What would you do?

[lbsf1]

Yeah the one you have is 1/3 and the other is 1/2.

 

[AlexGTV]

I hope I can shed a light by saying this case is like a closed system where the host has a 100% probability of being right and the player has 33% of being right. By exposing a door which now is 0% probable of being a car, the host transmits that information to the player who can now work out his odds.

Of course for a single try the choice to switch would be trivial but, according to the law of large numbers, if the player plays numerous times he will gain profit.

Yeah the one you have is 1/3 and the other is 2/3.

fixed.

 

[Minty]

Depends...what if I want the Goat?

 

[pampsu]

As I can eventually only pick one of the doors it gives no benefit changing my mind.

 

[Famine]

It has everything to do with poker and probability. Poker just has waaay more variables.

Yes. This doesn't have any.

You have 5,000 doors. You take away 4,998. There's a 50/50 chance of it being behind the first door.

I note you haven't made your guess yet. There's a month's Premium behind the right number for you to give to anyone of your choice. Yes, I already wrote the correct number down and took a screenshot.

 

[Villain]

My brain just exploded Mr. Famine.



There is still a 50/50 chance, it's the past information that is the dealbreaker.

My guess is 2

 

[lbsf1]

My guess is 452, and can you save the premium untill this one ends?

 

[AlexGTV]

I did an experiment in Excel with 100 random numbers (1 or 2), "1" meant Stick and "2" standed for Switch. Thus, for picking the doors at random after the reveal I had 58% success.

So the random/doesn't matter method ranks 2nd after the Stick and before the Switch one.

EDIT: The above applies on the game TB posted above in post #22.

 

[Famine]

You misunderstand the problem - you need three fields, for initial guess, winning door and stick/switch, as I detailed in an earlier post.

My brain just exploded Mr. Famine.



There is still a 50/50 chance, it's the past information that is the dealbreaker.

My guess is 2

The "past information" is what makes it a dependent field and not an independent one! Coins retain no information. Each coin toss is an independent event. Each toss is 50/50. This is a dependent event and the larger the field the more likely it is that sticking will make you lose.


Removing 4,998 wrong numbers, your options are now 2 or 2,983.

There is a 1 in 5,000 chance that 2 is correct and you should stick. There is a 4,999 in 5,000 chance that 2,983 is correct and you should change.

My guess is 452, and can you save the premium untill this one ends?

Removing 4,998 wrong ones, your options are now 452 or 3,441.

There is a 1 in 5,000 chance that 452 is correct and you should stick. There is a 4,999 in 5,000 chance that 3,441 is correct and you should change.


I am willing to bet my own money that, with a field of 1 to 5,000, I can generate a random number and always end up with you having to change to get the number right - because the odds of you guessing the right number and sticking are literally thousands to one against. 5,000 to 1 against in fact - 0.02%

In the interim, has anyone who doubts the maths actually done the Excel experiment I suggested to prove it to themselves?

 

[Lucas]

I switch. When I originally chose, I had a 1/3 of picking the car. That is, I had 2/3 chances of picking a goat. It is more probable to pick a goat in the first place than to pick a car. In other words, it is more likely that, if I stay with my choice, I will get a goat.

Asuming what I just said is correct (anyone mind to verify with a simple yes or no?), I finally understand this problem.

EDIT:

I am willing to bet my own money that, with a field of 1 to 5,000, I can generate a random number and always end up with you having to change to get the number right - because the odds of you guessing the right number and sticking are literally thousands to one against. 5,000 to 1 against in fact - 0.02%

And I think you would lose, Famine, due to the fact that it is not impossible, just very, very unlikely.

 

[Sting]

I'd have the courage of my convictions (if thats the correct way of putting it) and just stick with my original answer. At best I'll have a free car, and at worst I'll have a goat I could sell on to a farmer.

Thus I still leave with something after coming into the show with nothing if you get my drift.

 

[AlexGTV]

You misunderstand the problem - you need three fields, for initial guess, winning door and stick/switch, as I detailed in an earlier post.

I edited my post, I forgot to mention I applied that on the game TB posted. Pretty interesting don't you think?

So to recap, selecting to pick randomly after the reveal is a better strategy than staying with your first pick always, and a worse one than switching.

 

[Villain]

Yeah, I get it now. You made a believer out of me. Thanks for your patience. Once I sat down with the bigger numbers in my head, it was "duh!"

So how's my guess? I have two worthy GTPers on my mind that'd do fine with a Premo stint. Maybe I should think up a third, then eliminate one, and the. choose again. That way I'd know I picked the right member.

 

[Famine]

And I think you would lose, Famine, due to the fact that it is not impossible, just very, very unlikely.

Eventually I would. On average, once every thousand goes. I can live with buying a month's Premium once every thousand guesses.

 

[Stevisiov]

Once I sat down with the bigger numbers in my head, it was "duh!"

Indeed, increasing the number of doors makes this seeming paradox much easier visualise. It just goes to show what a poor perception of probability we often have.

It also goes to show, that we can be completely convinced that our logic is correct, and yet it turns out we were missing the true picture all along.

 

[Famine]

The big question is... what would happen if you put the doors on a treadmill?

 

[Stevisiov]

What would happen if you put a plane on a treadmill and the speed of th.......

....Okay, perhaps not a good idea to open that can of worms.

It's another good example of how the most intuitive answer, of which people can be absolutely convinced of, is completely wrong.

 

[AlexGTV]

of which people can be absolutely convinced of, is completely wrong.

Well, most people answer that it won't make a difference (apparently GTPers are smart ) so they at least avoid the pitfall of standing by their first choice.

 

[Moglet]

Give this a try.

I just got 2 out of 10 right by staying with my first door and 6 out of 10 by switching, very close to the expected results.

I got the complete opposite Just my luck

 

[Villain]

I have 24 treadmills at my disposal. Does anyone have extra doors? (I work at gym )

 

[AlexGTV]

It's interesting how the information of one door being a goat (0% prob.) is as important as your initial choice, in that you know you have (and where) to switch. If you arrive at the show after the one goat has been exposed, it makes no difference what you will choose, and it is indeed a 50/50.

The other remark I have is what "doesn't matter" means. It can either mean that we probably will stay with the initial choice (do our disadvantage), or that we will roll a dice to select between the remaining 2 doors. In the last case, I wonder if we have a feeling that the exposing of a goat changed the equilibrium or else we should stick with the first choice, in the same sense as sticking with the same roulette number... even if Ι have an itching on my hand.

So, it is fascinating how a really smart player can arrive at the right "Switch" conclusion with this rational:

1) I have a 1/3 chance with my first choice
2) Now the choices are two AND a wrong one is out (GOOD observation)
3) I have a 1/3 chance still sticking with my first choice, but 1/2 if I roll a dice
4) ...Wait, if my chances are better off with rolling a dice, maybe they are better with the other door
5) Therefore, I go with the other door! 👍

 

[Keef]

What is the math behind the 2/3 odds? With three doors you have a 1/3 chance, but with 2 doors you have a 50/50 chance...either there is a goat or there is a car. I see no 2/3 here.

Even when things have positive mathematical odds, I usually stick to the 50/50 rule I don't end up disappointed. Even if there is a 90% chance of rain that day, the fact is that it will either rain or it won't, and therefore the odds are 50/50.

 

[AlexGTV]

The math behind the 2/3 odds is in those pictures.

 

[Stevisiov]

What is the math behind the 2/3 odds? With three doors you have a 1/3 chance, but with 2 doors you have a 50/50 chance...either there is a goat or there is a car. I see no 2/3 here.

Even when things have positive mathematical odds, I usually stick to the 50/50 rule I don't end up disappointed. Even if there is a 90% chance of rain that day, the fact is that it will either rain or it won't, and therefore the odds are 50/50.

If I have a 1 in 15 million chance of winning the lottery, I can Either win, or I can loose.

Would You say my odds are 50/50?

[edit] For those struggling, wiki actually has a few good explanations of this problem.

 

[sems4arsenal]

So the reason you are not left With a 50-50 chance is that the door with the goat behind is still there (counted as a Probability)I tried this at school today ,some of my friends got it right .You learn something new everyday .