Three Doors Two Goats

[Milk]

Here's something which maybe many of you will have already heard. I read it in the excellent "the Curious Incident of a Dog in the Nighttime". It's maybe something which goes down better in a Pub, but we'll try it here anyway.

Theoretical gameshow.

The contestant is asked to choose between one of three doors.

Behind one is the prize beyond all wildest dreams, behind the other two are gnarly old goats.

The contestant chooses a door but is not allowed to open it. Instead the host opens a different door revealing a goat. The host then asks the contestant if they want to change their choice of door.

What should the contestant do? (assuming they don't have a goat fetish)

[toecutter]

Put a empty glass against a door to listen for any goat noises?

[Milk]

Unfortunately they are very very quiet goats. The doors also have the latest generation of goat shielding installed (ISeeNoGoat^tm)

All the contestant can do is stick with the original choice or choose to change.

[toecutter]

thanks for clarifying, so i cannot dial a friend either, mmm

[Milk]

No afraid not, but to help with your decision, what is the probability going home with a goat if you stick, and what is the probability of going home with a goat if you change?

[toecutter]

50/50?

[Milk]

Wrong answer.

But in fairness the question is deliberately set up for you to come up with that conclusion.

[toecutter]

I was thinking to investigate the game called:

Two-up - a traditional Australian gambling game.

I believe there is some equation that predicts the chance of winning in a similar environment as yours.

but i took the moron route and just speculated

[jemidiah]

I believe there is some equation that predicts the chance of winning in a similar environment as yours

Yes--a computer simulation run for many trials approximates the analytic solution arbitrarily well with vanishingly small expected variance . If you're curious, this is the Monty Hall problem, IIRC. I really liked it when I first saw it.