Which box should you open?

Open the other box. I have no idea why – I just remember my old maths teacher once asking us an identical question.

You should always switch ;) A lovely friend of mine is a math major, though she told this riddle using goats and not cabbage.

Curious. There is a one in three chance of the diamond being in any particular box. Why should you imagine that changing your mind will improve your chances?

I like cabbage and diamonds… so I would open the one on the left

It’s the Monty Hall paradox: you begin with a one in three chance. When one of the boxes is opened and proven to be nothing but cabbage, one naturally thinks, “Well, there are only two left – I have a fifty/fifty shot at being correct; I’ll just stick with my box.” But if they were to switch, they would actually have a ⅔ chance.

Of course, that sucks the fun out of riddles, so, um… “When is a door not a door?”

@flutherother, you’re in good company: the great Hungarian mathematician Paul Erdős also got it wrong, and was said to be very difficult to convince what the right answer is. See the Wikipedia article that @muppetish links to.

The catch in logic is that the emcee knows which door has the prize—he has more information than you do. His opening a door is not an independent event.

I would’ve stayed with my first choice being it wouldn’t matter to me if I was never told I could keep it.
If I am given the choice of choosing 2 out of 3 than my chances are 66 % but, if I have to remain with just the one than my chances go down to 33 percent chance of getting it right. I would think that after the extra cabbage is revealed and out of the equation than I drop from 66% to 50% or what is remaining unrevealed.

I would sniff all 3 boxes. ;-)

@muppetish When it’s a jar.

@worriedguy Thank you for humouring me :) I love that riddle more than I probably should.

Do not switch, stick with it. They would be expecting you to switch.

@muppetish That is one of the first riddles I ever learned. I still think it when I see the “Door Ajar” message on my car dashboard display.