## Is Who wants to be a millionaire just a game of luck?

For the discussion of math. Duh.

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τππ
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### Is Who wants to be a millionaire just a game of luck?

I mean, there's 33.34% chance of being right unless the person happen to know the answer, and lifelines can only get you so far into the game.

Let's say there are 15 questions with 4 choices each. Let's also say there are 3 lifelines: call-a-friend, 50-50, and ask-the-audience.

For each of the 15 questions, there is only 1 correct answer, and 3 incorrect answers, so immediately your chances are 1/3 = 33.34%. You can use each lifeline once. Using phone-a-friend, let's say gives you a 95% chance the person you call is correct. So 1 question is 95%. Similarly, we can say ask-the-audience gives you a 95% chance. Finally, 50-50 will remove 2 wrong answers, so you have 1 right answer and 1 wrong answer, so you basically know the answer. To recap:

Question 1: 33.34%
Question 2: 33.34%
Question 3: 33.34%
Question 5: 33.34%
Question 6: 33.34%
Question 7: 33.34%
Question 8: 33.34%
Question 9: 95% <--- phone-a-friend
Question 10: 33.34%
Question 11: 33.34%
Question 12: 33.34%
Question 13: 33.34%
Question 14: 33.34%
Question 15: 100% <--- 50-50
Total: 690.08%

Divided by 15 questions = 46.00%

So basically, it's more a less a game of chance, but more than half the people on the show will lose, so it's not very fair. That show is making tons of money off of people.

Deva
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### Re: Is Who wants to be a millionaire just a game of luck?

Point 1: 1/4 chance of answering correctly per question.
Point 2: 1/2 chance of answering correctly after 50:50.
Point 3: Multiplies those numbers together.

(.25)12 * (.95)2 * .5 = .00000268966% chance of winning.
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brenok
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### Re: Is Who wants to be a millionaire just a game of luck?

To expand from Deva's post:

If you have four choices and only one is correct, the chance is 1/4=25%

To find the odds of many independent events happening, you have to multiply them.

Think about it: what is more likely, getting a heads on a coin once or getting twenty in a row? By your reasoning it's the same.

CLD
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### Re: Is Who wants to be a millionaire just a game of luck?

Deva is correct with respect to the correction of your math, but you also have to take into account the difficulty of these questions. Most people can do a lot better than randomly guessing the answers.
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### Re: Is Who wants to be a millionaire just a game of luck?

Another point is that we rarely round 33.33333333... up to 33.34. Not that that's terribly relevant, since the actual probability of randomly guessing the one correct answer out of four possibilities is 1/4=25%, as others have said. (The OP seems to use odds in place of probability.)

CLD wrote:Deva is correct with respect to the correction of your math, but you also have to take into account the difficulty of these questions. Most people can do a lot better than randomly guessing the answers.
Yes, but the OP was wondering if it's reasonably possible to win even if you're not doing better than random guesses.

But with the correct math, then even if you're quite smart and have, say, a 95% chance of getting each one correct, you still have only a 46% chance of getting all of them, which is coincidentally quite close to the OP's own miscalculation.
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NathanielJ
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### Re: Is Who wants to be a millionaire just a game of luck?

τππ wrote:Finally, 50-50 will remove 2 wrong answers, so you have 1 right answer and 1 wrong answer, so you basically know the answer.

Question 15: 100% <--- 50-50

Ignoring all of the other mathematical mistakes, I'm having trouble understanding how someone could think that if you're randomly guessing between 2 options, you have a 100% chance of being right.
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### Re: Is Who wants to be a millionaire just a game of luck?

I think he's using a rule of the game that allows him to ignore the question by halving his winnings.
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### Re: Is Who wants to be a millionaire just a game of luck?

Frimble wrote:I think he's using a rule of the game that allows him to ignore the question by halving his winnings.
τππ wrote:Finally, 50-50 will remove 2 wrong answers, so you have 1 right answer and 1 wrong answer, so you basically know the answer.
No, it looks like the OP thinks removing two wrong options (out of the 4 total) means now you know the answer, despite the fact that there's still one wrong answer up as an option.

While a fairly straightforward confusion of odds and probability explains the 1/3 figure for the other questions, I really don't get what's going on with this one.
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### Re: Is Who wants to be a millionaire just a game of luck?

Hmm, well 1:1 odds is kinda like 1/1, which reduces to 1 or 100%.

One would think when you arrive at that conclusion that you'd recognise something was wrong with your reasoning, but apparently not.

Figuring out the probability of winning given the probability you know the answer decreases as a function of question number (and guessing randomly if you don't know) might be interesting. Also maybe determine if it's ever worth it to guess when you still have lifelines left (saving them for later questions you're less likely to know the answer to, which are also worth more money), or if you'd ever want to use more than one lifeline on a single question.

Since the game ends if you get something wrong I imagine the answer to the first one is no, but maybe playing around with expectations could spit out a different result.

tomtom2357
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### Re: Is Who wants to be a millionaire just a game of luck?

Maybe he thinks there is an answer on every question that you know is wrong, which explains his 1/3 probability on the non-50-50 questions. Maybe he extends this to being able to guess the correct answer out of two options.
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### Re: Is Who wants to be a millionaire just a game of luck?

Ignoring the OP's butchering of statistics, his question is this:
"Is a game where you randomly guess the answer to 15 questions a game of chance?"

LaserGuy
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### Re: Is Who wants to be a millionaire just a game of luck?

There's probably a more interesting analysis in terms of the expectation values per question--when are the best times to use the lifelines, when is it best to stop, how confident in your answer should you be before you select an answer, based on the value of the question and the potential associated losses. But I'm sure somebody has already worked this out at some point.

I think a better example of a game that is really just based on math and probabilities is Deal or No Deal. They even help you out by calculating (more or less) the expectation values of your current board for you.

kha-khees
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### Re: Is Who wants to be a millionaire just a game of luck?

τππ wrote:So basically, it's more a less a game of chance, but more than half the people on the show will lose, so it's not very fair. That show is making tons of money off of people.

Screw the maths, how are they making money off the contestants? Because they make it with ad revenue...

incidentally, I read this last night:
http://www.damninteresting.com/who-want ... usandaire/

elasto
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### Re: Is Who wants to be a millionaire just a game of luck?

kha-khees wrote:
τππ wrote:So basically, it's more a less a game of chance, but more than half the people on the show will lose, so it's not very fair. That show is making tons of money off of people.

Screw the maths, how are they making money off the contestants? Because they make it with ad revenue...

In the UK at least, it's a premium phone number to enter also.

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### Re: Is Who wants to be a millionaire just a game of luck?

This must be a troll. Every mathematical statement in the post is false.
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brenok
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### Re: Is Who wants to be a millionaire just a game of luck?

He may or may not be.

As we don't know, there is a 1:1 chance of being or not.

So, the odds of him being a troll is 1/1 = 100%

And the odds of not being a troll is 1/1 = 100%

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τππ
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### sage

The correct term is copypasta.

You people are just too serious.

brenok
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### Re: Is Who wants to be a millionaire just a game of luck?

Did you thin this thread was too serious? Try this one.

eSOANEM
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### Re: Is Who wants to be a millionaire just a game of luck?

Yeah, if you want to see the better trolling that went on here take a look at this or this or any of this guy's threads.

Yeah, this was a pretty rubbish troll.
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### Re: sage

τππ wrote:The correct term is copypasta.

You people are just too serious.

The correct term is nerd-sniping, but you did it poorly.
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### Re: Is Who wants to be a millionaire just a game of luck?

Not really. Nerd sniping needs to be an actual, interesting problem. This was just a bad troll-y copypasta.
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ConMan
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### Re: Is Who wants to be a millionaire just a game of luck?

Hence done poorly.
pollywog wrote:
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