think you can mathematically fault the leader for wagering either $0 or $1.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by danspartan » Tue Mar 22, 2016 3:03 pm

2nd under wagering 1/3 of the time really skews the math. Used to seeing big over bets from close 2nd place but 33% can't multiply by 2 or figure that is their only option????

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by BigDaddyMatty » Tue Mar 22, 2016 3:16 pm

Do we know what portion of the 33% who don't risk it all risk everything but a dollar?
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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by BigDaddyMatty » Tue Mar 22, 2016 3:55 pm

opusthepenguin wrote:
danspartan wrote:Do we know how often 2nd does not bet it all?

GTO is clearly to wager >0.
I take it game theory requires rational bettors in both first and second place? If so, GTO is as useful for Jeopardy! purposes as postulating a frictionless environment when modeling how a velcro-encased hockey puck travels over hot tar. JTO is clearly to wager 0.
Based on my analysis of the numbers, the category-blind GTO and JTO are each to wager $1. Assuming the following:
34/19/19/28 RW distribution
The leader wins 60% of tiebreakers (the higher this probability, the better a $0 wager is, of course)
For the JTO calculation, all 33% of the second-place contestants who don't go all in leave only a dollar behind (any number lower than this reduces the downside risk of a $1 wager)

GTO: $0: 78.8%; $1: 81%
JTO: $0: 85.8%; $1: 87.3%
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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by Bamaman » Tue Mar 22, 2016 4:00 pm

What do GTO and JTO mean?

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by jpfeifer » Tue Mar 22, 2016 4:15 pm

I just registered and this is my first post.

Did you know this: One of the clues left unrevealed at the end of Double Jeopardy! (The 20th Century for $400) was to have been provided by local news anchor Lucy Bustamante from my own hometown Jeopardy! affiliate, WVEC Channel 13!

Any chance of that clue appearing on a future show before the end of the season? It's only the latter half of March, and the season runs until the last week of July.

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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by hbomb1947 » Tue Mar 22, 2016 5:07 pm

BigDaddyMatty wrote: The leader wins 60% of tiebreakers (the higher this probability, the better a $0 wager is, of course)
Where do you get this number from? That's even higher than DoT's 57.5% figure.

I would respond that first as was pointed out above, you can't extrapolate from play on the regular boards because the tiebreaker clue is another FJ-type clue (at least that's the way it's been in the limited instances when we've had tiebreaker clues in tournament play, and I don't see any reason to expect it would be any different in a regular game). Ex ante, in deciding whether you want to risk getting to a tiebreaker round, it's very hard to predict the percentages for it because you have no idea what the category will be and, for example, whether it will favour one contestant over the other (leaving aside that category titles are of limited utility in gauging the expected difficulty of the clue). On top of that, if the clue isn't an instaget for you, then you'll spend more time than with a regular clue just trying to solve it, thereby taking regular-clue buzzer dominance out of the equation -- but at the same time being cognizant that if your opponent buzzes in first and solves it correctly, you're toast. So that increases the pressure on you to buzz in without being fully sure that you're right, creating the risk that you'll buzz in first but respond incorrectly (whereas if you'd had the luxury of taking the full 30 seconds you might have gotten it right) -- which gives your opponent a free shot at then responding correctly, after having had more time to think about the clue and having one wrong response eliminated. At best in that situation, your opponent negs too and then you would go to yet another tiebreaker clue. Rinse, repeat.

So I would fall back on first principles. Bet the $1, bet on yourself to win outright on the FJ; an overwhelming majority of the time, that wager will result in the victory (but for reasons noted upthread, don't wager more than $1). And you thereby avoid the anything-can-happen scenario of a tiebreaker clue, and all the risks that entails. The only exception would be if you really hate the category, and even then that's subject to the caveat regarding the opaqueness of category names; plus, maybe your opponent will hate the category as much as you do (although you will probably lack the information to know that last factor).

We'll see a tiebreaker clue eventually, but I think that due to risk-averseness of the type that Steve showed last night in a lock-tie situation, it's overwhelmingly more likely to come in a prisoner's dilemma scenario, where the co-leaders either both bet zero, or both bet it all and solve the FJ clue correctly.
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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by BigDaddyMatty » Tue Mar 22, 2016 5:28 pm

hbomb1947 wrote:
BigDaddyMatty wrote: The leader wins 60% of tiebreakers (the higher this probability, the better a $0 wager is, of course)
Where do you get this number from?
Thin air. I was setting the assumptions as favorably as possible for the $0 wager in order to demonstrate that $1 is definitely the better choice.
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Re: Monday, March 21, 2016 Game Recap & Discussion [SPOILERS]

Post by sumithar » Tue Mar 22, 2016 5:55 pm

hbomb1947 wrote:Congrats to Melissa on the win. And I can't fault Steve for betting the dollar; I most likely would have done the same. The rule change kind of forced him into it (and this scenario is the principal reason why I still feel that the rule change is unfortunate). .
Excuse my ignorance but what is this rule change again? I haven't been watching J! for many years now, and have resumed due to enforced stay at home due to illness!.

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