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 08-05-2002 08:04 AM

The Quizshow

Hi there...

Here is an old but good one. (please excuse my spelling and choice of words - english is not my first language)

You are the last person left in a quizshow. You now have the possibility to win a car. The quizmaster shows you 3 doors. Behind 1 of them, there is a car. Behind the other 2 there is nothing. He tells you to pick a door, and you do. The door remains closed. Now he says: "I'll help you - I'll show you a door with nothing behind. He opens 1 of the doors that you didn't pick. Now he says: "Would like to change your mind and pick the other closed door, or would you like the one you've picked in the first place?"

Now you have 3 options:

1) Change your mind, and pick the other door

2) Stick to the door you've picked first

3) It doesn't make any difference

Well - what's it gonna be (And why!)

Yours

Mik

 08-05-2002 08:33 AM

switch

I'll let other's elaborate.

 08-05-2002 12:37 PM

Re: switch

Ditto as to Bruces' response.

Jimbo

 08-05-2002 03:08 PM

Re: switch

Originally, was 2/3's chance of NOT being the door you selected... so it's 66.7% that it's behind the other door

 08-05-2002 07:24 PM

Re: The Quizshow

It doesn't make any difference.

They are going to show you a door with nothing behind it anyway, whether you pick the right one or not. The 33.3% chance that the door they opened will split evenly between the two doors remaining.

If in a three-handed no ante HE game all three of you are dealt AKs, preflop your chance of winning is proportional to the number of players in the hand. One of them folding doesn't suddenly give either one of you 2/3 of the equity.

 08-05-2002 09:19 PM

Re: The Quizshow

Ok Monte let's play. I'll switch doors and give you even money odds. Since you think I'm an 2-1 dog you should be eager to play.

 08-06-2002 03:19 PM

Re: The Quizshow

BruceZ is right. Here's how it works:

Let's say that you don't change your mind. The probability that you pick the door with the car behind is 1/3. So if you don't change your mind you will win the car 1 out of 3 times.

Now, let's say that you change your mind every time. The probability that you picked the door with the car behind is still 1/3. Let's say the car is behind door #1:

1) You pick door 1 (Quizmaster opens door 2 or 3)You switch = No car

2) You pick door 2 (Quizmaster opens door 3)You switch = Win the car

3) You pick door 3 (Quizmaster opens door 2) You switch = Win the car

The correct answer is to change your mind and switch. The strange thing is, that 4/5 people that you give this riddle to, will stick to their intuition and hang on to the door they picked first.

Has anyone got any ideas on how to use this at the pokertable? How about you BruceZ?

Yours

Mik

 08-06-2002 07:34 PM

Re: The Quizshow

There are many poker applications of Bayes' therorem which is what this is based on. Sklansky gave an example recently from jacks or better draw poker where the odds that your opponent has a set go from 2% to 10% once the player opens since you now know that he has jacks or better.

In fact, much of reading hands involves modifying the probabilities of what hands your opponent has based on additional information you gain on each round by the way he bets. You in turn attempt to keep your opponent from doing the same thing to you by making him miscalculate the probabilites of certain hands that you might hold. You do this either by playing in a way that changes the probability of the hand you are holding relative to other hands, or by sometimes playing hands in a way that is different from how you normally play them so that your opponent will miscalculate on future hands.

Revealing information which causes others to calculate whatever probabilities you want them to calculate is also used between nations in economic matters.

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