The movie that we have chosen for the review of Math Chronicles is inspired by the true story of the MIT Blackjack Team as told in Bringing Down the House, the best-selling 2003 book by Ben Mezrich.  The film 21 tells the story of MIT students who "count cards" in order to increase their chances of winning in the casino card game Blackjack. This film has a lot of math in it, which is unsurprising. The "counting of the cards," which is based on Edward O. Thorpe's 1962 book Beat the Dealer, is the actual inspiration of this movie.

 

The movie possesses an enthralling and interesting plot. Ben, a mathematics major at the Massachusetts Institute of Technology, is accepted into Harvard Medical School but cannot afford the $300,000 tuition. He applies for the prestigious Robinson Scholarship which would cover the entire cost. Despite having a Medical College Admission Test score of 44 and high grades, he faces fierce competition and is told by the director that the scholarship will only go to whichever student dazzles him. Back at MIT, a professor, Micky Rosa, challenges Ben with the Monty Hall Problem which he solves. After looking at Ben's 97% score on his latest non-linear equations test, Micky invites Ben to join the MIT Blackjack Team, consisting of fellow students Choi, Fisher, Jill, and Kianna. Using card counting and covert signaling, they increase their probability of winning at casinos, leading themselves to earn substantial profits.

 

Over many weekends, the team is flown to Las Vegas Valley, and Ben comes to enjoy his luxurious life as a high roller big player. The team is impressed by Ben's skill, but Fisher becomes jealous and fights him while drunk, leading Micky to expel him. The head of security, Cole Williams, has been monitoring the team and begins to focus on Ben.

 

Ben's devotion to blackjack causes him to neglect his role in an engineering competition, which estranges him from his friends. During the next trip to Las Vegas, he is emotionally distracted and fails to walk away from the table when signaled, causing him to lose $200,000. Micky is angered and quits the team, demanding Ben to repay $200,000. Ben and three of the students decide that they will continue to play blackjack without Micky but they are caught by Williams, who Micky tipped off. Williams beats up Ben and warns him not to return.

 

Ben learns he is ineligible for graduation because his course taught by an associate of Micky is marked as incomplete (with Micky's influence, the professor initially gives Ben a passing grade throughout the year without him having to work or even show up to class). His winnings are stolen from his dormitory room. Suspecting Micky, Ben confers with the other blackjack students, and they persuade Micky to make a final trip to Vegas before the casinos install biometric software. The team puts on disguises and returns to Planet Hollywood, winning $640,000 before Williams spots them.

 

Micky flees with the bag of chips, jumping into a limousine but realizes it was a setup when he discovers that the chips are fake. It is revealed that Ben and Williams made a deal to lure Micky to Las Vegas so that Williams may capture and beat him, as he has grievances against him. Williams proceeds to hold Micky hostage and subject him to beatings. In exchange, Williams commits to allowing Ben to keep his winnings for that day, but later double-crosses him as he is leaving, taking the bag of chips at gunpoint. When Ben protests, Williams explains he needs retirement funds, whereas intelligent people like Ben will always find a way to succeed.

 

Ben's long-time friends (with whom he has reconciled) Miles and Cam also turn out to be quite good at card-counting while working with Choi and Kianna during Micky's capture and as such, the 6-person team makes a lot of money despite Williams's robbery of Ben and Micky's chips. The film ends with Ben recounting the tale to the dazzled and dumbfounded scholarship director.

 

This was the whole plot of the movie. If you haven’t read it all, I suggest you go watch the movie; it is immersive. The math-related part of the movie is of course the “card counting.” 

 

Card counting is a blackjack strategy used to determine whether the player or the dealer has an advantage on the next hand. Card counters are advantage players who try to overcome the casino house edge by keeping a running count of high and low valued cards dealt. They generally bet more when they have an advantage and less when the dealer has an advantage. They also change playing decisions based on the composition of the deck.

 

Card counting is based on statistical evidence that high cards (aces, 10s, and 9s) benefit the player, while low cards, (2s, 3s, 4s, 5s, 6s, and 7s) benefit the dealer. High cards benefit the player in the following ways: they increase the player's probability of hitting a natural, which usually pays out at 3 to 2 odds. Card counters do not need unusual mental abilities; they do not track or memorize specific cards. Instead, card counters assign a point score to each card that estimates the value of that card. They track the sum of these values with a "running count." Even though it seems like it is only statistics and probability that card counters benefit from, this is not the case. There are a variety of systems that card counters use to beat dealers in casinos. However, I can’t tell you them... 
 

References: 

 

“21.” IMDb, IMDb.com, 28 Mar. 2008, https://www.imdb.com/title/tt0478087/. 

“Card Counting.” Wikipedia, Wikimedia Foundation, 29 Sept. 2021, https://en.wikipedia.org/wiki/Card_counting. 

“The Mathematics of the Movie ‘21.’” The Mathematics of the Movie "21", https://sites.me.ucsb.edu/~moehlis/21.html.