A Home Game-the Monty Hall Problem
What about playing a game? I need three cards
What about playing a game? I need three cards. One will be a king and the other two cards will be twos of different suits. It is not important which suit. What matters is that you have to pick the king when I place them face down on a table.
It's a fun game to play because the odds can either be on your side or not. If you are the one holding the cards, the odds are on your side. But, let me explain something first.
The problem was first appeared when Steve Selvin wrote a letter to the American Statistician in 1975. The very same problem often appears in the popular game show Let's Make A Deal made famous by Monty Hall. That is why this particular statistical problem is called the Monty Hall Problem.
There is a car behind one of the curtains, but there are two goats behind either of the other two. In our card game, we have twos symbolizing the goats. And we have a king that can be any prize you want to make.
Now, let's go back to the card game. It works just as Let's Make A Deal. If you are the one that holds the cards, put the three cards face down on the table and tell your contestant to choose one from the three cards. No matter which card they choose, reveal one of the other cards. Then, let them switch the cards.
In the game show, the host knows what is behind each curtain. So, the host will reveal a curtain that has a goat behind. When you are holding the cards, in order to let this to work you have to know which card is the king. It's not cheating if you make it clear to your contestants. The way to get them to play is by offering a prize. Playing this at home can make the game more fun.
The way it works is really a paradox that once stumped even the cleverest people. That's because they think sloppily about the problem that is being presented to them. When you have got three cards in front of you, you have one out of three odds that you will pick the king.
First of all, the actual question is whether it is wise for you to change your choice. Most people would think it doesn't matter. When asked what their odds are at that point in the game, they normally will say they have a fifty percent chance of choosing the right card.
That is the direct way of thinking and it can get most people in trouble at first. Besides, emotionally they are drained from the first decision. It is difficult for a person to make a choice between three things. It's also hard for most people to switch a choice once they have made it.
So if you are holding the cards, the odds are on your side. The fact is that you have a better chance of winning if you switch your answer. Let's undergo that way of thinking.
Let's assume that you are the one posed with this challenge and your challenger is now holding the cards. You have to deal with the problem with the knowledge that you have a two out of three chance of choosing a two. When you have made your decision, your opponent will reveal a two. At that time, you won't have a fifty percent chance that you have the king. Your odds have been greatly increased.
Because of the knowledge that the third card is a two, if you switch your choice, you will have a sixty seven percent chance of winning, Let's go over all the possible scenarios in this game just to give you an idea of what I mean.
The first one is the loser. You pick the king. Your opponent discloses a two. You switch your answer and your opponent reveals that you have chosen a two. You have lost the game. That's the worst case scenario.
But two out of three times, you are going to pick a two. Your opponent will reveal the other two, and then you switch your choice. Two out of three times, you are going to land on a king and get the prize. Now, that's the way of thinking.
Most card games are based on odds. But the way we deal with the game will make the difference. Generally, you have to think a little differently than you normally would. But that's a little hard to do in most of games.
by: Mary Solinna
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