XKCD: It's more than a comic

Well, when I did it for the Bar exam I just decided that I would arbitrarily choose D for every single question on the test before I even opened the booklet. Which... is maybe less than arbitrary, but I'm not sure why that would make a difference, if it works.

Anyway, it didn't take much extra effort.

edited 22nd Apr '17 1:15:15 AM by Clarste

Well- there's the question of whether the answer are in random order or not- perhaps D is less likely to be correct- but since you don't have that information, it doesn't make a difference to the numbers from your perspective.

All things considered, and given that you were only able to properly apply it to 5 questions... I haven't crunched the numbers here, but I think that most likely earned you two correct answers you wouldn't have otherwise gotten. Maybe three if you were lucky.

Wouldn't it be easier in the long run to, you know, just study?

Assuming the correct answers are randomly distributed over the possible answers to each question, then guessing randomly would be exactly as likely to work as using a specific pattern (A-B-C-D-E-A, all 'D', etc.). If the answers are not randomly distributed, then you'd have to engage a professional statistician to tell you your odds.

The reasons why lotteries are "a tax on people who are bad at math" are both figurative and literal.

• Lotteries are a form of revenue generation by states.
• Lotteries are deliberately targeted at poor people, who tend to be less educated and therefore more likely to buy into the message.
• By simple logic, the state takes in more money in lottery purchases than it pays out, even when you ignore taxes. That's the entire point. Research has shown that the payout ratio varies by state but averages out to about 2/3 of revenues.
• Any given player can expect a payout proportional to the overall payout ratio for the lottery in question, which means that you lose money over time.

Statistically, you would lose less money by playing slot machines (casinos tend to have payouts in the 90%+ range). In a lottery, you are paying the state for the chance that the state will give you some of the money other people pay the state. It's a net loss no matter how you look at it. It's dangling the carrot of hope to get poor people to voluntarily lower their quality of life. It's one of the most predatory and disgusting things government does.

edited 22nd Apr '17 3:26:03 PM by Fighteer

Fun fact- I have never bought a lottery ticket.

Of course the rejoinder is that people dont buy lottery tickets strictly for the chance of a money payout- it's a form of entertainment. A relatively cheap one at that.

edited 22nd Apr '17 5:57:21 AM by DeMarquis

I've never bought a lottery ticket, either, but I've been given free ones a couple of times as part of some promotions and such (as in, "buy X and get a free lottery ticket", in which case I was going to buy X anyway, and not for the ticket).

As for using Monty Hall to answer an exam, it will only work if one of the options you're removing is wrong and you know it's wrong. If you do know that it's wrong, though, then effectively you've already removed it before you've made your pick, because you wouldn't pick it as your answer and then remove one of the options that you know are more likely to be correct.

@Gilphon: I'm not sure how you got "more judgmental against everyone" from my post? I'm not saying "everyone's an asshole for judging those people", just that it's not always as simple as "dumb people can manage money".

You also study. It's about getting an advantage in edge cases where you're unsure.

That's why I emphasized that you make a pick before you read the question, because then it's truly random. And then you remove answers that you know are wrong based on your own knowledge, which is what you're supposed to do on tests anyway. Basically you would incorporate this into a totally normal test-taking strategy.

edited 22nd Apr '17 12:57:22 PM by Clarste

So let's say you've got options A-D and you've picked D at random before you read the question. Then you read the options and see that, based on what you're certain you know about the subject, C and D are definitely wrong. That leaves you with the choice of A or B. How does it help that you picked D before you saw that you needed to eliminate it anyway?

Or do you mean that if it just happens that the option you picked wasn't one of the obviously wrong ones, then you'll get an edge?

The latter, yes.

I don't think it would work. The Monty Hall "paradox" works because there's a guarantee that the door that was picked will not be the one revealed to be wrong, which skews the probabilities toward the remaining door. This guarantee does not exist in the quiz scenario, so the effect does not exist and all remaining answers have the same probabilities of being true. (How did you get that 37.5% probability, Gilphon?)

In other word, because choosing an answer beforehand has no effect whatsoever on which answers are eliminated and which answers are kept, it is an entirely superfluous step.

There's a 75% chance of initially choosing an incorrect answer, and then you eliminate one of the incorrect ones, and have a 50% chance of choosing the right answer from the remaining two. Thus the chance of getting the right answer is 50% of 75%, which is 37.5%.

Of course I'm making the assumption that there are four choices, which is not given, but nor is it particularly unreasonable.

But that's in the case of a "true" Monty Hall situation. In reality, there's only a 50% chance that the initially chosen answer was incorrect and was not eliminated. So the odds of getting the right answer by switching are 25%. If you only count the cases where the initially chosen answer was not eliminated (75%), that makes 33.3..%, which are the same odds as getting the right answer by not switching.

The fact that in practice, the initial chosen answer will frequently be eliminated is besides the point- it's why Clarste initially said he was only able to use it on 4 or 5 question. The question we're trying to answer is 'in the case where the initially chosen answer was not eliminated, does switching increase the probability of getting the right answer?'; the game show metaphor, in this case, is that the host doesn't deliberately avoid opening the door the contestant chose, but if he does so, the show instantly ends, so every 'successful' instance of the show will have the host opening a door the contestant didn't choose.

If you say switching doesn't affect the probability in that case, you're going to have to walk me through your math a bit more- it seems logically equivalent to the 'true' Monty Hall show to me.

But the cases of opening the chosen door always replace cases where another door was opened and the chosen door was incorrect, not ones where the chosen door is correct.

Math-wise, the probabilities (assuming exactly one choice is eliminated, and you always switch) are:

• 25% chance D is correct; 0% chance of correct guess
• 75%*33% = 25% chance D is eliminated; 25%*33% = 8.3% chance of correct guess
• 75%*67% = 50% chance D is incorrect and not eliminated; 50%*50% = 25% chance of correct guess

Total: 33% chance of correct guess – same as if you hadn't bothered to pick an answer at the start.

edited 22nd Apr '17 10:02:03 PM by Zizoz

While I can't see it working out mathematically, I can see this exam strategy helping a bit psychologically just by having a set plan, helping the test-taker be a bit calmer.

Let's call A the event "the initial choice was correct" and B the event "the initial choice was not eliminated". We want to know P(A|B), the odds of being right by not switching. According to Bayes' theorem, P(A|B) = P(B|A) * P(A) / P(B) = P(A) / P(B), since P(B|A) = 1 (A implies B).

Furthermore, let's call n the number of choices and k the number of eliminations. Switching is more advantageous if P(A|B) < 1/(n-k).

In the Monty Hall problem, the initial choice cannot be eliminated: P(B) = 1. The odds of the initial choice being correct are obviously P(A) = 1/n, so P(A|B) = 1/n < 1/(n-k). It is better to switch.

In the quiz, situation, we still have P(A) = 1/n. However, there's a possibility that the initial choice is eliminated, with probability k/n: therefore P(B) = 1 - k/n = (n-k)/n, so P(A|B) = 1/(n-k). Switching is neither better nor worse.

I think for the quiz thing you're fundamentally misunderstanding how Monty Hall works. In Monty Hall, you make a guess and are then given another piece of information which depended on your guess. Say, if you pick door 1 he'll eliminate door 3, but if you picked door 3 he would have had to eliminate a different door. On your multiple choice test, you aren't given any information that depends on your initial choice. You'll be able to eliminate the same wrong answers no matter what you pick as your starting answer. So you might as well just skip that step and guess normally.

#1828: ISS Solar Transit

I got a good chuckle out of this one. I don't think that's what that particular light balance setting is intended for.

edited 24th Apr '17 9:39:00 AM by Fighteer

Well, you certainly can't get more direct than that.

Yes you can, by removing the filter. .

I don't think I'm getting that one. Must not use enough of those softwares.

Camera filters are not generally designed to be staring directly at the sun. That's the joke.

Explanation.

#1829 Geochronology

15,000th post!