Stick or Switch

[Marco]

I don’t often go into the games room, but I thought I’d drop in a wee puzzle since it’s Friday, I’m feeling good (with a little help from fluoxetine), and I’m on some annual leave as from today

OK so you’ve just made it to the final of this TV quiz show and here you are facing three curtains behind which one of them is a shiny, new sports car. If you pick the right curtain, it’s yours. The quiz master asks you to choose a curtain. Your heart’s pounding, you make your choice - ‘the green curtain’, you manage to stutter. The compere smiles, and then he theatrically pulls back the yellow curtain to reveal there’s nothing behind it. You’re now down to two curtains - your choice the green one, and the red curtain. Your host then says ‘OK, you know the script,’ then beckoning the audience to join him they chant ‘Stick or Switch, Stick or Switch….’. What do you decide? Stick with the green curtain or switch to the red?

[Jan135]

I would choose green! Green is my favourite colour and some sports car won't change it!

Also, you will tell me if it is a right choice, right?

[Sisyphus]

Switch, always. (Just call me Monty )

[biscuits]

Switch!

Red is my favourite colour!

[Sisyphus]

^ in that case wouldn't you have chosen the red curtain first?

If you did choose the red curtain first, would you then switch to another colour? What if I told you the car was red?

[Sisyphus]

^^^^ If the car was just the right shade of green, would you switch then?

[biscuits]

^^ hey, Marco made up the scenario in which I chose green first

I would have picked red first, yes. And no I wouldn't have switched. The car being red would be perfect. My current car is red.

[Sisyphus]

^ I now feel bad making you change to stick.

[biscuits]

^ you'll have to smack your own bottom.

[Marco]

Don’t let the colours of the curtains get in the way of your decision lol. Let’s say if you choose the right curtain, you get to choose the colour of the car. However, there is a little bit of logic you can apply here, which might improve your chances of making the right choice. I’ll say no more just now in case you want to give it some more thought.

[biscuits]

Oh

Pick the curtain on the right?

[Marco]

^ Do you mean the curtain on the right because, well, it’s the right one? Haha……but, nope.

[Marco]

If you chose to switch, you’d probably double your chances of getting the car

The first thing you’d have to assume is that the game show host knows which curtain the car is behind. He’s highly unlikely to risk ruining the show by pulling back a curtain only to reveal the car and deprive his audience of the drama of a ‘stick or switch’ finale. So with that in mind, the chances of picking the right curtain from three curtains is 1 in 3, which means there’s a 2 in 3 chance the car is behind one of the curtains you didn’t pick. So far so good? When the host (knowingly) pulls back the empty yellow curtain, the chances of the car being behind the curtain he’s left (the red curtain) has now become 2 in 3, while your choice remains a 1 in 3 chance of being right, i.e. counterintuitively, it’s not down to a 50:50 chance when you’re left with these two curtains. Switching to the other curtain very probably will double your chances.

[biscuits]

^

Originally Posted by biscuits

Switch!

Red is my favourite colour!

DUDE, WHERE'S MY CAR?

[Marco]

^ Haha, but of course I'm not guaranteeing you'd get that red sports car by switching, just trying to improve your chances...C'mon, give me a break, I'm doing the best I can!

[Sisyphus]

Now the cat is out of the bag, this one actually has a name. It is the Monty Hall Problem.

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

[Marco]

^I just remember coming across a puzzle like this years ago. I didn’t realise it had a name and was even on Wikipedia lol.