A teaser to see how you think about equity!

TheEdge949

Ok so here's the scenario.

You are the final contestant in a game show. You have to pick from a choice of 3 envelopes marked A, B and C. One envelope contains a cheque for £50,000, the other two contain nothing.

You choose envelope B.

The gameshow host knows the location of the winning envelope and before accepting your answer, reveals that envelope A is empty.

With this knowledge do you stick with B or change your answer to C ?

stokefc

Stick to your first envelope
In Sunday's forum comp i chose arsenal to win by 2 goals while typing i hit 3 by mistake but chose not to edit, mistake, because if I did edit i probably would have won a prize

Essexphil

TheEdge949 said:

Ok so here's the scenario.

You are the final contestant in a game show. You have to pick from a choice of 3 envelopes marked A, B and C. One envelope contains a cheque for £50,000, the other two contain nothing.

You choose envelope B.

The gameshow host knows the location of the winning envelope and before accepting your answer, reveals that envelope A is empty.

With this knowledge do you stick with B or change your answer to C ?

I always struggle with these.

Here is the bit I do know. If the host knows it is B, he was free to choose to reveal either A or C. Whereas, if the host knows it is B, then his only option for the reveal is A.

So I think it is better to swap to C.

Enut

Essexphil said:

TheEdge949 said:

Ok so here's the scenario.

You are the final contestant in a game show. You have to pick from a choice of 3 envelopes marked A, B and C. One envelope contains a cheque for £50,000, the other two contain nothing.

You choose envelope B.

The gameshow host knows the location of the winning envelope and before accepting your answer, reveals that envelope A is empty.

With this knowledge do you stick with B or change your answer to C ?

I always struggle with these.

Here is the bit I do know. If the host knows it is B, he was free to choose to reveal either A or C. Whereas, if the host knows it is C, then his only option for the reveal is A.

So I think it is better to swap to C.

Fixed your post (I think).

Essexphil

Enut said:

Essexphil said:

TheEdge949 said:

Ok so here's the scenario.

You are the final contestant in a game show. You have to pick from a choice of 3 envelopes marked A, B and C. One envelope contains a cheque for £50,000, the other two contain nothing.

You choose envelope B.

The gameshow host knows the location of the winning envelope and before accepting your answer, reveals that envelope A is empty.

With this knowledge do you stick with B or change your answer to C ?

I always struggle with these.

Here is the bit I do know. If the host knows it is B, he was free to choose to reveal either A or C. Whereas, if the host knows it is C, then his only option for the reveal is A.

So I think it is better to swap to C.

Fixed your post (I think).

Correct-thanks

green_beer

https://m.youtube.com/watch?v=iBdjqtR2iK4

dragon1964

You swap envelopes.
You had a 1 in 3 chance of picking the right envelope originally.
Therefore 2 in 3 chance of money being in one of the others.
The host was always going to open an empty one.
It doesn't change the original odds.
You are still only 1 in 3 chance you picked correctly, so 2 in 3 the money is in the other envelope.
Swapping doubles your chances of winning.


Edit.
I spent too long typing it. I should have just let Kevin Spacey explain it.

kapowblamz

Trick question or not?

B and C have same EV so it doesn't matter which you pick.

tai-gar

Mathematically correct to change just like poker.
However, if you are there and can get some sort of tell from the presenter whether he wants you to win or not then you might stick with your gut.
Just like poker?

Allan23

Always change.

Always changing guarantees a win 2/3 times, never changing guarantees a win 1/3 times

mumsie

Its a swap for me.

stokefc

Aha ever likely I never win owt

Humphrey43

someone has watched 21 haha

Enut

Interesting dilemma, but it's not quite carrot in a box is it?

For those that haven't seen it this is comedy gold, RIP Sean Lock.

https://youtu.be/8nnni9JvBi4

TheEdge949

Ok just googled it and now I get the Kevin Spacey reference that @dragon1964 alluded to.

Sorry haven't seen the film but I'm assuming from the title it has something to do with a blackjack system.

Is it worth a watch?

dragon1964

TheEdge949 said:

Ok just googled it and now I get the Kevin Spacey reference that @dragon1964 alluded to.

Sorry haven't seen the film but I'm assuming from the title it has something to do with a blackjack system.

Is it worth a watch?

@TheEdge949 .
It's the video clip in the post just above mine.

TheEdge949

Really wasn't aware of the example being used in a film. I have now watched 21 by the way and well meh!

Ok well as most of you correctly said the answer is to change your pick to C as you pick up an extra 33.333%.

Or do you ?

Would there be any merit given to the assumption that actually its only really an extra 16.666% as with one option removed from play your original pick is now 50% .

mumsie

It is a good puzzle.

Compare 3 horse races to a 2 horse races.

Over time, you'll pick more winners in the 2 horse race, thats why swapping is best.

The puzzle turns the 3 horse race into a 2 horse race.

I think.

Or, imagine you have 1,000 envelopes.

One has the prize, the rest are empty, when you chose one, the host shows you 998 empty envelopes.

Do you stick with your first choice or take the unopened one?

cabbaz

You're supposed to change envelopes, but I still can't get my head around it lol.

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

kapowblamz

TheEdge949 said:

The gameshow host knows the location of the winning envelope and before accepting your answer, reveals that envelope A is empty.

With this knowledge do you stick with B or change your answer to C ?

Because the host reveals the envelope BEFORE the contestant has made their pick then the equity of the 2 boxes is exactly 50%. That one line in bold makes this situation very different to the Monty Hall problem in which the host reveals an envelope AFTER the contestant has made their choice.

EDIT: Turns out the contestant had made their pick and that bolded line is preempting the swap offer. Fail.