Monty Hall Game

I was just recently introduced to the Monty Hall Game paradox by my friend Andrew Penry. When he first proposed the game to me I thought it was simply absurd—and my intuitive thinking process would not allow me to accept the statistical conclusions that the game entails.

The game is simple. A dealer puts out three cards, one of which is a winning card. The player may choose a card at random but may not see the card. The dealer then shows the player a losing card that the player did not choose… and the player is given the choice to keep his first choice or switch to the remaining card.

Intuitively, it seems like this is a game of fifty-fifty odds—that you can flip a coin and make a good statistical decision. But that is actually not the case. Empirical statistics prove that you are twice as likely to win when you switch cards than if you keep your original choice.

My mind would not let me believe it. I went so far to write my own JavaScript-driven program to beat it into my brain that this is the truth.

The reason for the mental block is that our brains are psychologically unable to see pure statistics. We assume that because the choice comes to a fifty-fifty decision, it really is fifty-fifty. But Andrew set me straight by explaining something to me.

Assume that the dealer does not show you the one losing card. In that case, the dealer is saying to you, “Keep your card or choose the other two cards.” Even though you know it can’t be both of those cards, you know there is a 66 percent chance that you will win by switching.

It’s crazy, it hurts your head… but over the long run you are always better off by switching your choice.

Go ahead... play the Monty Hall Game and challenge yourself to understand it.