A few months ago I tried a similar process to this with my dad who’s pretty smart but like most does not know the Monty Hall Problem.
I put three cards down, showed him one ace which is the winner, shuffled the cards so that only I knew where the ace was and told him to pick a card, after which I would flip over one of the other loser cards. We went through it and he said that it didn’t matter whether he switched or not, 50-50. Luckily he did not pick the ace the first time so there was a bit of a uh huh moment.
I repeated the process except using 10 total cards. As I was revealing the loser cards one by one he started to understand that his chances were improving. But he still thought that at the end it’s a 50-50 between the card he chose and the remaining card although his resolve was wavering at that point.
I hinted, “What was your chance of selecting the ace the first time”, he said, “1 out of 10″, and then I gave him the last hint he needed saying, “And if you selected a loser what is that other card there?”
A few seconds later it clicked for him and he understood his odds were 9⁄10 to switch with the 10 cards and 2⁄3 to switch with the 2 cards.
He ended up giving me additional insight when he asked what would happen if I didn’t know which card was the ace, I flipped cards at random, and we discarded all the worldlines where I flipped over an ace. We worked on that situation for a while and discovered that the choice to switch at the end really is a 50-50. I did not expect that.
A few months ago I tried a similar process to this with my dad who’s pretty smart but like most does not know the Monty Hall Problem.
I put three cards down, showed him one ace which is the winner, shuffled the cards so that only I knew where the ace was and told him to pick a card, after which I would flip over one of the other loser cards. We went through it and he said that it didn’t matter whether he switched or not, 50-50. Luckily he did not pick the ace the first time so there was a bit of a uh huh moment.
I repeated the process except using 10 total cards. As I was revealing the loser cards one by one he started to understand that his chances were improving. But he still thought that at the end it’s a 50-50 between the card he chose and the remaining card although his resolve was wavering at that point.
I hinted, “What was your chance of selecting the ace the first time”, he said, “1 out of 10″, and then I gave him the last hint he needed saying, “And if you selected a loser what is that other card there?”
A few seconds later it clicked for him and he understood his odds were 9⁄10 to switch with the 10 cards and 2⁄3 to switch with the 2 cards.
He ended up giving me additional insight when he asked what would happen if I didn’t know which card was the ace, I flipped cards at random, and we discarded all the worldlines where I flipped over an ace. We worked on that situation for a while and discovered that the choice to switch at the end really is a 50-50. I did not expect that.