Probability question.

[Oz the Gay and Powerful]

No doubt some of you will have heard this before. Or maybe even most. Anyway, suppose you are on a game show and the prize you want to win is a PS3. The PS3 is behind one of three doors. Behind the other two doors are snakes. You pick door number One. The host doesn't open that door. Instead he opens door number Two, which he already knew to be a snake. He offers you the choice to pick door Number Three instead, or stick with your original choice.


What do you do?

[Mr 3vil]

Answered.

[Oz the Gay and Powerful]

Why is that?

[Mr 3vil]

Why is that?

Look over there! A giant snake!

[Korra]

Stick with your original answer; the probability of it being correct in a multiple choice answer is high. Or; alternatively...pick (c)

[Oz the Gay and Powerful]

You would be surprised how many people get this wrong, 3vil. Nature just did.

[Mr 3vil]

Forty-two.

[Avarice]

Why wouldn't it be 50/50 shot between Door 1 and Door 3 at that point? Mr. 3vil's answer makes no sense to me.

[Oz the Gay and Powerful]

@3vil: Well we're bound to see a post which holds the answer... I didn't think it would be three posts in. :p But thank you.

edit: Well since Avarice caught the answer but didn't understand (which is perfectly understandable), I'll explain it further.

It isn't 50/50 because the host removed a variable. You have 1/3 odds of picking the PS3 and 2/3 odds of picking a snake. Therefore the odds that you've picked the snake on you first guess are higher than the PS3. You have a better chance of picking the PS3 by switching. A more detailed explanation would be this: The chance of you picking a snake is 66%, and the chance of you picking the PS3 is 33%. The host shows you a snake, and the switch raises your odds of picking the PS3 to 66%, and lowers the odds of picking the snake to 33%, since it is likely your first pick was the snake anyway.

A spoiler tag is fair this early in the game I think

[Mr 3vil]

You could have made this poll last longer. My posts are now random as Hell. Clearly the answer is 42.

[Avarice]

On your first guess yeah of course there is a 2/3 shot of getting a snake.

But when he asks you to switch to Door 3 at that time isn't it a 50/50 shot? Either your door has the PS3 or it has the snake. If your Door has the other snake, then you know Door 3 has the PS3. Two options, both equally possible ONCE THE FIRST SNAKE IS REMOVED.

[Oz the Gay and Powerful]

No, the variables don't suddenly become 1/2. You're not thinking about the first door you've chosen. The odds that you've chosen a snake in the first place are higher than that of the PS3, therefore switching would increase your odds of picking the PS3. I've edited my previous post to make it clearer.


You could have made this poll last longer.

The poll is open indefinitely

[Avarice]

So wait... If I were to explain this with math, it would be

[chance of initially getting a snake] / [number of unique choices] = [Percent chance your first guess holds the other snake]

.66/2=.33



EDIT: Confused percents with whole numbers there for a moment.

EDIT 2: No wait I am screwing this up hold on.

EDIT 3: Wow that was embarrassing.

I'm not a mathematician for a reason.

EDIT 4: Now that I think about it some more, and am not drained from a long day's work on a lack of sleep, I was right in the first place. It's a 50/50 shot. Not a 33/66 shot.

[Mr 3vil]

So wait... If I were to explain this with math, it would be

{[chance of initially getting a snake] / [100/number of unique choices]} = [Percent chance your first guess holds the other snake]

66/(100/2) DOES NOT EQUAL 33



How the heck did you get that? I'm afraid you may need to take Algebra again. :eek:

Oh, I see, well, remove the parenthesis. Now that I think about it, the whole math itself doesn't make sense at all.

[Jinjonator]

this is one'a them there math-ee-matical tricks, innit?

[wkw427]

This makes no sense.


Three doors
1 door has a ps3
2 doors have snakes

If you remove one door that has snakes, then
1 door has ps3
1 door has snakes

Seriously, where do you get this? Order of operations. At the start you are 66% likely going to pick the snakes, but before you DO pick the snakes, the % of snakes goes down to 50%..

Order of operations.. Once you complete part of the problem, it is gone and you don't turk back to it, because it is GONE.

[Grey Jinjo]

The two choices are separate entities. You are making up math in an attempt to be tricky. The first choice was 1/3. The second was 1/2. There is absolutely no link between the two.

[Weldar-Kazooie]

The two choices are separate entities. You are making up math in an attempt to be tricky. The first choice was 1/3. The second was 1/2. There is absolutely no link between the two.

What Grey said here.

IF, however, the doors were mixed again, and the snakes were re-added into the now empty door, the probability of door 1 being a snake door remains to be 1/3.

HOWEVER, I do see a potential area where you may be coming from. If this snake door that has been opened, door #2, is then closed once more. The probability of the other two remain at 1/3. However, this does not sway the chances of 1/2 being a snake door, and 1/2 being the PS3. All this does is allow you to eliminate one of the known doors leaving two. Which, again, leads back to 1/2.

Also: I would pick Door 3. 'Cus I feel like it.

[wkw427]

If there are three doors, two with snakes, and one with a ps3..
You pick #1, and door #2 is shown to have snakes.
Then the likelyhood of snakes and ps3 in #1 and #3 is 1/2
Period.

Unless door #2 is closed and everything is randomized again, then it is 1/3 ps3 and 2/3 snakes. But that didn't happen, and you are trying to make us confused.

I am above your math comprehension, laborer. I am able to divide by zero and win!

[Weldar-Kazooie]

It isn't 50/50 because the host removed a variable. You have 1/3 odds of picking the PS3 and 2/3 odds of picking a snake. Therefore the odds that you've picked the snake on you first guess are higher than the PS3. You have a better chance of picking the PS3 by switching. A more detailed explanation would be this: The chance of you picking a snake is 66%, and the chance of you picking the PS3 is 33%. The host shows you a snake, and the switch raises your odds of picking the PS3 to 66%, and lowers the odds of picking the snake to 33%, since it is likely your first pick was the snake anyway.

Your logic is flawed. The chance of picking a snake is 66%, and the chance of picking the PS3 is 33%. Swapping the decision would not swap the variables nor would they swap the chances. In fact, you did indeed eliminate a variable by opening the door. Now, one door is gone, being a snake door. There are two doors remaining. The chance of the third door being a snake door remains to be 50%. You did not change the percentages of the variables. What you did is take every factor to be 33% and apply it as such. Because of this, the snake doors would sum to 66%, which...somehow, you apply it to a single door now that one is eliminated. This is not the case.

Shuffling three containers, one holding a ball. You already possess a 33% chance of getting the right answer. After you eliminate a container, two remain. Instead of there being a continuous 66% chance of getting the answer wrong, your chances increase. That is how trial and error works. You seem to be swapping variables and percentages, which can't happen in this case.

That. Or I'm missing some play on words this question pertains in an attempt to throw off the reader. In any way, your logic that you used there is incorrect.

[wkw427]

I think he tried to punk us, but being the colelctive of th einternet, we punked him

[StarFox]

I really had no clue where SC was going with his explanation. It'd be 1/2 after the one door is removed. :I

[Greendrag]

Since the only viable reason to buy a PS3 is for MGS4, there is a 100% chance of picking Snake.

[StarFox]

Hey yeah, what if I want a snake? o-O

[Breegullbeak]

Every one knows that the gameshow host is trying to trick you so the company dosen't have to give you anything. There actually is no PS3 and behing each door is Ripper the killer beast.

[MetalHeroOfTime]

My answer, of course, is to switch doors.

[OldKingCoal]

Ah, I read a version of this in a book years ago, switch to door no. 3...

[Oz the Gay and Powerful]

The chance that you've ALREADY CHOSEN the snake is higher than the chance of you already having chosen the PS3. It is that simple. It's a probability question. If you switch you will have a higher chance no matter what. Yes it appears to go against common sense, but this is a logic puzzle that, even when people have it explained to them, they still don't get it.

Switching is the most logical thing to do.

[Grey Jinjo]

You are bad at probability and will fail any course you take on it. Your scenario doesn't hold up, because they are two independent decisions. Whether or not you chose door one does not factor into the second decision in any way, shape, or form. The second you carry over the 33% from the first session you have commited a mental crime against humanity.

It's only a "logic puzzle" in the sense that you have to be inherently illogical to fall for it.

[Zy0n7]

I've read this a long time ago and thought the answer was stupid, and it still doesn't make sense to me. It seems more like a play on words or a logical fallacy than real probability.

The fact that at the start you only had 1/3 of winning doesn't factor once one of the choices is gone, thus converting it to 1/2, or 50%. Opening a bad door boosts your chances regardless of you switching or not.

If the probablity carried over to the next round, by that logic if instead of opening one door you added another one with a snake, all of a sudden your 33% chance would've become a 25%, that's bs.

edit: let's say you where only watching up to the point when one of the doors is opened, and then given the chance to play and choose a door. It'll be 50% for you. The same as for someone who had already chosen a door, really.

[Oz the Gay and Powerful]

No amount of explanation does us any good. I did not make the scenario up, although it does hold up. It is called the Monty Hall Problem. A quick Google search will tell you that you are mistaken. The probability does not become 1/2. Not in the least.

[Zy0n7]

I know it's a famous problem, but it still appears as dubious to me.

Use my example, if you where watching until the moment a door is opened and then choose, you have 1/2. But if you where playing from the start and switch, you would have 2/3 according to this. Doesn't make much sense to me.

Edit: after reading a wikipedia article on it I'll concede.

[Gruntling]

Because the host knows which door is correct and he influences your decision, the probability changes in a weird way. Excluding that, the probability should stay at 1/2. Right?

[Zy0n7]

The thing is, that it's already determined from the start wether you'll win or not by switching.
3 doors and a PS3 equal to 3 possible arrangements of snakes/Ps3. Two of those situations will end in a ps3 upon switching.


ps3-snake-snake
snake-ps3-snake
snake-snake-ps3

if you pick one from the first column and the host picks a snake from any of the others, you'll only end up loosing if you switch if it was case 1, which is just 1 out of 3.

[Oz the Gay and Powerful]

Because the host knows which door is correct and he influences your decision, the probability changes in a weird way. Excluding that, the probability should stay at 1/2. Right?

I'm not sure what you are trying to say but I'll address it anyway. The host will always choose a door with a snake, yes. This is the key event. People are willing to concede that the variable does change, but to 1/2. This logic is actually faulty, considering the information the host just gave you.

http://www.maa.org/devlin/devlin_07_03.html

That is one explanation for it, better than mine.

[Grey Jinjo]

Here's where this entire "puzzle" breaks down. By the way, the article states that 1,000 PhDs "got it wrong." Maybe they "got it wrong," because they are more intelligent than the owner of a game show and actually "got it right." But I digress...

Say you pick door A. He reveals the snake behind door B. Now door C is the statistical favorite.
Say you pick door C. He reveals the snake behind door B. Now door A is the statistical favorite.

I shouldn't even have to elaborate on why that doesn't make sense.

[1UP]

No doubt some of you will have heard this before. Or maybe even most. Anyway, suppose you are on a game show and the prize you want to win is a PS3. The PS3 is behind one of three doors. Behind the other two doors are snakes. You pick door number One. The host doesn't open that door. Instead he opens door number Two, revealing a snake. He offers you the choice to pick door Number Three instead, or stick with your original choice.

solutions are almost always based on the additional assumptions that the car is initially equally likely to be behind each door and that the host must open a door showing a goat, must randomly choose which door to open if both hide goats, and must make the offer to switch.

This is different from a scenario where the host simply always chooses between the two other doors completely at random and hence there is a possibility (with a 1 in 3 chance) that he will reveal the car. In this instance the revelation of a goat would mean that the chance of the contestant's original choice being the car would go up to 1 in 2.

We were not given the information that the host had to open a door with a snake. We were told that he opened the door and it happened to be a snake. 1/2 is correct in this particular scenario.

[Grey Jinjo]

We were not given the information that the host had to open a door with a snake. We were told that he opened the door and it happened to be a snake. 1/2 is correct in this particular scenario.

Yeah pretty much changes the dynamic entirely.

[DekuScrubby]

I don't see why the presenter showing you a door with a snake in it makes your first choice to be less likely to be correct.

[Oz the Gay and Powerful]

Here's where this entire "puzzle" breaks down. By the way, the article states that 1,000 PhDs "got it wrong." Maybe they "got it wrong," because they are more intelligent than the owner of a game show and actually "got it right." But I digress...

Say you pick door A. He reveals the snake behind door B. Now door C is the statistical favorite.
Say you pick door C. He reveals the snake behind door B. Now door A is the statistical favorite.

I shouldn't even have to elaborate on why that doesn't make sense.

The host didn't invent the problem but the show was the basis for the idea. You're focusing on the doors "A" "B" "C" as separate choices without acknowledging what is behind them, although that information has already been given.

ps3 snake snake

You have likely chosen a snake. A snake you haven't chosen is revealed. Given that you have probably chosen the snake, the odds of switching and obtaining the ps3 are higher.

http://en.wikipedia.org/wiki/Monty_Hall_problem

This helps too.

Also the host does indeed know which door the things are behind, and will always open a snake door. I wasn't clear on that either so my bad, I'll fix it. So the host's part is clear. I did screw up the question by not stating it properly but in my defense I was suffering from low energy and lack of sleep. Even with the host's role defined people will still screw this up, guaranteed.

[Jinjonator]

How does it not become 50%? Ok, there's 3 doors, a PS3 and two snakes. 33% odds. Makes sense. One door is opened, revealed to be the snake. So obviously unless you're mentally retarded and decide that door is still a viable option, what choices are left? Door 1 and 3.

Is it that wrong? Or is door 2 still an option despite being proven to have the undesirable snake? No, it isn't. Door 2 is out of the equation.

So that leaves door 1 and 3. You have two choices. 50%. Unless there's a secret fourth door we're not being made privy to, this whole thing sounds terribly stupid and logically unsound.

Or can you explain how having 2 choices does not equal a 50% chance?

[Oz the Gay and Powerful]

snake snake ps3

1. What is more likely, that you have chosen the snake or the PS3? Obvious answer.
2. The host always eliminates a snake, one that you definitely haven't chosen, therefore changing everything.
3. The probability that your initial choice is a snake remains the same. Why? Because you chose it when the probability of choosing a snake was high, and the snakes remain at the door they're placed behind.

I think that's all the information you need to make the switch. They are not two separate equations.

[Madous]

snake snake ps3

1. What is more likely, that you have chosen the snake or the PS3? Obvious answer. 33%
2. The host always eliminates a snake, one that you definitely haven't chosen, therefore changing everything. 3 choices. Take 1 choice. 2 choices. Guess = 50%.
3. The probability that your initial choice is a snake remains the same. No Why? Because you chose it when the probability of choosing a snake was high, True and the snakes remain at the door they're placed behind. Obv.

I think that's all the information you need to make the switch. They are not two separate equations.
You never explained how there's a higher chance of your choice being a snake.

[Oz the Gay and Powerful]

Uh... because there are two snakes and one PS3 maybe?

[Jinjonator]

Yes, two snakes and one Ps3, odds of getting a snake are higher, until one of the snakes is removed from the equation, then there's 2 choices left, and that will always be 50% unless you're severely mentally crippled.

Are you saying that when there are 2 choices, it isn't 50%? I want you to answer that because it sounds like that's what you're saying. And that's so wrong it hurts. I mean, if you aren't trolling all of us right now I'm going to headdesk so hard.

[Oz the Gay and Powerful]

I just explained this to you. You aren't taking the first variable into the equation and you HAVE to for it to work. You've already likely chosen a snake. You are given one more choice, and one of the variables are removed. They aren't separate equations. You are stuck with the same likelihood of your first choice being a snake, because that's how it was in the beginning.


Assume, for heaven's sake, in all likelihood that you have chosen a snake, because there are two to choose from. Now that one of the snakes is gone, does the probability change? No, why would it? If you have chosen a snake, it won't change to another door. So the odds that you've already chosen a snake are high, and switching to another door and revealing a snake is absolutely zero, therefore switching and finding the PS3 yields a higher probability than it did before the snake was taken out. The host's information changes the damn outcome. If you just arrived on the scene and there were two doors and he told you to pick, THAT'S 50/50. Given the above information you should infer that this isn't the case.

[wkw427]

If you are allowed to pick any of the three doors at random, and get the snakes, and are allowed to pick between the two remaining doors, you have a 50/50 chance of winning..

[Eggbert]

How about you pick the snake and be happy with it you pansies snakes are ****ing awesome.

[Grey Jinjo]

If you just arrived on the scene and there were two doors and he told you to pick, THAT'S 50/50. Given the above information you should infer that this isn't the case.

Person A comes in.
Scenario is dealt.
Person A picks door 1.
Snake is revealed behind door 2.
Person A exits.
Person B, unaware that anything has just gone on, comes in and sees two doors.
Person B is told one has a snake and one has a PS3.
Person B picks at 50% odds.

Your move.

[Jinjonator]

First part of equation: Choose a door; 33% chance of being right

Second part of equation: One door is taken out; choose whether to stay with the same door or change; 50% chance of being right

The second part is a separate choice altogether, and you're assuming it's not. For some reason you keep acting like no one is capable of comprehending this, which isn't true. We get it, it's just stupidly fallacious, and only works if you don't know what you're talking about.

[Oz the Gay and Powerful]

Person A comes in.
Scenario is dealt.
Person A picks door 1.
Snake is revealed behind door 2.
Person A exits.
Person B, unaware that anything has just gone on, comes in and sees two doors.
Person B is told one has a snake and one has a PS3.
Person B picks at 50% odds.

Your move.

I'm not disagreeing with this. In fact it's what I was getting at. I've thought about this exact same scenario but it defeats the purpose of the entire question because it would be two people making different decisions based off different information. You already know the probability that you've chosen the snake is high. Another person walks in, doesn't know what the first person has chosen, and therefore cannot make an informed decision.

@Jinjonator: When the study was first released, it was actually hard for intelligent people to comprehend. Nowadays it's generally accepted and any mathematician would disagree with your logic. I've said why they are part of the same scenario. Just because you haven't heard of the problem before doesn't mean you're not giving the intuitive wrong answer without assessing the problem.

[Tooie]

Uh, guys, Stephen is right.

http://www.youtube.com/watch?v=mhlc7peGlGg I think this video explains it perfectly.

[Grey Jinjo]

First part of equation: Choose a door; 33% chance of being right

Second part of equation: One door is taken out; choose whether to stay with the same door or change; 50% chance of being right

The second part is a separate choice altogether, and you're assuming it's not. For some reason you keep acting like no one is capable of comprehending this, which isn't true. We get it, it's just stupidly fallacious, and only works if you don't know what you're talking about.

Not watching the video, but I can explain it in a way that makes it understandable.

Let's say there are 100 doors instead. The situation plays out like this:
1) You pick door X.
2) The host eliminates 98 other doors.
3) You pick between door X and remaining door Y.

Now, let's actually run through this situation...

1) You pick door 1.
2) The host eliminates 98 other doors.
3) You choose between door 1 and the remaining door.

1) You pick door 2.
2) The host eliminates 98 other doors.
3) You choose between door 2 and the remaining door.

...

1) You pick door 100.
2) The host eliminates 98 other doors.
3) You choose between door 100 and the remaining door.

Now, we are running through possibilities which means that in all 100 trials the right door was the same. Let's say it was door 68. That means the ONLY trial, trial 68, is the one in which it is worth it to keep your case. In the other 99 instances, trading would have given you case 68.

Thus it's better to trade.

[Oz the Gay and Powerful]

Yes increasing the amount of doors does make it easier to understand. And if that didn't sell anyone who didn't previously understand, try this

http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html

It's a computer simulation. First, always switch. Look at your number of wins. Reload the page and then always stay with your original choice. You can do it for as long as you like, but if you somehow come to the conclusion that it is 50/50, you're beyond help. The first time I heard this problem I was confused, but that was yesterday. Then I reconsidered what my intuition told me was the right way.

[Madous]

Uh, guys, Stephen is right.

http://www.youtube.com/watch?v=mhlc7peGlGg I think this video explains it perfectly.
Welp. Now I get it.

[Avarice]

Makes sense to me now, though I think it makes more sense to call it a riddle as opposed to a question.

[Mr 3vil]

Makes sense to me now, though I think it makes more sense to call it a riddle as opposed to a question.

There is math and proofs for this question (it's a legitimate math question with an answer). It takes the situation and reverses the probability if you weren't allowed to switch. I got the answer thanks to a brief session on statistics. Say you just chose without the option, it's 1/3 ps3 and 2/3 snake. Now that you're allowed to switch, it's 2/3 ps3 and 1/3 snake if and only if you switch.

The fallacy is ignoring the first condition, your first choice being of no affect to the second, which is false. Because the first choice was a precursor to the second choice with new conditions.

[1UP]

There is math and proofs for this question (it's a legitimate math question with an answer). It takes the situation and reverses the probability if you weren't allowed to switch. I got the answer thanks to a brief session on statistics. Say you just chose without the option, it's 1/3 ps3 and 2/3 snake. Now that you're allowed to switch, it's 2/3 ps3 and 1/3 snake if and only if you switch.

The fallacy is ignoring the first condition, your first choice being of no affect to the second, which is false. Because the first choice was a precursor to the second choice with new conditions.
I think it still qualifies as a riddle because it is meant to deceive. All riddles can be solved with proof and logic, they're just proposed in a misleading manner.

[Oz the Gay and Powerful]

Yes, and as such it reveals certain weaknesses in the human brain that I do not have the qualifications to comment on,but I will paraphrase what I've learned. Even people who are presented again and again with an explanation do not want to admit they're wrong. As Mr. 3vil said people will ignore the terms of a certain condition (that being the host's mid-problem interference) and no matter how many times you explain it people are adamant that their way is right when it just is illogical. It's been clearly evidenced in this thread and when I read about it I was curious to see if I could confirm it on RWP. I'm not sure if I did using the initial explanation (as in I ****ed up and made the host's interference seem relative) but even after I corrected myself there were still members who kept missing the key component. Suffice to say it was interesting. Whether it was actually meant to deceive is subjective. It is a math problem, and you can get it wrong just like any other math problem. Does this mean math problems are riddles? Of course not. Riddles don't always use logic, math does.

[Avarice]

Yes, and as such it reveals certain weaknesses in the human brain that I do not have the qualifications to comment on,but I will paraphrase what I've learned. Even people who are presented again and again with an explanation do not want to admit they're wrong. As Mr. 3vil said people will ignore the terms of a certain condition (that being the host's mid-problem interference) and no matter how many times you explain it people are adamant that their way is right when it just is illogical. It's been clearly evidenced in this thread and when I read about it I was curious to see if I could confirm it on RWP. I'm not sure if I did using the initial explanation (as in I ****ed up and made the host's interference seem relative) but even after I corrected myself there were still members who kept missing the key component. Suffice to say it was interesting. Whether it was actually meant to deceive is subjective. It is a math problem, and you can get it wrong just like any other math problem. Does this mean math problems are riddles? Of course not. Riddles don't always use logic, math does.

Except you kind of really sucked at explaining it. Once a clear explanation was posted (The video and/or Grey's post) people admitted they were wrong.

[Grey Jinjo]

Yeah, I think this thread did more to go against your point and prove that when faced with legitimate, understandable evidence the logical among us will change their minds. There hasn't been anyone since my post or the video that has entered the thread and argued against the riddle.

[Mr 3vil]

I think it still qualifies as a riddle because it is meant to deceive. All riddles can be solved with proof and logic, they're just proposed in a misleading manner.

:thinking:

Okay, I concede, you have a point that the question is in the context of a riddle. Had the question have been, find the probability if you switch or don't switch, then it's a legitimate math problem. However, not all riddles can be solved by first-order logic, some of it is way out there and the answer you hear may not be the one at all. Trust me, I've heard some very stupid riddles in the past. The question would just allow you to stretch into infinite answers and you guess until hopefully the person who asks the question tells you that answer is correct.

[Weldar-Kazooie]

Uh, guys, Stephen is right.

http://www.youtube.com/watch?v=mhlc7peGlGg I think this video explains it perfectly.

Thank you, this explained the problem and solution much better than anything else in this thread. :) I understand how it would indeed be wiser to swap the door.


Yes, and as such it reveals certain weaknesses in the human brain that I do not have the qualifications to comment on,but I will paraphrase what I've learned. Even people who are presented again and again with an explanation do not want to admit they're wrong. As Mr. 3vil said people will ignore the terms of a certain condition (that being the host's mid-problem interference) and no matter how many times you explain it people are adamant that their way is right when it just is illogical. It's been clearly evidenced in this thread and when I read about it I was curious to see if I could confirm it on RWP. I'm not sure if I did using the initial explanation (as in I ****ed up and made the host's interference seem relative) but even after I corrected myself there were still members who kept missing the key component. Suffice to say it was interesting. Whether it was actually meant to deceive is subjective. It is a math problem, and you can get it wrong just like any other math problem. Does this mean math problems are riddles? Of course not. Riddles don't always use logic, math does.

I don't think you can say that. As what you observed here was not merely ignorance, but the way the readers perceived what you were telling them. Your explanation was relatively vague and did not provide a clear enough answer to the problem. The solution was not clearly evidenced until Tooie posted that video documenting the solution. Since then, not one person has gone against the actual answer. In fact, what can be seen here is the opposite of what you were trying to "prove" or "observe". People have been shown here to follow what is logical when presented with logical evidence. When presented with doubtful, unclear evidence, people are more prone to carry on their own beliefs and ideas. At least, based on what has been seen in this thread.

Edit: Grey and Avarice kind of beat me to it on this one, but I went a little bit more in-depth.

[Oz the Gay and Powerful]

I did correct myself and post an article explaining the answer in detail and the wikipedia page (which aren't vague, and both of which hold Grey's explanation, the one I admittedly should have used) and there were still people who maintained that they were right.

...Even with my original incompetence there isn't an honest excuse. People that said NO BUT 50/50 after reading those explanations is failure on their part, not mine.

[Grey Jinjo]

I did correct myself and post an article explaining the answer in detail and the wikipedia page (which aren't vague, and both of which hold Grey's explanation, the one I admittedly should have used) and there were still people who maintained that they were right.

...Even with my original incompetence there isn't an honest excuse. People that said NO BUT 50/50 after reading those explanations is failure on their part, not mine.

You can't just post links to two ten-page articles and say "there." You are supposed to cite sources as factual explanations for your argument - not be lazy and just post them and say "read up." I doubt most of the people here actually read them, and you can't blame them given A) their length and B) the fact the first means they use to explain them is a mathematical proof and not an actual explanation.

[StarFox]

Aha, I get it. :I

[Madous]

So in Pre-Calc today we started going over this exact problem. Ironically I was telling a friend about it the day before at lunch. He turns around and looks at me like I'm a genius while the entire class is entirely clueless on the problem. I'm the only one able to explain it decently, all thanks to this thread.

Thought that warranted a bump. :p

[ConkerTribe]

I just explained this to you. You aren't taking the first variable into the equation and you HAVE to for it to work. You've already likely chosen a snake. You are given one more choice, and one of the variables are removed. They aren't separate equations. You are stuck with the same likelihood of your first choice being a snake, because that's how it was in the beginning.
Alright, let's make this simple with an analogy:

If I gave you 3 apples, right, and I said that two of the apples have worms in them, your chances of biting into a worm-filled apple would be 2 in 3.

Now let's say I take one of the apples away before you get to bite. What are you chances now? 1 in 2.

It's the change in the amount of options that changes the entire scenario. You can't retroactively evaluate your chances of biting into an apple when you had three because the entire situation is different now.

The change in the amount of apples directly affects your chances. 'Nuff said.

EDIT: Sorry I was late to the party. lol

[Bartimaeus]

http://img545.imageshack.us/img545/129/76066585.png

Does this prove I'm luckier at getting lower percentages, or what?

[Strandomguy]

Does this prove I'm luckier at getting lower percentages, or what?

Lol nice

I remember when we were replicating this scenario at school, one group got the "prize" evey single time, regardless of if they swapped or not (out of about 20 tries)