50:50 vs Double Dip: Which would a contestant prefer?

[slam]

Playing with some probabilities in my spreadsheet suggests that in the situations where you can completely eliminate one response, DD gives the better outright chance of getting the question right.

You mean, when you have a strong hunch among the remaining three? That seems right.

I definitely agree you're modeling the most likely situation of a person in the chair. My intuition was that DD was usually better, if you had a strong hunch.

Heh heh... trickier than it looks...

It doesn't even have to be that strong a hunch. For example, if your probalities are 40%, 31%, 29%, 0% for the 4 choices, the results are:

DD: 71% correct, 29% incorrect
50-50 but won't walk: 70.3% correct, 29.7% incorrect
50-50 but won't guess between the 31% and 29% choices: 60% correct, 20% walk, 20% incorrect.

[sunflower]

Too. Much. Math.

Feeling dizzy...and weak...

[LastMinuteRequest]

Yes, that's a good point, too. Though, on the other hand, you could discuss what to double dip with the expert or a PAF.

Does Ask the Expert have the same 30 second time limit that the PAF lifeline does? Can the Expert see the Q&A over the web link, instead of relying on having it read by the contestant?

Sources tell me that in principle there's no time limit, but in practice they want experts to be snappy. I suspect they might clarify their attitude towards this over the August break.

But there's definitely no ticking clock, like there is with a PAF.

Source also tell me that the expert sees the question over the web link, which saves time and prevents inaccuracy, though I've heard there's sometimes a delay before the question appears. Maybe they're just getting the bugs ironed out. Also, inexpert experts sometimes have to fiddle with the Skype setttings to make sure they see all of the question on the screen, or so I heard. But I'm sure that's only those <i>bumbling </i>experts...

Also, sources say the expert CANNOT google or use books or shout to a friend or rely on telepathic energies. Though I suppose there's not much incentive, seeing as the expert doesn't get any of the winnings.

[MarleysGh0st]

Too. Much. Math.

Feeling dizzy...and weak...

Hey, sunflower, you're hanging out with the hardcore fans now, not those contestants who grab for the ATA as soon as they see a math question!

[slam]

I think I prefer the 50/50, initial reaction anyway. Also, I think it changes as the $$ question increases.

Going for $50,000 (being a free guess and having no idea of the correct answer) and I have 50/50 or Double dip, I would take 50/50 hands down.

One guess with two choices. DD I have to guess 1 of 4 then 1 of 3.

Again initial reaction.

One random guess with two choices is 50%.

Guessing 1 of 4 then 1 of 3 is also 50% (chance of both wrong = (3/4)*(2/3) = 1/2, therefore chance of being right is also 1/2).

[slam]

Too. Much. Math.

Feeling dizzy...and weak...

But math is fun!

[sunflower]

Too. Much. Math.

Feeling dizzy...and weak...

But math is fun!

I was on the front page of our town newspaper with a picture and the caption "math whiz".

I was in the math club and got a near perfect score on my math SATs.

I think math is fun too. However, I have never had an affinity for statistics. I can do it when forced and I can do it well. But too much of it and my brain turns to jello!!

[bazodee]

As far I can recall, I'm the only person on the Board who has actually invoked the Double Dip. I really wish I had the problem of deciding between DD and 50-50; or even better, using both. Alas, I had already burned my 50-50.

I think the flaw in some of the mathematical analysis is as follows: either you know the answer, or you don't. I cringe when people say they think they can eliminate one of the answers. At the higher level questions, they are usually making a faulty assumption. If pressed to explain with clarity why they think they can eliminate one of the answers, their reasoning will generally fall apart. Contestants often do this to rationalize their behavior- if I can eliminate one answer then I'll be willing to take a guess.

If you know the answer to a question, then you also understand the reasoning behind the writers' choice of distracting answers.

What's my point? If you don't know the answer cold, then in most cases (on high value questions), you shouldn't be eliminating any of the choices.

Then again, even with two shots to answer my question I managed to get it wrong...

[NellyLunatic1980]

Can we talk about the phone game too?

Oh boy, let's beat that dead horse again.

[LastMinuteRequest]

I think the flaw in some of the mathematical analysis is as follows: either you know the answer, or you don't.

That's definitely true much of the time -- perhaps most of the time -- but some players definitely work with hunches, with gut feelings, with a vague yet unsettling intuition.

If you want to get the big bucks, it might be beneficial to exploit your hunches as best as possible.

But I bet you're right that for many players, they're going to know it or not, and might only damage themselves if they talk themselves into an unjustified DD.

[kayrharris]

I feel like I'm reading the J! board. There are threads over there I absolutely have to avoid. I feel just like Sunflower.

[KillerTomato]

"My brain hurts!" -- Mr Gumby

Look, 19% of us know that 92% of all statistics are made up, and 37% of Americans don't trust them.

[slam]

I think the flaw in some of the mathematical analysis is as follows: either you know the answer, or you don't. I cringe when people say they think they can eliminate one of the answers. At the higher level questions, they are usually making a faulty assumption. If pressed to explain with clarity why they think they can eliminate one of the answers, their reasoning will generally fall apart. Contestants often do this to rationalize their behavior- if I can eliminate one answer then I'll be willing to take a guess.

Although I agree that many times you either know the answer cold or are totally clueless, it certainly doesn't have to be that way. Let's look at this question that I just made up:

What is the capital of the Central African Republic?

A) Bamako
B) Malabo
C) Bangui
D) Bujumbura

Let's say that you know essentially nothing about capitals of African countries, but, as it turns out, your niece just returned last week from a stint in the Peace Corps during which she was posted in Mali. You were forced to sit through an hour long slide presentation about her trip. During that slide show she mentioned the capital of Mali at least ten times. "Oh, here are some pictures of the day we were allowed to leave our village and went to the big city, Bamako", "This is the view from the plane as we landed at the airport in Bamako", etc... Now you're in the hot seat and you'd bet your niece's life that Bamako is definitely NOT the capital of the Central African Republic. But you still have no clue about the other 3 choices.

Obviously, real life situations won't be this clear, but hopefully this example illustrates that it is reasonable to be able to confidently eliminate one answer. And if that can happen then more complex situations like the ones I tried to model in some of my posts could also happen.

[silverscreenselect]

I think the flaw in some of the mathematical analysis is as follows: either you know the answer, or you don't. I cringe when people say they think they can eliminate one of the answers. At the higher level questions, they are usually making a faulty assumption. If pressed to explain with clarity why they think they can eliminate one of the answers, their reasoning will generally fall apart. Contestants often do this to rationalize their behavior- if I can eliminate one answer then I'll be willing to take a guess.

On the infamous Katy Knudsen question, (What was the most recent member of the United Nations?), I was "sure" that the correct answer of Tonga was wrong, because I remembered our trip to Hawaii over ten years earlier, when we went to the Polynesian Cultural Center. At the Tonga exhibit, they made quite a point of stating that they had been a nation for quite some time. As a result, if I had that question and had the 50/50 and been given the choice between Tonga and something else, I would have picked the other answer.

[Thousandaire]

Ed Toutant pointed out to me that I was too quick to dismiss the 50:50, arguing that the old 50:50 lifeline can actually be preferable to the Double Dip. The more I thought about it, the more complicated the comparison seems to be, but I do think Ed's general impression may be right.

Now, if we imagine a case where a contestant truly has no idea what the answer is -- where it's a blind guess -- then they're equal (both have a 50% chance of being correct).

Let's say a contestant can eliminate one choice. Let's say you know it's not D.

With the 50:50, there's a 33% chance of that known wrong answer remaining ( for example, A D). But then you can be 100% sure of getting the right answer. If the wrong answer is eliminated, well, now you've got a 50:50 chance of getting it right. Thus, overall, if you can eliminate one answer -- and you're going to guess no matter what -- then the 50:50 gives you a 60% chance of getting it right. *

But the real benefit is that you have a 1 in 3 chance of being guaranteed a correct answer.

With the DD, if you can eliminate 1 wrong answer, then you have a flat 67% of getting it right. So, higher odds in general... but, no guarantees!


Let's say you can eliminate 2 choices. Ah, now the tables are turned! The Double Dip guarantees you the correct answer! Woo hoo!

The 50:50 isn't bad... you've got a 67% chance that one of your known wrong choices will show up... but oops, 33% of the time, you'll still be stuck with two possibly correct answers. If you guess, you've got a 50% chance. Overall, assuming you're going to go for the answer no matter what, you've got a 75% chance of getting a correct answer.

SUMMARY
According to these admittedly hurried calculations, I think:

- DD and 50:50 are identical if you can't eliminate anything.
- 50:50 is probably better if you can eliminate 1 choice, since you have a shot at getting a guaranteed correct answer, even though overall the DD gives better odds to guessing.
- DD is definitely better if you can eliminate 2 choices.

So which is better? I guess it depends on how much you know!


* If you can eliminate D, and the answer is A, then the three possible post 50:50 outcomes are A-B, A-C, A-D. You'll never choose D. Therefore, there are 3 out of 5 correct outcomes (the 3 A's).

Yeahbut, all that is assuming you have correctly eliminated one of the choices. Many times I have said, "Well, it can't be that one," and it is that one.

[bazodee]

Slam uses the African capitals as an example here of being able to positively exclude one answer. I agree this does happen, but the point that I really didn't make in my original post is that questions in the top tier are rarely written like this.

At least in Super Millionaire, Mr. Davies explicitly stated that the questions at $500K and above are written and tested for google-ability. They are rarely in a format where one single fact can be validated with ease. They are more likely in the format "which of these isn't ..." or "whom among these did both x and y". Rare are the contestants who can reason or intuit at this level.

[Bob78164]

Slam uses the African capitals as an example here of being able to positively exclude one answer. I agree this does happen, but the point that I really didn't make in my original post is that questions in the top tier are rarely written like this.

At least in Super Millionaire, Mr. Davies explicitly stated that the questions at $500K and above are written and tested for google-ability. They are rarely in a format where one single fact can be validated with ease. They are more likely in the format "which of these isn't ..." or "whom among these did both x and y". Rare are the contestants who can reason or intuit at this level.

Then they screwed up. On Ogi's question, the combination "etymology KEYWORD" along with the four city choices in the OR window would have come up with the answer quickly. --Bob

[TheConfessor]

Slam uses the African capitals as an example here of being able to positively exclude one answer. I agree this does happen, but the point that I really didn't make in my original post is that questions in the top tier are rarely written like this.

At least in Super Millionaire, Mr. Davies explicitly stated that the questions at $500K and above are written and tested for google-ability. They are rarely in a format where one single fact can be validated with ease. They are more likely in the format "which of these isn't ..." or "whom among these did both x and y". Rare are the contestants who can reason or intuit at this level.

I can't think of any of the top winners who had to answer a question like that. Let's see, there was:

The President on Laugh In
Distance from Sun to Earth
Who invented helicopters
First aerosol containers held what
Letter used to identify USA airplanes
First computer bug insect
Profession of Uncle Sam model
American Gothic farmer model
(plus three more I can't recall at this moment)

[Shade]

This sounds like a good question for Marilyn vos Savant...but she has never published an answer to any of my questions, lol