[Brain Teaser] Three doors

[matt4054]

If you already know about the original version of this problem please don't spoil the answer too soon, let's keep it fun, thanks



Suppose that you're given the choice of three closed doors. Behind one door is 1BTC, behind the others, 1 satoshi. You pick a door, say #1, but you can't open it yet. The game master, who knows what's behind the closed doors, opens another door, say #2, which has 1 satoshi.

Then the game master asks you whether you want to pick door #3 instead of door #1.

Is it to your advantage to switch your choice?

[b!z]

Yes, you should switch.

[ndnh]

Switch to get 2x advantage.

Were the funds escrowed? Was it a physical bitcoin?

Revenge for asking stupid questions..

[protokol]

Yes, you should switch.

+1

It's a weird one, most people think you should hodl but switching is mathematically the best option.

[ndnh]

Yes, you should switch.

+1

It's a weird one, most people think you should hodl but switching is mathematically the best option.

How is it weird?

and Most people think thinks hodling and switching has the same odds, and there is no advantage is switching.

[protokol]

Yes, you should switch.

+1

It's a weird one, most people think you should hodl but switching is mathematically the best option.

How is it weird?

and Most people think thinks hodling and switching has the same odds, and there is no advantage is switching.

  It's weird because it's counter-intuitive. I guess you're right in saying that most people think that it doesn't matter (not that hodling is better haha), but you can prove with a bit of simple maths that you increase your chances significantly if you switch. I won't put details, that would spoil the fun!

[ndnh]

  It's weird because it's counter-intuitive. I guess you're right in saying that most people think that it doesn't matter (not that hodling is better haha), but you can prove with a bit of simple maths that you increase your chances significantly if you switch. I won't put details, that would spoil the fun!

I know the last part, bud. Pretty everyone knows that around here.

Switch to get 2x advantage.

Were the funds escrowed? Was it a physical bitcoin?

Revenge for asking stupid questions..

[matt4054]

Well, I guess it's a bit too much of a classic for those willing to click on brain teasers... gg

Were the funds escrowed? Was it a physical bitcoin?

Revenge for asking stupid questions..

Yes, rest assured, funds were escrowed by Monty Hall.

"Stupidity is a talent for misconception." -- Edgar Allan Poe

[Gleb Gamow]

I voted yes sans reading the first word in the OP, for I knew what this thread was about. I wasn't disappointed.

[ndnh]

Well, I guess it's a bit too much of a classic for those willing to click on brain teasers... gg

Were the funds escrowed? Was it a physical bitcoin?

Revenge for asking stupid questions..

Yes, rest assured, funds were escrowed by Monty Hall.

"Stupidity is a talent for misconception." -- Edgar Allan Poe

Was the transaction fee covered??

"Stupidity is a talent." -- Sam Gamgee

\o/

[jmintuck]

I read the explanation on wikipedia a while back. Still doesn't feel right, and I will never have an intuitive understanding of it I suppose.
I think of it like dice at times , and its like saying that select a range between 1 and 100, between 1-33,34-67,68-100(dont worry about the differnce of 1, just consider it 1/3) . Now you select 1-33. Dice site owner checks seed to tell you its not 68-100. Then how does switching to 34-67 increase odds ?

[Bardman]

I read the explanation on wikipedia a while back. Still doesn't feel right, and I will never have an intuitive understanding of it I suppose.
I think of it like dice at times , and its like saying that select a range between 1 and 100, between 1-33,34-67,68-100(dont worry about the differnce of 1, just consider it 1/3) . Now you select 1-33. Dice site owner checks seed to tell you its not 68-100. Then how does switching to 34-67 increase odds ?

There is an example to make it easier: You have 3 doors, Red Yellow and Green.

In the case that the Bitcoin us behind the red door:
If you pick the red door switching would make you lose
If you pick the yellow door switching would make you win
If you pick the green door switching would make you win

Lose 1/3
Win 2/3

[ndnh]

I read the explanation on wikipedia a while back. Still doesn't feel right, and I will never have an intuitive understanding of it I suppose.
I think of it like dice at times , and its like saying that select a range between 1 and 100, between 1-33,34-67,68-100(dont worry about the differnce of 1, just consider it 1/3) . Now you select 1-33. Dice site owner checks seed to tell you its not 68-100. Then how does switching to 34-67 increase odds ?

Or take it like this. Really simple to understand.

What is the chance that you miraculously picked the correct door? It is 1/3

What is the remaining chance? 1-1/3= 2/3 !

That is 1:2. You should switch.

[AltcoinInvestor]

it's a 50/50 chance it really doesn't matter which one you choose.

[Bardman]

it's a 50/50 chance it really doesn't matter which one you choose.

Did you just come with that conclussion by yourself?? Seriously what kind of useless post is this? Switching the door gives you a 2/3 chance of winning not a 50% like did you even read the thread?

[ndnh]

it's a 50/50 chance it really doesn't matter which one you choose.

Did you just come with that conclussion by yourself?? Seriously what kind of useless post is this? Switching the door gives you a 2/3 chance of winning not a 50% like did you even read the thread?

The question he answered was deleted.

Thanks

[9000]

This is a great example of a counter-intuitive solution, the vast majority of people answer that there is no difference.

[hedgy73]

If you already know about the original version of this problem please don't spoil the answer too soon, let's keep it fun, thanks



Suppose that you're given the choice of three closed doors. Behind one door is 1BTC, behind the others, 1 satoshi. You pick a door, say #1, but you can't open it yet. The game master, who knows what's behind the closed doors, opens another door, say #2, which has 1 satoshi.

Then the game master asks you whether you want to pick door #3 instead of door #1.

Is it to your advantage to switch your choice?

Does the game master have to give you the chance to change your mind? Does he want the contestant to win or lose?

[matt4054]

Does the game master have to give you the chance to change your mind? Does he want the contestant to win or lose?

Yes he does. His intention is unknown and should be irrelevant.

[(oYo)]

My initial choice has a 33% chance of being right. (You could also say there's a 66% chance of choosing the wrong door.) That's a gimme, since there are initially 3 doors to choose from.

If one of the doors (which I didn't choose) is revealed to be a poor choice and subsequently removed from the equation, that leaves 2 doors to choose from, ergo there's a 50% chance now of choosing the right (or wrong) one.  Since both of the remaining doors now have an equal chance of being the right (or better) choice, this also means that my odds of having already chosen the right door just shot up from 33% to 50%. Another way of looking at it is that my odds of choosing the wrong door went down from 66% to 50%. Hence there's absolutely no advantage (or disadvantage) to switching to the other door.

This 'brain teaser' feels somewhat like that joke where the three guys get a rebate on their hotel room and you are misdirected to account for a missing dollar.