We went to see the movie 21 over the weekend. While the movie itself was just average, there was some fun math in the movie. If you took a statistics class in college, you probably came across this problem:
You're on a game show and the host asks you to choose one of three doors. After you choose, the host opens one of the other doors and reveals a goat. You are now offered the option to change your guess or keep it the same. Should you take the other door?
YES. Always. If you keep the same choice, you have a 33% chance of winning. If you switch you have a 66% chance of winning. It's a bit confusing at first, but it's just statistics.
When you made your first choice, there was a 33% chance you were right a 66% chance you were wrong. The host shows you one of the wrong answers, and since he knows which door is correct, the odds behind your two guesses are related. When you give your second answer, you should always switch your guess and take advantage of the 66% odds of winning.
You can visit this website and play the game for yourself. Stats are tracked for all players and you can see that about 2/3rds of the players who switched won the game. Only 1/3 of the players who did not switch were able to win. It all works out as expected.
If it still doesn't make sense, you can read the explanation from that site as well. They draw out a diagram of all the possibilities and that makes it all a bit more clear.
Want to learn how to count cards like they do in the movie? I'll write that up in another post. The math behind card counting is easy. Doing it successfully is hard.