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Monte Carlo Theory and goats

Posted by TheFallen on October 16, 2004

This was referenced by someone in a post slightly lower down and is a neat term to describe the scientific truth that past events do not affect future probabilities - so if you've spun a coin 19 times and it's come down heads each time, there's still an exact 50/50 chance that it'll come down heads or tails on the 20th spin... presuming the coin's perfectly balanced and that it doesn't land on its edge.

This reminds me of the famous TV game show goats paradox, which I'll outline briefly for those who don't know it. You get to the final of a TV game show - there's just you left. You're presented with three closed doors by the host, who tells you that behid one of the doors is a brand new Ferrari, but behind the other two there are goats... so three doors, one sportscar and two goats. You are invited to pick a closed door, so you do. The host, who obviously knows in advance what's behind each door, then decides to open one of the two doors that you didn't select to reveal a goat - he does this every week. He then asks you whether you want to stick with the original door you picked, or whether you want to swap to the remaining closed door. The simple question is - if you want to maximise your chances of getting the Ferrari, would it be best to stick with your original choice, should you swap, or does it make no difference at all?

(Apologies if you've all heard this before).