for the gamblers amongst you

[Roger Kettle]

I know I'm going to regret this but why?

[Vulture]

I know I'm going to regret this but why?

You had to do it, didn't you! Roger, when will you learn to leave things alone? And to ask the 'why' question of Mince.....  Well, all I can say is, YOU asked for it!

[Mince]

When you first choose your drink, you have a 1 in 3 chance of living and a 2 in 3 chance of dying.

Notice what happens when you switch drinks (choose the other drink).

If you have a non-poisoned drink and you switch, you end up with a poisoned drink (since the other two are both poisoned and so it does not matter which one the barman removes).

If you have a poisoned drink and you switch, you end up with a non-poisoned drink (since the other poisoned drink was removed by the barman).

Switching means changing either from poisoned to non-poisoned or from non-poisoned to poisoned.

So by switching, your 1 in 3 chance of living becomes a 1 in 3 chance of dying, and your 2 in 3 chance of dying becomes a 2 in 3 chance of living.

So by switching your initial 1 in 3 chance of living is doubled to a 2 in 3 chance of living.

[Roger Kettle]

That's false logic. It's a one in three chance however you go about it. You can add all sorts of nonsense about choices and the barman's intervention but, in the end, you have to pick one glass from three.

[Mince]

That's what everyone thinks, but intuition lets you down with this one.

Here is a web page that allows you to play an identical game (but with doors, donkeys and prize money). Try it first without switching. Then try it with switching.

http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html

[Roger Kettle]

There is absolutely nothing amazing about this. You have to choose one drink from three which, obviously, gives you a one in three chance of selecting the non-poisonous option and this is the way the question is phrased. In actual fact, you're being given TWO choices which, also obviously, alters the odds. In other words, you're first being asked to choose one from three and then being asked to choose one from two. Of course that reduces the odds! The chances of you selecting the non-poisonous drink are two to one against. Full stop.

[Mince]

So do you agree that you increase your chances by choosing the other drink?

[madjock]

In 36 games when I didn't switch, I won 18 times. In the 36 games when I did switch, I won 18 times!  Ok what does that mean then?

[Mince]

You were lucky. Try again.

[Tarquin Thunderthighs lll]

I'm back. 

[The Peepmaster]

It's interesting to observe Mince being a pillock all the way from Manila.

[Malc]

I hate arriving at these conundrums late. The remaining glass on the bar does not contain poison, and we know this because there are now only two glasses on the bar and the barman told us:

"The one that I remove has poison in it."

He did NOT say "one of the glasses I remove has poison in it"

Therefore the one which remains on the bar does not contain poison.

[madjock]

Yes but at the begining there was two glasses with poison in them.  And as you have chosen one of them, it might have poison in it aswell.

[Diamond Lil]

This is all making me feel like Madjock's avatar

[The Peepmaster]

Yes but at the begining there was two glasses with poison in them.  And as you have chosen one of them, it might have poison in it aswell.

In fact, knowing Mince, they might all have poison in them, but, what with him being an unscrupulous, conniving, individual....