Letís play a game. Iíll choose three cards. Two cards will be twos of different suits and one will be a king. It doesnít matter which suit. All that matters is you have to pick the king when I place them face down on a table.
Itís 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 a little bit first.
The problem was first presented when Steve Selvin wrote a letter to the American Statistician in 1975. The very same problem often presents itself in the popular game show Letís Make A Deal made famous by Monty Hall. That is the reason 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 which symbolize the goats. Then, we have a king which can be any prize you want to make it.
So, letís get back to the card game. It works just like Letís Make A Deal. If you are the one holding the cards, lay the three cards face down on the table and tell your contestant to choose one of the three cards. No matter which card they choose, reveal one of the other cards. Then, offer them the chance to switch cards.
In the game show though, the host knows what is behind each curtain. So, the host will obviously reveal a curtain that has a goat behind it. When you are holding the cards, in order for this to work you have to know which card is the king. Itís not cheating if you make that clear to your contestants. The way to get them to play is by offering a prize. Normally a drink will be sufficient.
The way it works is actually a paradox that has stumped even the smartest of people. Thatís because they think forwardly about the problem that is being posed to them. When you have three cards in front of you, you have one out of three odds that you are going to pick the king.
First of all, the actual question is whether or not it is beneficial for you to change your choice. Most people would say it doesnít matter. When asked what are their odds at that point in the game, they normally will say they have a fifty percent chance of choosing the right card.
That is the straight forward way of thinking and itís what gets most people in trouble in the first place. Plus, emotionally they are drained from the first decision. It takes so much for a person to make a choice between three things that they are more likely to stay with what they have. Itís hard for most people to switch an choice once they have made it.
Thatís why if you are holding the cards the odds are on your side. The fact of the matter is that you have a better chance of winning if you switch your answer. Letís go through that way of thinking.
Letís say that you are the one posed with this challenge and your challenger is now holding the cards. You have to approach the problem with the knowledge that you have a two out of three chance of choosing a two. When you make a decision, your opponent will reveal a two. At that time, you donít 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, you now have a sixty seven percent chance of winning if you switch your choice. Letís 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 reveals a two. You switch your answer and your opponent reveals that you have chosen a two. You have lost the game. Thatís 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, thatís the way to think.
Most card games are based on odds. But the way we approach the game makes all the difference in the world as to whether you win or lose. Most of the time, you have to think a little differently than you normally would. In most drinking games, thatís a little hard to do.