Does It Matter?

#1 09-19-2002, 07:36 PM

2 cards red and 1 card black, are face down on a table. Let's say this nice man tells you that if you choose black, you win $100.
So you point one card. Let's say the card in the middle. The man gives you a favor and turn up one red card from the other two cards that you didn't choose. Now do you want to stick with the cards that you chose in the first place (the middle one,) or it doesn't matter?

Soh

p.s. no trick question, rather logic.

Ed Miller · #2 09-19-2002, 07:40 PM

I love this question.. so much so that I ask a variant of it as an interview question.

lorinda · #3 09-19-2002, 08:34 PM

Do we know that the guy always points to one of the cards for this question, or is this the only time we have ever seen it done?
If it was a one off, and I knew he knew i was a mathmatician then I would stay with the same card, because I would assume he was misleading me to think that I should switch with a 67% chance.
However, if I have seen the guy doing this many times then I would switch....see my post "Game Show" on Internet gambling a few weeks back [img]/forums/images/icons/laugh.gif[/img]

BruceZ · #4 09-19-2002, 08:35 PM

Yes of course switch. Now, when can I start, how much will I make, and what will I do?

#5 09-20-2002, 05:50 PM

Chances of picking the correct card start out a P=.33

So chances are that .66 that the correct card is 1 of the 2 that you haven't picked. By showing you a dead card, he is increasing your chances by switching.

irchans · #6 09-21-2002, 09:22 AM

How about this variation:

2 cards red and 1 card black are face down on a table. Let's say this nice man tells you that if you choose black, you win $100. ASSUME HE KNOWS NOTHING ABOUT LOCATION OF THE BLACK CARD. So you point to one card. Let's say the card in the middle. The man gives you a favor and RANDOMLY CHOOSES A CARD FROM THE TWO REMAINING. HE TURNS IT UP AND IT IS RED. Now, do you want to stick with the card that you chose in the first place (the middle one,) or it doesn't matter?

#7 09-21-2002, 11:15 AM

change

#8 09-22-2002, 04:39 AM

if he doesn't know if the card is red or black, it doesn't matter if you switch or not.

if he does know, then you switch.

irchans · #9 09-22-2002, 10:34 AM

sdplayerb said:
>if he doesn't know if the card is red or black, it doesn't
>matter if you switch or not.
>
>if he does know, then you switch.

I believe that sdplayerb's conclusion is correct. What reasoning could support this conclusion?

baggins · #10 09-23-2002, 05:16 AM

if he doesn't know, then he could just as easily have shown you a black card. showing you a red card means that now you both know that there is one red and one black left, but neither knows where. whats the point in switching then?

if he knows, however, then of course he's going to show you the red one. every time. and then give you the option to take the worst of it, instead of giving you even money.