program for Monty Hall puzzle

Hi all,

in order to convince a friend of mine, who is one of the remaining sceptical people who refuse to accept the right solution and mathematical proof (he does not understand) i wrote a little program which simulates 10000 times the two possible strategies. It shows that you double your chances to win, when you choose another door.

You can download from: http://www.geocities.com/ziege71/ Das_Ziegenproblem.html

Give it a try. At least you must see the perfect goat.

Bye,

Usenet is not the World Wide Web, but a forum for plain ASCII text.

What IS the monty hall puzzle???

Rick

No, I reach the same conclusion.

Ma thinks that if her son sticks he will win with probability 1/3, and so should switch to raise this to 2/3.

A general form of the puzzle is here:
http://xraysgi.ims.uconn.edu/rpa-output/decision/ monty.hall.p

But it's necessary for you to be told in addition that (1) Monty Hall knows where the big prize is, and (2) he always opens a door that he knows contains nothing. Without those conditions the only correct answer is 'it depends', and the puzzle is relatively dull and uninteresting.

The answer is here:

Doesn't that 'conditional probability' concept seem a bit awkward to you? It sure does to me. Probability is an absolute state of nature and is never conditional upon what someone happens to know or believe. Why speak of probability at all in a case like this when you can instead refer to each individual's confidence instead? Since different people can have different levels of confidence about something, based on their differing knowledge, all of that 'probability for you vs. probability for me' awkwardness suddenly disappears.

I just tossed a coin. It's sitting on my desk now.

What is the probability that it shows 'tails'?

I *know* the answer, because I can see the coin. The best you can do is guess between two equally likely outcomes.

Not really. It's just a different way of saying the same thing.

That's a good example. There is of course no probability involved here at all. Probability is a concept that only concerns events that are to take place in the future, but you flipped that coin in the past. The coin either shows tails or it doesn't.

Exactly! And since we are discussing an uncertain state of nature, the issue here is not a property of the coin but a property of ourselves. Your confidence that the coin shows tails is either 0% or 100%, while my confidence is 50%.

Wrong. Here's an experiment you can try at home. You need two other people - a guy who doesn't understand probability, and a guy who does.

Take an ordinary six-sided die. Score it as follows:

1: LOSE 2: WIN $1 3: WIN $2 4: WIN $4 5: WIN $8 6: WIN $16

The game costs $6 to play.

Put the die in a cup, toss it around a bit, and then invert the cup. The die is hidden, but stationary. The event has taken place in the past. No probability involved, according to you.

Now thumb through your dollar wad with a professional air, ask your two friends to place bets, and watch the probability-aware guy decline with a polite smile.

Right.

Which? You don't know, obviously. The best you can do is guess. There are two possibilities. How do you weigh them? That's what probability is all about.

No, it's a property of reality, a reality about which we (meaning, on this occasion, everyone except me!) have incomplete information.

Rather, my confidence that I know what the coin shows is 100%. (It's still here on my desk, by the way - so, for a sufficient bribe, I can *tell* you which way it landed.)

So is everyone else's (except mine, of course). This is not, then, a property of ourselves, but of an external reality which we all recognise, even if we can't agree on the best way to describe it. If it *were* a property of ourselves, we would not have agreed so quickly on the probability being 50%.

It's surprising to see you resort to a personal attack like that. Since I seem to have struck a sore spot with you, let's just conclude that your definition of the word 'probability' is very different from mine, as your use of the cryptic phrase 'I believe with high probability' indicates.

That's not a cryptic phrase. For some people, including myself and, apparently, David Karr, it is normal speech. I means the same as 'I think it very probable', or 'I think it very likely'.