Re: The Monty Hall Paradox

[ko0ldudeZz]

Ok i understand! This is pretty cool thanks!

[xPeaceloveandmusicx]

Great vid. Very easy to understand. Thanks for this.

[c6h10n2o4]

I have a dagree in math. (did crypto work for a while) .. this prob was given in a class of mine. I found that the best and shortest way was to do this. whats importent? well we know each door is 1/3. and then the switch question. there are 2 ends to this. you switch or you don't, but the question makes 2 sets the door you origonally picked and the ones you have left. if you don't swich it was like the question was never asked. but if you do then the question changes your game.

[Goldiney]

For all of you who fail to understand this, I do not blame you; However, think of it in this perspective:

You are on a game show, hosted by an MC, in which there are 100 doors to choose from. Behind 1 door is a car, behind the rest are goats. The MC says that once you pick your door, he will eliminate all wrong doors but one. Because the MC had 99 doors to begin with, there is a 99% chance that the remaining door is the car. Therefore, there is a 99% chance of winning if you switch to his.

[mrKirosana]

It's right, websnarf isn't breaking any rules of statistics. When you pick a door you are forcing the host to give you more information about the system, assuming he knows where the car is. Then the chance to get the car is 2/3 when player switches.

The chance is 1/2 if the host is clueless about where the car is and happens to open a goat door.

Whether the host knows where the car is or not is very much relevant.

[giovea]

no mather what your name or alledged I.q. is , it's wrong. you break all rules of statistic. pre-test and post test recalculation of probabilities enters altering events and not solutions, that circles it. it's amazing how such illusion can crack people's minds so much. best pre and post test or "event" probabilitie calculation e.g would be a couple of coin trous. 2 equal at start would be 0.25. 1 equal afterthe first would be 0.5. the "head or tails" result is irrelevant (always0.5) get it???

[websnarf]

What do you think my name or IQ is? (Allegedly or otherwise?)

This video is very old and I am not in the mood to revisit this. Please read the other comments, watch the video replies and look this up on Wikipedia. All are sound and explain the problem sufficiently.

[themountainviewguy]

they had to dress up in weird costumes because it made it more likely to get picked to participate in the show, not for some strange reason.

this is an interesting discussion and i like your looking at the monty hall long term strategy. it's been so long since i watched the show i forgot what he actually does.

there is also no state information or replays for the contestant, the constestant gets one chance.

framing the question, and making the actions predictable make a difference.

[OzzieGr]

Thanks for the video, you re a gifted educator.

[seanmft]

in the second example you wouldn't care if Monty was selectively opening doors or randomly opening doors because choosing to switch 100% of the time would still yield 2/3 probability, equally as high as adopting a strategy that took Monty's selection into account.

[websnarf]

Yes but its not the *only* strategy to achieve a 2/3 outcome. Marilyn Vos Savant omits this consideration, and if you watch the rest of my video a the response video by Prepoceros you will see that its probably something that you would want to take into account in the real world.

[seanmft]

I see. Pretty cool, I'll remember this if I'm ever on a game show.

[alex10stan]

Did anyone notice a big hole in the "professor" T-shirt? ... or you were fascinated about the solution which is nice, btw :)

[andrechi]

hahahah I DID just paused the video to see if anyone had commented on that

[Andrew0Bonesdog]

It makes perfect sense. But doesn't apply if the host doesn't show a wrong door. (Like what ur showing..)

[utkuozdemir]

amazing

[sgj101]

Thanks for posting this video. Clarifies a lot. I had a hard time before as I did not look at the situation regarding probability.

[jdohe]

The biggest criminals in the world (the government) steal many billions every year with deceptive odds and prizes. For instance, consider a lottery. What is the supposed payout in prizes for every dollar wagered? 25 cents on the dollar? And then, lets say the "prize" is 100 million. That 100 million is not 100 million. A lump sum after taxes is a small fraction of 100 million. Also 100 million paid out 20 years from now is hardly worth 100 million today.

[shadyparadox]

It's not just taxes. The "cash value" option devalues the jackpot to the expected value of the prize had it been distributed over 20 years (this is done by the lotto company, so that they are indifferent to the option you choose). THEN the government steps in and takes even more money away as taxes.

[jdohe]

I just remembered that it was even more complicated than just trying to figure out the odds and whether or not Monty was trying to help or hurt you or whether Monty knew where the car was... He also did things like offer cash to give up on selecting any door.

I think the big lesson here is that statistics can be useless or even worse than useless if the data is not truly random.

[jdohe]

The idea here is basically how devious is Monty? For instance, if the only time Monty offered a swap was when you were right, you should never swap.

[websnarf]

Yes, but if the contestant knows that Monty *might* not present him with a choice, she can be defensive and simply never switch; guaranteeing a 1/3 big prize pay out. So Monty can never reduce the payout to below that.

[jonahansen]

Very well done. Maybe could have added the case where Monty only allows them to switch when they had chosen the big prize (1/3 of the time). That reduces the producer's payout to 1 out of 6, no?

[hpwicked77]

Great Video. Thats so cool! We touched on this briefly in Pre-calc the other day, but i think half the class was completely lost! But I have a question.

Does this work with more than 3 doors? Like if you have 10 and you know the prize isn't in 8 of them, should you still switch?

[nd1008]

look at the wikipedia article. it covers this case very well.

[billybob1212]

thats really cool. thanks for making it a lot more clear.

[yaduke]

thx for sharing your knowledge.

[Harley492]

Stop right there! In your first graphic example, you said that it would be better to switch, but in reality, and I think this is where people have a hard time grasping the concept- is that if he picked the prize in the first place, he would NOT switch doors, and that would render your odds of winning if you switched equal.

[websnarf]

*Sigh*. Some people are just not capable of understanding this by any means I guess.

[VVesss]

Yet, the chance that you picked a car originally (and would win by staying) is only 1/3. The chance that you picked a goat originally (and consequently would win by switching) is 2/3. SWITCH!

[nicanicabad]

I love this video--and I love the natural grommets in your shirt. ahhh

[zadeh79]

So next time I'm on a three lane highway, and one of the other lanes comes to a dead stop due to heavy traffic, then I should switch over to the remaining lane? (Exclude the fact that some cars in the stopped lane will attempt to move over to the adjacent lane, slowing it down as well)

[websnarf]

I don't see the analogy. How do you know that only one lane of three will remain moving, and that this lane has been predetermined before you notice the other lane stopping? Its not the same problem at all.

[zadeh79]

That was not the best example. Instead lets say that it's your wife's birthday, and that you can only imagine three things that she would possibly like to have (lets say, perfume, jewlery, and a new microwave). So you go to the store and decide to go with some perfume. As your standing in line, she calls you and says, "whatever you do, don't get me a microwave". Should you go back and buy her a piece of jewelry?

[websnarf]

Yes. Now go off with your pencil and paper and figure out why.

[zadeh79]

I hope your not being sarcastic, because Monty Hall does apply in such a scenario (even in the car example, although with certain restrictions). I hope your not one of those linear losers who can understand rote solutions, but can't see where to apply them in the real world.

[websnarf]

What makes you think I was being sarcastic?

[junkyjuice21]

You, get your wife the jewelery! Websnarf is right, zadeh79. Have not you been paying attention to his video? You, pay attention!

[GentleSavage1]

junkyjuice21,

he does not have to get the jewelry. monty hall does not apply here, because his wife might be appealed to by BOTH of the left choices. He only knows of the microwave that it's bad. The two other things can be just equally perfect to her liking.

[edacafa99]

u have a hole in your shirt under your arm.

This is obvious stuff.. I can't understand how someone could get it wrong. cheers.

[izeman458]

I do understand it as do most people AFTER IT HAS BEEN EXPLAINED TO THEM. What I am saying is...the key is EXPLAINED TO YOU...how many of us would have figured it out by ourselves? A lot fewer because its counter intuitive...what I am saying is what if another counter intuitive version lies just beyond grasp?

[websnarf]

You seem to have a weak grasp on truth, calculations, mathematics, probability and/or reality. The solution to this problem can be calculated, demonstrated, or tested at which point the truth of it is clear. The relation between that and your intuition does not affect the reality of the solution.

[izeman458]

I agree with the video(although I was misled at first) but I was just remarking that in general(not in this paradox) if a person has a first intuitive answer and they are debunked by a logical yet counter intuitive solution...who is to say that there is not a THIRD solution in the shadows that has not yet been grasped.

[izeman458]

I don't buy it! The two doors that are left both have an equal chance of holding the car. That equal chance used to be 33% versus 33% and after eliminating the third door that equal chance has now become 50% versus 50%. I know people say its just my intuition but its intuition + logic as I just explained.

[websnarf]

You have not used one iota of logic. The explanations by Nate, Prepoceros and myself are fairly comprehensive. Please watch the playing card demonstrations by myself and howtofoldsoup as well. The odds do not change just because a door opens. That's not how probability works. By opening the fake door, MH gives you the equivalent of picking either one door, or *BOTH* of the remaining doors.

[izeman458]

What you seem to have forgotten is that the contestant does not have 1 chance in 3 of winning the car, he has 1 chance in 2! Because Monty always eliminates the third choice. The third choice is just an illusion which deludes everyone into using the wrong algorithms to compute the different permutations.

[websnarf]

If the contestant's first choice never deviates from a 1 in 3 chance of being correct. Eliminating the 3rd choice has nothing to do with anything because its elimination is after you make a free 1 in 3 choice (and is dependent on which choice you make.) The third choice is not an illusion -- in fact it can be seen as joined with other non-initial choice, thus giving the 2/3 chance of winning.

[izeman458]

You don't seem to understand what I am saying. The contestant's first choice IS NEVER REVEALED AFTER HE MAKES IT. It could be a car or a goat, it doesnt matter because Monty DOES NOT TELL THE CONTESTANT HE WAS RIGHT OR NOT. All Monty does is eliminate the third(goat) choice. The contestant is always always always always always choosing between one goat and one car. This "free 1 in 3 choice" that you tout is not a choice WITH ANY MEANING its just a diversion which should not even be considered.

[websnarf]

His probability of being correct is fixed at the moment he makes a choice. Suppose instead of revealing a door with a goat in it, he adds a door (or 10 doors), but claims there is still only one door with a car behind it. Do your odds of being correct now decrease to 1 in 4 or 1 in 11?

[izeman458]

My odds of being correct decrease only if I switch. However if he had started out with 11 doors or 5 doors with just one car, and he removed 5 goats or 11 goats, only then would my chances increase if I switched. But in the Monty Hall scenario its different cuz whats left is ONLY TWO DOORS...50-50. Either way you flip it...its still half. 1/10 vs 9/10 is not the same when you flip. 1/2 vs 1/2 is the same. You people keep ignoring that anamoly..

[websnarf]

There is no anomaly. Please run the experiment yourself, or write a computer program or roll some dice with a friend or whatever it takes to convince your. You are just plain flat wrong.

[izeman458]

Look at it this way, had you not been TOLD that the answer is not 50-50 would you ever have guessed it? Probably not. Fact is you were *guided* to this solution, it did not come to you intuitively because it is counter-intuitive. Now, what if there is yet ANOTHER counter intuitive solution that debunks this one?

[websnarf]

I don't know what you are talking about. Its *NOT* 50-50. Its 1/3 vs. 2/3 and I didn't need to be *TOLD* it, as this video clearly shows; I know how to calculate it directly. The degree of intuitiveness has nothing to do with anything -- this is just a pure calculation.

[izeman458]

I know this is just pure calculation but I was just remarking as to how easily intuition can mislead the part of the brain responsible for problem perception. My musings are just aimed generally at similar scenarios and paradoxes, not this specific one ANY MORE. Hypothetically people can be fooled from one wrong answer into a second wrong answer just as easily...not in this case but in other cases it can be possible.

[sandmnch]

you suk cock ho! Monty Hall is rollin in his grave. You ain't got none better to do then to post answers to math problems already solved! I could solve this problem striagh out of the womb. Bitch I do what I want! You make a deal and understand it is cleary a one third chance retard! This is the sand munch keepin it real!

[rookieninetynine]

The deals which preceded the Big Deal used Boxes and Curtains. Doors in Let's Make a Deal were used for the Big Deal of the Day only. In the Big Deal of the Day were no "zonk" prizes. The prizes were all good; but those behind the incorrect door were merely less valuable. Monty didn't offer to swap doors for other doors...Once doors were chosen for the Big Deal of the Day, they could not be traded. The Monty Hall Paradox is inaccurate.

[Astrosteed]

nice comments. I remember reading that in the Vos Savant column and then programming my computer to simulate 1,000 trials... by the time I finished the program I realized what the answer had to be. Good ol logic :) I liked the alternate strategies though, I've not seen them before. I agree that producers, being what they are, would most likely go for the minimum payout strategy whenever possible.

[trondreitan]

You asked for maximum collusion. Monty's strategy can be that Monty only gives you the opportunity for a switch when you choose incorrectly. By always switching when he gives you the opportunity, you're garanteed to win. This might irk the producers after repeated sessions, but the original formulation only mentions only one such event. Thus, it is entirely within the the frame of the described problem.

[trondreitan]

Opposite strategy: Only present an empty door and a possibility for a switch when the contender chooses the correct door. Quite outside the intentions of most who describe the problem, but again inside the frame of the description and very economic for the producers. Correct contender strategy: Never switch.

[clockworkhorrorshow]

Great instruction. You chose some amusing tags: "monty hall let's make deal marilyn vos savant IQ PhD" You explain things so effectively, you probably hate hearing this but you'd make a great math teacher. All my math teachers sucked.

I once explained this problem to a philosophy TA. She was a dense lady and she hated me because I always smelled like alcohol.

[joekarim87]

I'm impressed with your additional examples. Both realistically practical and mathimatically interesting.

[TheMathGuy]

Another fascinating fact is that even if the contestant knows this is Monty's strategy he cannot use that knowledge to his advantage. The fact that Monty is offering you a chance to change your mind doesn't convey any information to you.

[TheMathGuy]

I like your explanation! Very clear and precise.

[dexarouskies]

Amazingly clear. I could understand the math guy's explanation after some thinking, but your approach is even more clear. Thankyou for a crystal clear explanation.

[websnarf]

I do not teach for a living. I teach for fun. :)

[CauchySchwarz]

Great example, but still my brains says YES and my logic says NO. Or is it the other way around?. [5/5]

[trondreitan]

Two thirds into your presentation, I was thinking about doing my own clip. I thought that the ill-defined problem and the different possible strategies needed more attention. I even did a game-theory calculation with my different strategies. The last part of your clip hit the nail and saved me a lot of work. Thanks, man!

[olllj]

A Wikipedia link says more than 20 minutes youtube.

[websnarf]

Hmmm! I had no idea that the Wikipedia article was so extensive. However, they don't seem to exactly cover the corporate funding scenario as I suggested it.

[trondreitan]

It does have something similar though, which was describe as "The host, to minimize the show's budget for prizes, only offers the option to switch when the player's initial choice is the winning door." If this is the strategy, the optimal response is not to switch. Your last strategy is a kind of hybrid between that and the strategy which corresponds to the normal interpretation of the problem.

[KingLoser66]

I like when you do your math vids.

Fun & informative.

5 stars

[krew1618]

Nice one. I would love to see more math based vids.

[websnarf]

Because its not *COMPLETELY* correct! :) That's the point of the other 15. :)