Understanding "Variable Change", The Monty Hall Problem

[Thorcar629]

if anyone dosnt get it still watch this vide /watch?v=mhlc7peGlGg

[DrewDosCuatro]

Good Explanation and I think the best way to think about it is to look at that chart with all outcomes really close and accept that you are wrong 66.7 % of the time when you start out.

[rGNinjaBear]

Great explanation

[MistyGothis]

Nice video. One thing I'm curious about is if the phrase "Variable Change" is a real term, and if so, what does it mean? I understand the Monty Hall problem and why switching wins 2/3 of the time. i understand conditional probability. But outside of the movie 21, I've never heard of the specific phrase "Variable Change" before. I googled it, and only found references to the movie 21. I wonder if they just made it up.

[DeChief1]

It makes total sense...the chances of you picking the car on the first pick is 1/3 so it's 2/3 chance you'll get it wrong so the smarter choice would be to switch seeing that more than likely your initial pick is wrong...

[pivotman64]

it's not about the probability changing based on switching or not, it's about the probability of you picking a goat at first and either switching or keeping. if you keep every time there's a 66% chance of loosing, but, if you switch every time, there's a 66% chance of winning.

[cbr4]

The chart made all the difference in the world. Bitchin'~

[Foshomyno]

i'm pretty sure that's the ace of hearts

[TaroGabunia]

Bad quality i can't see and hear. can't you afford a good camera?

[abcwatup123]

I get it...Think about it you have a 2/3 chance of getting a goat which means your pick will most likely be a goat it doesnt matter if u c 1 of the choices and now you only have 2 left. Its not 50% .. because you started off at 66% which means you most likely chose a goat than than the car but if you switch your basically switching your goat for the car.

[bennyboy08878]

Stick to stealing stereos, dude

[duce2231]

This is definitely the best video I have seen on this.

[andymatt123]

totally get it now! thanks man!

[gergoooooooo]

purposefully?! hahahha

[lxCaseyxl]

So if i did this say 100 times, and i changed my pick after he showed me an incorrect card I would be right 66 times?

[boatyboatrite]

@lxCaseyxl Statistically speaking, you would be right close to 66 times.

[sk8er1226]

the table helped me the most, i didnt get it until i saw it thanks

[gikatilla]

The problem is easier to understand if you use 10 cards, allow partner to pick 1, show 8 goats, and ask if he wants to switch. It's the same principle but now more obvious 90% v. 10%.

[phtmexplo]

yep if u change (swap) when u pick a goat (66%) u always get the car.

when u dont swap, u have 33% chance of that car.

[babyaiko]

this is confusing

[telecoustic]

Yes, it is! Sorry if I may have made it more confusing... The last 2 minutes are the most helpful; I kind of babble. The chart in my own opinion helps the most. If you are still confused after, let me know!

[imwahyou2]

can u help me understand this cuz i have a problem with ur chart.. cuz you wrote picking goat 1 and picking goat 2 as 2 different scenerios but then if you picked car you only listed one scenerio yet i believe there should be two. 1. you pick car, host reveals goat 1 and 2. you pick car, host reveals goat 2.

[craijona]

It all really comes down to that 33.3% of getting it wrong that the host takes away.Now some people believe that the 33.3% should just flop over to door number 2. Wyile it should be equally distributed between the other 2 doors, giving each a 50/50 chance. OR you could consider that the 33.% chance is "gone" in which case eahc is left with 33.3. I dont get it, I knwo Im wrong but im not sure how. lol

[brewster102]

Your chart reveal the progression of logic more than anything else

[ctiger69]

Let me explain it for you real quick. You have three doors. There is a 1/3 chance you will pick the right door. There is a 2/3 chance you will pick the wrong door. So that's 33.3% for the right door and 66.7% for the wrong door.

So based off of this stat you pick the wrong door the majority of the time.

[leth41x]

But you still get the goat! you still win!

[jz335ch]

Ah! thank you, i finally get it

[einewelle]

you are geniuos!:-) after watching the movie i was also confused, but now i got it! If you switch, you have 67% chance to take the right card, then from the beginning (33%) Thanks!

[InsaneOverlord666]

Now... I understand completely, what your saying. But if the person always reveals a third door and gives you a chance to change, no matter what the situation, then wouldn't that affect how you match the probabilities?? I understand if he knows what is what and chooses to ask you, it would make sense this way. BUT, if he always has to no matter what, then, I dont think this would work like this? Any help?

[7271422013]

ahh it makes more sense nowwhen you just look at it in black and white - its all dependant on the host and initially chosing the incorrect card/door. in a nut shell, its like in poker if you are a 3 - 1 underdog to lose, but then the dealer removed a third of the cards that would NOT help you win the hand thus would give you now a 66.6% chance of winning. Thanks

[telecoustic]

Exactly! Glad I could help.

[7271422013]

What happens if you pick the correct card/door straight away, does the host still offer the swap or does he reveal the car straight away. If he still offers the swap you would then be left with a 66.6% chance of losing according to this theory.

[telecoustic]

Yes, he still offers a switch; but NO, you would only be left with a 33.3% chance of losing because he already opened a door with a goat; eliminating 33.3%. But... Since you ALWAYS switch, you would lose if you guessed the car. Understanding that you only pick the car 1 out of 3 times is KEY to understanding how this paradox works. Percentages and stats aren't always based on one time recordings. Knowing that may help your understanding.

[7271422013]

i understand the concept, that origionally u have a 33.3% chance of getting your "chicken dinner". by removing one of the losing cards/goats i now have a 66.6% chance of winning from the origional 100% but that 100% was from when i origionally had to make a choice based on 3-1 odds. but now your decision is totally different, with the choice of picking any of the 2 remaining cards why is the percentage not spread even over those 2. Maybe an answer to this question could help...

[telecoustic]

The main thing that needs to be remembered is that the host (and remember this is only a paradox and a mental issue if it goes according to plan; explained in text early in the video) opens a door with a goat EVERY TIME. Since he does this, he eliminates 1 of 2 failures. The best way to understanding the problem is to look at the chart in the video. Even the best professors in the world have difficulty explaining it without pen and paper! They don't call it a paradox for no reason!

[superman0017]

Wow. Great video. I had to repeat it to myself over a few times befoe it finally clicked. Like traux said, the line "You pick a goat and you win" explains it well. :)

[noel4140]

Good explanation.

[traux]

Nice explanation. I think the line "you pick a goat and you win" explains it perfectly.

[luffy3]

clearly understood

[PenguinLord2]

ohhhh.... Thanks man,the chart at the end really helped.Thats Cool

[schematic2]

There's no Goat 1 and Goat 2, you can only pick one goat, therefore giving you a 50% chance each time. This works with probability, but there are other factors to considers, like common sense.

[telecoustic]

lol

[gtbanuh]

it is not 50/50. think about it! initially the percentage of u chosing the right card is 33%. the card you have chosen is 33% meaning the next 2= 66% (33 and 33%).if you subtract 1 card from the remaining 2 that means the 1 you have 33% and due to the change, the next card becomes 66%. the initial card percentage remains the same.

[suhasratan]

how? if am left with two cards, the probability of any of them being the right one is 50%, isnt it? the 'new' probability, that is...

[benji07]

it does make sense (finally). there is a 66.6% chance of picking a goat in the beginning. if i switch after monty shows me, i win every time i pick a goat. hense, 66.6%. thanks!

[dorris1989]

long live, FatLordVe !!

[dtmhawk2]

err.. you never explained why. i know that it is the case (if you change you have better chance) but my physics/maths c teacher and i who is the most intellgent man ive ever met can't figure out why. as far as i can see it should be 50-50 i can see why it could be 33-66.

when you change its like choosing option 1 (1) and option 2 (2 and 3) giving you 33 - 66, but that doesnt explain why it cant be option 1 (1 + 3) and option 2(2) giving 66-33, which returns it to 50-50. ne1 feel free to pm me

[telecoustic]

well, your instructor must not know enough about probability, because this is all true. And explined moderately well. If you would like me to explain it in better detail, let me know through a message. Thanks!

[dtmhawk2]

thank you very much for the offer, but a just wiki'ed it. and a understand it well now. Unfortunately he doesnt know enough about probability, but like i said he is a math c and physics teacher, not a liner eqautions proffessor ha. thanks again for the offer.

[ankitanand25]

i'm sure there's a mathematical explanation for this..i'm afraid the chart at the end doesn't help....you've picked two instances with the car on the "switch" with Goat 1 AND Goat 2 on the initial pick, but you've only picked one instance with the car on the "initial pick" with Goat 1 OR Goat 2 on the switch..you would use one of AND/OR on the chart...either way, it would be a 50:50..i even tried the trial and error and got 8 and 8..but maybe i'm just havin a bad day :)

[telecoustic]

Not sure exactly what you are saying; but the chart is correct, and so is everything else. If you would like me to explain it further, I would be happy to! Just message me.

[frankputtemans]

The scheme made it very clear!

[telecoustic]

If you mean the scheme as my video, Thank You!! lol. I'm glad it now makes sense.

[SVvEv]

The switch is derived from Bayes' theorem. Fascinating paradox.

[grappler8AKI]

i understand what you are saying, but say if my first choice is the car in the first place?? then if i go for the variable change i just shoot myself in the foot don't i? I think what we have to consider is CHANCE, as we can never be 100% sure, instincts matter here because the host will know either way so what im saying is, variable change may be a trick if you get what i mean.

[telecoustic]

Yes, you make a great point; but a viewer needs to look past the problem and view it in pure probability form instead of a one time "story problem" occurrence. Since every time you switch there is a 2/3's chance(table in video is the most helpful), and you are not sure what you picked until all is shown, you should still switch whether you are only doing it once or not. b/c there is only a 1/3 chance you are going to pick the car... It's a chance you have to be willing to take!

[FatLordVe]

I think the best way to explain the Monty Hall problem is instead of using 3 doors, use more, like 1.000.000 for example, you pick door #1 and the host opens 999.998 other doors it only leaves your door "#1" and number 865.782 for example, you had 999.999 chance to pick wrong, and knowing that the host knows where the car is you should switch to the door he didnt open. That is ofcourse, if youre smart.

[farzena]

if you pick the car and the host doesnt show you that car but shows you the goat would you still change? how would you know?

[telecoustic]

well, like I said, a third of the time you will pick the car, but you should still always switch. 2/3 of the time you won't pick the car; and you will win.

[farzena]

oh ok, so you might only win two out of three times.. makes sense now... thanks

[atlfalconsfan84]

ya that last sentence really did make so much sense...i feel smarter!

[Eagleyex]

The last sentence was the most helpful for me "if you pick a goat, you win" i got it now ;] 2 goats = 66.7% car = 33.3%

[telecoustic]

Glad I could help!

[l2ebelconvict]

I was still totally clueless on the whole thing up until you showed the chart. For me and my friend sitting next to me the card explanation didn't make any sense or help in any way, just kinda make us more confused, but once you showed the chart we were both like "ah, now I get it." Maybe it's just us, but if you showed the chart right away instead of doing the whole card thing, there would be no confusion. Still your chart helped me understand it so thanks.

[telecoustic]

Yeah, you are right; that's how it clicked for me too. But using the cards just gives a sense of a real world example; I could have explained it in an easier faster way though, for sure. I'm glad it makes sense though!

[tomy4you]

One one more:

3 doors (1/3 chanes each). We pick one door (1/3 chances), two dors are remainign (2/3 chances). The host will open 1 of the remaining doors; however the chances for the remaining, closed door will still stay 2/3 as opposed to our first door that we picked (which is only 1/3 chances for winning) - so we were just given extra 1/3 chances. So always switch!!!

I am not sure but this might have been that student's answer in the movie.

Regards.

[tomy4you]

Hi Telecoustic,

Good explanation. There are a few. Here's a simple one:

2 goats 1 car. Picking a goat - 66% chance. Picking the car - 33%.

Every time we pick a goat (66% chance) the host will open another door containing a goat, so if we switch, we switch right to the car (therefore 66% chances for winning).

If we choose not to - we will stick with a goat (66% chance).

If we pick the car the first time (33%) and switch - we will lose - but there are only 33%chances for that.

Regards!

[ahajjaj]

Great explanation, finally it makes sense.

[rvfharrier]

Ok, this will solve problems once and for all. Door 1 = car. On all 3 occasions we switch.

You pick 1, host opens 3 and you switch to 2 = lose.

You pick 2, host opens 3 (HAS to open 3 because he can't open 1 because that has the car) and you switch to 1 = win.

You pick 3, host opens 2 (again, HAS to open 2 because 3 is your pick and 1 has the car) and you switch to 1 = win. We switched all 3 times, won twice and lost once. = 2/3 chance of winning if you switch. 1 - 2/3 = 1/3 chance if you stick.

[telecoustic]

Yup! Good job reinforcing exactly what I showed; dont think there was a problem, but explained well.

[jbaldwin343]

I do have a question. Just so you know I do understand this very well, and did before this video, I just wanted to see other explanations. But, can you think of a situation in real life, not a game show, that variable change would apply to?

[telecoustic]

Yes, here is one:

If you meet a lady on the street and she has her son with her and she says "I have two kids, this is one of them... my son... what's the probability that my other child is a boy?" You would think 50/50... but you'd be wrong, it's 1/3. If you would like this explained further, message me and I would be happy to.

[jbaldwin343]

I understand its similarity with the demonstartion before, but yes, I would like a further explanation.

[telecoustic]

Sure. Your probability list of two children are BB, GG, BG, and GB. (G=girl, B=boy) If you already have a boy, then GG is eliminated, since GG says you have two girls. Since you have a boy, you only have a 1/3 chance because there is only one BB; meaning both children are boys. If this does not make sense, let me know... I will do my best to explain it differently.

[jbaldwin343]

Why would the probability list matter what order the kids are in ( BG and GB) ?

[telecoustic]

The list is only there to show you there are only four combinations of genders of her two children. You can only have a boy and a boy, a girl and a girl, a girl and a boy, or a boy and a girl. It's kind of like rolling dice. you can roll a seven 6 ways, 2 of which are 5 and 2, and 2 and 5. It's some what confusing but is just the way probability works; confuses me too sometimes. Hopefully this makes sense.

[jsrusa]

thanks alot

[redazure]

Isn't bg and gb the same thing in this case?

If not, than gb would be eliminated too, since the first kid is a boy. So it'd still be 50/50.

[redazure]

I'm pretty sure you are mistaken there... I'd be worried about teaching people mistaken math.

I don't believe that is variable change at all. The reason it isn't the same, is the number of boys vs girls ration isn't given ahead of time. 1:2 car:goat. Where as with the kids, it is 50/50, always.

[telecoustic]

I am NOT mistaken. The term variable change can be taken many ways, but what I have written is correct. GB and BG are NOT the same, as explained earlier with the dice example; that is how probability works. I never said "the first kid was a boy", I said I have a boy with me, and another child that is not with me. The ratio IS given ahead of time, if you think about it; the chances are as explained before; GG,BB,GB,BG.

[telecoustic]

Message me if you would like to discuss this further; I would be happy to clear up any confusion.

[redazure]

A good example of RL variable change is, in fact, with the game Blackjack.

If a deck has 52 cards, and the dealer is showing a 9. The chances of him having 19 is 16/51 (4X10,4XJ,4XQ,4XK). If the dealer deals you an 8 and an ace, you got 19. The dealer's card's chance changes to 16/49, since two non- 10 cards were removed.

The Monty hall problem is a basic version of calculating odds. The math gets a lot tougher later on, but odds are the first step to counting cards, hence the movie plug.

[jbaldwin343]

Thanks, I understand your point now and how he might have been mistaken, however he did explain variable change very well.

[redazure]

I agree with theberengersniper. KNOWS = 100% so changing a variable into a constant affects the rest of the variables.

I find the best way to show this would be, instead of with 3 cards, with an entire deck. Have them try to randomly get the ace of hearts, then remove 50 cards that aren't and ask if they wana switch. OF course you do! The chances you hit it right of the bat are so low, you'll win a car almost every time!

[theberengersniper]

I find it easier to understand when you remember that the host KNOWS where the car is. Once you've picked your door it's out of the equation. That only leaves 2 doors for the host to choose from. Of course he can't reveal the door with the car behind it, so the very fact that he avoided a particular door is a visual indication of an increase in probability. Maybe that's horribly explained, but it is easier if you mull over the idea that the presenter KNOWS where the car is.

[telecoustic]

Yes, the host must know where the car is, or the whole thing will not work. (host opens door with a goat on purpose; :15-:30) Maybe I did not explain it well enough; but your logic is correct!

[MediaRevolucion]

It made a bit more sense now oh and btw i love you voice... Not in a gay way... Honestly =P

[telecoustic]

Thank You! That's very nice of you to say. I found a better video for the Monty Hall Problem, It's better than mine; more to the point. It's the first video under "Related Videos" by niansenx. Thanks again for the kind words!

[MediaRevolucion]

NOOO! I Watched that and Oh My God his voice.... ARGH! He... Must... Die! So friggin annoying

[aniln]

poor bugger who gets the car first ;)....for him that 33% would feel like a 100%

[telecoustic]

lol Yes, I'm sure that's true!