# Boards

## You're on a game show.

The host places a prize in one of three boxes. The other two boxes are empty. He asks you to choose one of the boxes. After you've made your choice, the host opens one of the other two boxes, revealing it to be empty. He then gives you the option to stick with your original choice or switch to the other unopened box.

Is it better to stick or switch?

### riddle/puzzle

mind game I don't know ahhh.

### i know that the answer is switch

but I can't remember why :-/

### It makes no difference surely?

Theres still a 50/50 chance that you'll pick your box.

or is this some sort of riddle?### Not really a riddle.

There's no trick, it's a matter of probability.

### If you've just watched him put the prize in the box, you'd know which one.

So stick to your original choice.

### In that case it makes zero difference.

The chances of it being in any box are equal.

There may be some skewed statistical way of measuring the chances of your original choice being correct, but I don't know it if there is and it wouldn't be any kind of guarantee in the slightest.

### ^ this.

it has to do with the fact the game show host picked one of the other two boxes. The chance your box holds the prize is a 1/3, the chance the other box holds the prize is 2/3.

### You switch

Imagine if there were 100 boxes, and you pick one, then he opens 98 of the other boxes and they're all empty, and he gives you the chance to switch... You obviously switch.

### This is the example I used to explain it to some people yewsterday.

Fucking morons still said they'd stick.

### Idiots!

More faith in their instincts than narrow statistical margins!

### I can't get my head around this

and it's really frustrating me.

### There's a 1/3 chance you picked the right box

and a 2/3 chance you picked one of the wrong boxes. Since it's more likely that you picked one of the wrong boxes, you switch.

### Same.

It makes no sense.

There is an equal chance that the prize could be in any of the three boxes.

This statistical difference seems totally irrelevant to me.### Damn you mathematicians

but yeah, I got this too. Thank god for theory of knowledge.

### it really isn't irrelevant.

Without the factor of the gameshow host, you would have a point. If you don't believe in statistics, consider that the gameshow host HAD to pick an empty box to show you. The case with 100 boxes illustrates the point well.

### I understand that is has to work

and that shows it clearly^

My brain just either clicks straight away, or i never seemed to get my head around it. This one's the latter, even though it is plainly obvious thanks to that explanation.

### the picking is irrelevant

once he's opened a box with nothing in it it's an independent factor.

### unless the host knows

which apparently he does

### It makes it clearer that it's hard to understand

and even when acknowledging the answer many people don't believe it.

'counter-intuitive'

## is this a riddle or something?