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.

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

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.