I went to watch the recent blockbuster movie “21“, a movie based on the book “Beat the Dealer” written by Professor Edward O. Thorp. There are some apparently factual inaccuracies, such as main characters are supposed to be Asian-Americans in the MIT blackjack team, and professor Thorp wasn’t corrupt as portrayed in the movie. Plus, film directing is little disappointing. Nevertheless, there are several interesting questions mentioned in the movie.
1). Is blackjack really beatable? The answer is YES. I am not an expert on this gambling game, but I believe that it doesn’t really need some disguised signals to cheat like what Ben’s team does. Perhaps the reason is that adding little drama is just part of marketing strategy. The card game strategy like card counting is a prerequisite. There are several websites and books online dedicated to beating blackjack. Anyone who is interested in this problem may visit the website Beat the BlackJack or download the book How to Beat the Dealer in Any Casino to get acquainted with the solutions. PS: Professor Thorp also wrote an article about beating the market (allegedly) in 2003, which might interest people working on quantitative finance.
2). At the beginning of this movie, there is one scene in which Ben gives a brilliant answer to a probability problem and attracts professor Rosa’s attention. This probability problem mentioned by professor Rosa in his non-linear equation class is:
There are two goats and one car behind each of three doors. The host of the show (or game) knows exactly which door the car is behind. You are asked to pick a door first, but the host doesn’t open the door you just chose. He/she opens a door with a goat behind it. Now, you are again asked to choose one of the two remaining doors. If the car is behind the door you choose this time, then you win this car, otherwise, you will get nothing. Now the question is: What should you do? Don’t change the first choice you made or switch to the other unopened door?
Usually, the first thought is that, well, of course, you have two doors to choose, so it doesn’t matter which one you pick, the chance of winning is always 1/2. Actually, this is a simple problem that is not too simple when one is under time pressure. Ben gives a beautiful solution that looks odd at first. To see the answer in the blank space below, you need to left-click any blank space on this webpage, and then press Ctrl+A (the so-called select all command).
The answer is that changing your first choice will give your 2/3 chance of winning. Here is the interpretation. By this tactic (i.e. change the door), if the first door you chose has a goat behind it, which has 2/3 probability, then you will definitely win the car after you make the second choice. But if the thing behind the first door you chose is the car, which has 1/3 probability, then eventually you will lose after you make the second-round choice. Anyway, 2/3 chance of winning is good enough.
The 21 is an overall good entertaining movie. At least, I didn’t sleep away half of time like I did while watching Forbidden Kingdom in theater ^_^.
Filed under: Miscellaneous, The Sciences (non-technical) , 21, blackjack, card counting, Forbidden Kingdom, Life, movie, movie 21
