Who wants to be a Millionaire logic question....

[Wi_N]

So i was thinking if i was a contestant and i got a question i had no clue what the answer was. and i wanted to use Ask the Audience and 50-50 lifelines, which one should I pick first? Is there a math logic to this?
Lets pretend its a question very doubtful the majority of the audience would know.

I was thinking Audience first since they have more choices to pick from..with 50-50 its just a coin toss then.
What do you guys think?

 

[phinds]

So i was thinking if i was a contestant and i got a question i had no clue what the answer was. and i wanted to use Ask the Audience and 50-50 lifelines, which one should I pick first? Is there a math logic to this?
Lets pretend its a question very doubtful the majority of the audience would know.

I was thinking Audience first since they have more choices to pick from..with 50-50 its just a coin toss then.
What do you guys think?

Are the questions yes/no or multiple choice?

 

[Wi_N]

Are the questions yes/no or multiple choice?

4 choices to every question. Ask the Audience they vote on which answer is the correct one and you see a chart of what they picked. 50-50 eliminates 2 wrong answers so you're left with 2 choices.

 

[Borek]

Depends on the question. "Who won last years 'Got Talent'" is a question for audience, 'What was the maiden name of Einstein's mother" is a question for 50/50.

 

[phinds]

I agree w/ Borek. Basically, this is not a question of mathematical probabilities, it's a question of how good is your general knowledge.

 

[Wi_N]

I feel like there should be some maths involved. Even with a simple question like who won the super bowl last year. you should still ask the audience first. and let's say the winning team gets 80% and the other teams get something evenly spread out. you pick 50-50 afterwards you're left with a choice of 80% correct vs (20/3)%.

I feel like you should always regardless of the question ask the audience first then 50-50. that's the debate really.

 

[fresh_42]

I agree w/ Borek. Basically, this is not a question of mathematical probabilities, it's a question of how good is your general knowledge.

Economists use the concept of subjective probabilities. I think there can be made some fundamental assumptions, depending on the stage of the required answer, as they get steadily harder per round. Those estimations can be made by several resources: analyses of former games, polls, statistics, experiences etc. E.g. I doubt that 50:50 can be assumed. Also does a selective audience joker heavily depend on the question: "Who won this years superbowl?" will probably result in quite good quotes in either case, whereas "Who wrote The Millionairess?" would have better chances in a selection of a single person than in the group. And next, it's an application of Bayes.

It is a real life example. The fact that it isn't perfect in a mathematical sense, doesn't make the question un-mathematical. It is just a confrontation of theory with reality!

 

[phinds]

It is a real life example. The fact that it isn't perfect in a mathematical sense, doesn't make the question un-mathematical. It is just a confrontation of theory with reality!

A good point. Thanks.

 

[Wi_N]

so does everyone understand the rules? you have to pick both lifelines for the question. which one do you pick first?

 

[fresh_42]

so does everyone understand the rules? you have to pick both lifelines for the question. which one do you pick first?

Again, it depends on the question, resp. round. The audience joker is usually of not much help on question 10 but almost a certain bet at stage 1. Fifty-fifty ahead of any other jokers is of course better than without. The game also reflects personal risk aversions, so you should try to figure out your personal risk function variance(expectation value) first. So to answer your question without any further knowledge, you will have to state some probabilities for correct answers first, i.e. make some assumptions.

 

[Janus]

Whenever I've watched the show and someone uses the 50-50 life line, it never seems like the two answers deleted were picked by random and they always end up with the two most reasonable answers. So let's say you ask the audience first, and then used the fifty-fifty. If the above observation is correct, then when you use the fifty-fifty, you are likely to end up with the two answers that were the top two audience choices, and you haven't really gained any extra knowledge using the 50/50.
If you use the 50/50 lifeline first, then the audience is left with just two choices. But remember, a certain percentage of the audience are those that would have chosen one of the least probable answers when given 4 choices, so can you really rely on them to choose correctly between the remaining two?

 

[Wi_N]

my "conjecture" is that you should always pick the audience first regardless of the question. if its an easy question well the audience will show you the answer and then the 50-50 will solidify the answer. if its a hard question you run the risk of people just guessing and with 2 options to guess between if you pick 50-50 first there is a big probability/almost certainty that both choices will have equal amount of votes unless you add the fact that some of the audience knows the answer and the rest will pick/guess at random so one of the choices will have (people that know + guessers) vs (just guessers) and the right answer will get more votes.
if you pick the audience first with the hard question there is more of a scatter with their votes and you can actually perhaps decipher the guessers from the people that actually know, there is more data there to make a sound choice.

i don't know if I am right I am really torn on this. but I am sure there IS a mathematical blueprint for which of these options is more sound regardless of the question.

Edit: I am changing my conjecture, you should pick 50-50 first then the audience. you will get guessers+people that know vs just guessers. the right option will always get more votes.

edit2: if you let the audience vote first and the majority pick the wrong answer and then after 50-50 you get 2 choices with the least amount of votes it would have been shown that it would have been detrimental if you did a 50-50 first and that wrong choice was not removed and then the same majority voted for the wrong choice. hmmm this is very hard. but I am certain there is an answer to this.

 

[fresh_42]

The formula you need is called Bayes' theorem. You want to maximize $P(A)$. As you can see, there are other probabilities involved, which you have to estimate first.

See also the subsections:
https://en.wikipedia.org/wiki/Bayes'_theorem#Derivation
and
https://en.wikipedia.org/wiki/Bayes'_theorem#Extended_form

 

[Wi_N]

The formula you need is called Bayes' theorem. You want to maximize $P(A)$. As you can see, there are other probabilities involved, which you have to estimate first.

See also the subsections:
https://en.wikipedia.org/wiki/Bayes'_theorem#Derivation
and
https://en.wikipedia.org/wiki/Bayes'_theorem#Extended_form

thank you! will look into it.

 

[Tosh5457]

If it's an easy question, the lifelines order is irrelevant - the public will get it right anyway.
If it's a hard question, by using Ask the Audience first, as you said, will spread out the "guessers" and the right answer should get more chances to get a higher vote %, than if there were 2 choices only. Even if there are trickster choices that make it look like it's the right answer, which leads most guessers to choose it, these tend to stay after the 50-50, so it'd be still better to go for Ask the Audience first, where at least some of the guessers would still be spread out by the other 2 wrong choices.
One advantage in choosing 50-50 first would be that some people could be undecided between one wrong choice and the right choice, and with the 50-50, the wrong one could be eliminated and they'd guess the right choice. Others could also be sure that one of the choices wasn't certainly right, and if that one stayed after the 50-50, they would then also guess the right one. But again, the 50-50 almost always keeps the 2 strongest choices, so I'd still go for Ask the Audience first and 50-50 afterward.

Edit: I am changing my conjecture, you should pick 50-50 first then the audience. you will get guessers+people that know vs just guessers. the right option will always get more votes.

Using Ask the Audience first would still be better, the amount of guessers on a hard question will be too high to get any statistically significant result with only 2 choices.

 

[John condon]

This is a good question with a definitive answer. Yes, there is a right and wrong choice as to which lifeline to use first. The lifeline that should be used first is the Ask the audience. After this, use the 50 50.

To understand why, imagine first that there are 100 choices for the answer, instead of 4. The 50 50 in this case eliminates all options except for one wrong one and one right one. By asking the audience first, all the guesses are spread among the 99 wrong answers, and the knowledgeable people will visibly pool into one answer. You won't need many people to know the answer in order to identify the correct choice. The 50 50 will then give you the final confirmation you need.
If you went 50 50 first, the guessers will be more influential by the time it comes to Ask the audience. You would need a lot more people to know the answer in order to outweigh the guessers when there are only two options.

All the same logic applies when there are 4 choices in the question, just with a lower level of advantage.

 

[profbuxton]

I must sadly admit that I do watch this show at times and am amazed at how little general knowledge is shown by many contestants. I don't know about the maths involved in picking an answer if you don't know, but I am continually am continually amazed by people who have absolutely no idea and hunt around for answers then change their mind in the last second and get it right! I am beginning to strongly suspect that there is some "fudging " going on, specially at the start. The show I watch is here in OZ by the way(down under) so the format may be slightly different.