Mit Students Counting Cards Movie

The Mathematics of the Movie '21'

by Jeff Moehlis

The movie '21' isthe story of MIT students who 'count cards' to improve their probabilityof winning the card game Blackjack at casinos. Not surprisingly, this movie has a lot of mathematics in it. Most obvious is the 'counting of thecards', which is based on the techniques published in Edward O. Thorpe's1962 book 'Beat the Dealer'. Discussions of the method and mathematicsof 'card counting' are described on various other websites. On this website, you can learn about other mathematical ideas which appear in the movie. I hope that this increases your enjoyment of the movie andperhaps teaches you some mathematics!

MIT student Jeff Ma and five of his classmates used fake IDs, disguises and high IQs to outsmart Nevada casinos to the tune of several million dollars in the mid-1990s. 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 his blackjack team, which consists of fellow students Choi, Fisher, Jill and Kianna.

The Fibonacci Series

In '21', when Ben Campbell (played by Jim Sturgess) is celebrating hisbirthday, the cake says

0, 1, 1, 2, 3, 5, 8, 13, ..

These are the first terms in the Fibonacci Series, which was used as an example in the book Liber Abaci published in 1202 by Leonardo Fibonacci.This is obtained by first writing the numbers '0, 1', then defining eachsubsequent number as the sum of the previous two numbers in the series. Thus, thethird number in the series is 1 = 1+0, the fourth number is 2 = 1+1,the fifth number is 3 = 2 + 1, etc. The next number on the cake wouldbe 21=13+8, for Ben's 21st birthday. Clever, huh? (Hmmm, does '21'refer to Blackjack or Ben's age?) Ben will have towait until he is 34 = 21+13 for his next 'Fibonacci birthday'.

One can define other Fibonacci Series by specifying different numbers inthe first two slots. For example, the Fibonacci Series starting with'2, 5' is

2, 5, 7, 12, 19, 31, 50, ..

The Mit Blackjack Team. The MIT blackjack team has become famous worldwide for their success at beating the game of blackjack in the casinos of Las Vegas.Even people who are unfamiliar with blackjack and gambling know the story of the MIT students, thanks in large part to the popular movie 21. Cfnm 3gstagette party videolayla69 cfntrailers cfnm site 16 cfnm secrelayla69 cfncfnm art school cfnm cfnm masturbation. Baths room and intimate ago room group sex part5. Two porn 3d autotoon lovers from the game dance pornily on the night club. Arabian boys gay porn thankfully, muscle daddy casey has some ideas of. Real ass fucked by cock free. A punched card (also punch card or punched-card) is a piece of stiff paper that holds digital data represented by the presence or absence of holes in predefined positions. Punched cards were once common in data processing applications or to directly control automated machin.

The Monty Hall Problem

Consider the following variation of the final round of the classic TVgame show Let's Make A Deal:

There are three doors, and behindone of them is a car, while behind the other two are goats. If you choosethe door with the car behind it, you win the car. Now, say you choose Door 1. The host MontyHall then opens either Door 2 or Door 3, behind which is a goat. (He knowswhat is behind each door, and neveropens the door with the car behind it.) Monty now gives you the choice:do you want to stick with Door 1, or switch to the other door. Whatshould you do? Or does it matter?

A similar question is posed to Ben Campbell (played by Jim Sturgess) by Professor Micky Rosa (played by Kevin Spacey) in the movie '21'. Withouthesitation Ben answers this correctly, which convinces Professor Rosa that Ben would be a good addition to their 'card countingteam'. Before reading on, try to answer this yourself.

One solves this problem by comparing the probability of choosing the car if youstick with your original choice to the probability of choosing the carif you switch after Monty opens the one door. Note that the car has an equal probability of 1/3 of being behind Door 1, Door 2, or Door 3. Free super jackpot party slot machine.

First, suppose that your strategy is to stick with your original choice of Door 1. Then you only win if the car is behind Door 1, so thatyour probability of winning is 1/3.

Next, suppose that your strategy is to switch doors. We break this intothree cases:

  • If the car is behind Door 1, Monty will open eitherDoor 2 or Door 3 to reveal a goat. You switch to the other of Door 2or Door 3, and in either case you switched to a door with a goat behindit (remember, the car is behind Door 1).
  • If the car is behind Door 2, Monty will open Door 3. This is becausehe always opens a door with a goat behind it, and he can't open Door 1because that was your original choice. So the only door you can switchto is Door 2, which is the door with the car behind it. Ding! You win!
  • If the car is behind Door 3, Monty will open Door 2. This is becausehe always opens a door with a goat behind it, and he can't open Door 1because that was your original choice. So the only door you can switchto is Door 3, which again is the door with the car behind it. Ding! You win!

    So if your strategy is to switch doors, you win 2/3 = 1/3 + 1/3 of the time. (Remember,the probability is 1/3 that the car is behind any particular door.)Therefore, a better strategy is to switch doors - the calculated probabilities indicate that you are twice as likely to win if you do this!Ben's correct answer in the movie '21' indicates that he is a good personfor 'counting cards'. Not only does it show that he is clever,but it also demonstrates that he realizes that it is best to go with the choice whichmaximizes your probability of winning. This realization is essential tothe success of 'counting cards' for Blackjack.

    In 1990, a similar question appeared in a letter to Marilyn vos Savant's Ask Marilyn column in Parade (which comes in some Sundaynewspapers). Marilyn gave the correct answer, but many readers(including mathematics professors) believed that this was incorrect.So don't feel too bad if you got it wrong when you answered it for yourself.But now you know!

  • The Newton-Raphson Method

    You might recall from an algebra class that the solutions to theequation

    are given by the quadratic formula

    Suppose instead that you want to find a value for x which solvesthe general algebraic equation

    f(x) = 0.

    Such a value for x is called a root of f(x). Except for special choices of f(x), such as f(x) = a x2 + b x + cas above, one cannot find the roots using algebraic operations.

    In the movie '21', Professor Micky Rosa (played by Kevin Spacey)is lecturing on the Newton-Raphson method for finding the rootsof f(x). This was developed independently by Isaac Newton and Joseph Raphson in the 1600's. The idea is to make a guess for a root of the equation (let's call it x0), then to use this guess to generate a value for x (let's call it x1) which is (hopefully) even closer to the root than the original guess. This isdone by drawing the tangent line to the function f(x) at x=x0, and takingx1 as the value for x at which this straight line goes through zero.(For those of you who know calculus, you will recognize that this tangentline is determined by the derivative of f(x).)By iterating this procedure over and over to generate x2, x3, etc, one (hopefully) obtains values which are better and better approximations to the root. I keep saying 'hopefully' because the Newton-Raphson Method isn't always successful, although it is more likely to be if you make a good initialguess. This figure illustrates the method:

    This method was developed well before computers existed, but turns outto be ideal for implementation on a computer: one uses a loop to generate successive values of xn.

    Counting Cards

    A nice discussion of 'counting cards' for Blackjack is givenin this Wikipediaarticle .

    Now let's count the number of times this page has been visited:

    Visit Author Jeff Moehlis'website. Also, check out his music site

    Directed byRobert Luketic
    Produced by
    Written by
    Based onBringing Down the House
    by Ben Mezrich
    • Kevin Spacey
    Music byDavid Sardy
    CinematographyRussell Carpenter
    Edited byElliot Graham
    • Michael De Luca Productions
    Distributed byColumbia Pictures
    • March 28, 2008
    123 minutes
    CountryUnited States
    Budget$35 million
    Box office$159.8 million

    21 is a 2008 American heistdrama film directed by Robert Luketic and starring Jim Sturgess, Kevin Spacey, Laurence Fishburne, Kate Bosworth, Liza Lapira, Jacob Pitts, Aaron Yoo, and Kieu Chinh. The film 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. Despite its largely mixed reviews and controversy over the film's casting choices, 21 was a box office success, and was the number one film in the United States and Canada during its first and second weekends of release.


    Ben, a mathematics major at MIT, 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. However, despite having an MCAT 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 his blackjack team, which consists of fellow students Choi, Fisher, Jill and Kianna. Using card counting and covert signalling, they are able to increase their probability of winning while at casinos, leading them to earn substantial profits. Over many weekends, the team is flown to Las Vegas and Ben comes to enjoy his luxurious life as a so-called 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 turn his attention to 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 his earnings of $200,000. Micky is angered and quits the team, demanding that Ben must 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, whom Micky tipped off. Williams beats up Ben and warns him not to return.

    Ben learns that he is ineligible for graduation because his course taught by an associate of Micky's 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 Las Vegas before the casinos install biometric software. The team puts on disguises and returns to Planet Hollywood, winning $640,000 before they are spotted by Williams. 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, because Williams has grievances against him. Williams proceeds to hold Micky hostage and subject him to beatings. In exchange, Williams allows Ben to play for one more night in Las Vegas, enjoying immunity from capture. as Ben is leaving with his winnings, Williams betrays him and takes the bag of chips at gunpoint. Ben protests and Williams explains that 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-man team make 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.


    • Jim Sturgess as Ben Campbell
    • Kate Bosworth as Jill
    • Kevin Spacey as Micky Rosa
    • Aaron Yoo as Choi
    • Liza Lapira as Kianna
    • Jacob Pitts as Fisher
    • Laurence Fishburne as Cole Williams
    • Jack McGee as Terry
    • Josh Gad as Miles
    • Sam Golzari as Cam
    • Helen Carey as Ellen Campbell
    • Jack Gilpin as Bob Phillips


    The filming of 21 began in March 2007. Principal filming of the Las Vegas scenes took place at the Planet Hollywood Resort & Casino, the Red Rock Casino, and the Hard Rock Casino in Las Vegas. Filming also took place at Harvard Medical School, Chinatown, in Cambridge, and the Christian Science Center in Boston, Massachusetts. As Massachusetts Institute of Technology did not allow filming on campus, the MIT school and dorm interiors, the gymnasium and the alumni reception were all shot at Boston University.


    Critical response[edit]

    Review aggregator Rotten Tomatoes reported that 36% of 169 critics gave the film a positive review, for an average rating of 5.17/10. The site's critical consensus reads: '21 could have been a fascinating study had it not supplanted the true story on which it is based with mundane melodrama.'[1]Metacritic gave the film an average score of 48 out of 100, based on 29 critics, indicating 'mixed or average reviews'.[2] Audiences polled by CinemaScore gave the film an average grade of 'B+' on an A+ to F scale.[3]

    Box office[edit]

    In its opening weekend, the film grossed $24,105,943 in 2,648 theaters in the United States and Canada, averaging $9,103 per venue and ranking first at the box office.[4] The film was also the number one film in its second weekend of release, losing 36% of its audience, grossing $15,337,418, expanding to 2,653 theaters, and averaging $5,781 per venue. The film dropped to third place in its third weekend, losing 32% of its audience, grossing $10,470,173, expanding to 2,736 theaters, and averaging $3,827 per venue. By the fourth weekend it fell to sixth place, losing 47% of its audience, grossing $5,520,362 expanding to 2,903 theaters, and averaging $1,902 per venue.

    By the end of its theatrical run, the film grossed a total of $157,802,470 worldwide—$81,159,365 in the United States and Canada and $76,643,105 in other territories, against a budget estimated at $35 million.[5]

    Casting controversy[edit]

    A race-based controversy arose over the decision to make the majority of the characters white Americans, even though the main players in the book Bringing Down the House, upon which the film 21 is based, were mainly Asian-Americans.[6] The lead role was given to London-born Jim Sturgess, who required a dialect coach to speak with an American accent.[7]

    Jeff Ma, who was the real-life inspiration for the character Ben Campbell and served as a consultant on the film, was attacked as being a 'race traitor' on several blogs for not insisting that his character be Asian-American. In response, Ma said, 'I'm not sure they understand how little control I had in the movie-making process; I didn't get to cast it.'[8] Ma said that the controversy was 'overblown' and that the important aspect is that a talented actor would portray him.[9] Ma, who is Chinese American, told USA Today, 'I would have been a lot more insulted if they had chosen someone who was Japanese or Korean, just to have an Asian playing me.'[10]

    Nick Rogers of The Enterprise wrote, 'The real-life students mostly were Asian-Americans, but 21whitewashes its cast and disappointingly lumps its only Asian-American actors (Aaron Yoo and Liza Lapira) into one-note designations as the team's kleptomaniac and a slot-playing 'loser.'[11]

    The Media Action Network for Asian Americans (MANAA) reported on their web site: 'After the 'white-washing' issue was raised on Entertainment Weekly's web site, [21] producer Dana Brunetti wrote: 'Believe me, I would have LOVED to cast Asians in the lead roles, but the truth is, we didn't have access to any bankable Asian-American actors that we wanted.'[12]

    Home media[edit]

    21 was released on DVD and Blu-ray in Region 1 on July 21, 2008.[13]

    Mit Students Counting Cards Movie Theme

    Reaction from casinos[edit]

    In pre-production, the producers and the book's original writers predicted that the Vegas casinos would be unhelpful, as a film that told viewers the basics of card counting might hurt their bottom line. A featurette included with the DVD completely and accurately describes the 'Hi-Lo' system used by the MIT Blackjack Club and by Rosa's team in the film.


    In fact, the writers were surprised when told by the producers that MGM Studios would finance the film, though all 'MGM' casinos (including one used by the real MIT Blackjack Team) are owned by MGM Resorts International and are no longer related to MGM Studios. In reality, as another DVD featurette reveals, the casinos (including MGM Resorts) saw the film as an attention-getter; people who saw it would be encouraged to go to Vegas and play: some just for fun and some attempting to count cards but failing to learn or memorize the entire strategy or making too many mistakes. The film withheld critical strategy details (such as the conversion from the 'running count' to a 'true count'), and most beginning card counters underestimate the number and value of the mistakes they make.


    Soundtrack album by
    • March 18, 2008
    Singles from 21 - Music from the Motion Picture
    1. 'You Can't Always Get What You Want' (Soulwax Remix)'
      Released: February 19, 2008
    2. 'Big Ideas'
      Released: August 11, 2008
    Professional ratings
    Review scores

    Mit Card Counting Scandal

    The soundtrack was released at the same time as the film.[14]

    1. The Rolling Stones—'You Can't Always Get What You Want' (Remixed by Soulwax) (6:07)
    2. MGMT—'Time to Pretend' (Super Clean Version) (4:20)
    3. LCD Soundsystem—'Big Ideas' (5:41)
    4. D. Sardy featuring Liela Moss—'Giant' (3:42)
    5. Amon Tobin—'Always' (3:38)
    6. Peter Bjorn and John—'Young Folks' (4:37)
    7. Shook One —'Soul Position' (4:16)
    8. Get Shakes—'Sister Self Doubt' (4:22)
    9. The Aliens—'I Am The Unknown' (5:27)
    10. Rihanna—'Shut Up and Drive' (3:34)
    11. Knivez Out—'Alright' (3:31)
    12. Domino—'Tropical Moonlight' (3:28)
    13. Unkle—'Hold My Hand' (4:58)
    14. Mark Ronson featuring Kasabian—'L.S.F. (Lost Souls Forever)' (3:32)
    15. Broadcast—'Tender Buttons' (2:51)
    Other tracks
    • Although it is not included in the soundtrack, Moby's 'Slippin' Away' (Axwell Vocal Remix) plays in the scene when Ben is passing through airport security.
    • The song 'Everybody Get Dangerous' by Weezer was also featured in the film, but not included on the soundtrack since it was not yet released. It would later be released on Weezer's 2008 record, The Red Album. It is played on a distant radio when the team is in a poker club.
    • The songs 'I Want You to Want Me' by Cheap Trick and 'Music is Happiness' by The Octopus Project were also featured in the film but not on the soundtrack album.
    • The song 'Magnificent' by Estelle (feat. Kardinal Offishall) was also featured in the film but not on the soundtrack album. It's played approximately 58 minutes in, after the Weezer song, in the scene where Ben buys Jill a beer. It's subtle, and has a reggae beat.
    • In the promotional trailers, 'Break on Through (To the Other Side)' by The Doors was used.
    • During the restaurant scene where the team explains to Ben how they work, 'Home' by Great Northern can be heard playing in the background.
    • The song 'Again with the Subtitles' by Texas artist Yppah is another uncredited song in the film.
    • The track played as the team makes off at the end of the film is 'Rito a Los Angeles' by Giuseppe De Luca, which features part of the main riff of 'In-A-Gadda-Da-Vida'. This track is also used in Ocean's Twelve, the first sequel to the caper film Ocean's Eleven, about actually robbing casinos in Vegas.
    • My Mathematical Mind by Spoon was featured in the trailers.

    See also[edit]


    1. ^'21 Movie Reviews, Pictures - Rotten Tomatoes'. Rotten Tomatoes. Archived from the original on 22 November 2009. Retrieved May 29, 2020.
    2. ^'21 (2008): Reviews'. Metacritic. Archived from the original on 2 April 2008. Retrieved 2008-04-02.
    3. ^'Find CinemaScore'(Type '21**' in the search box). CinemaScore. Retrieved May 19, 2020.
    4. ^'21 (2008) - Weekend Box Office Results'. Box Office Mojo. Retrieved 2008-04-06.
    5. ^'21 (2008)'. Box Office Mojo. Retrieved 2008-04-28.
    6. ^'Real MIT Blackjack Team - 21 Movie True Story'. Retrieved March 31, 2013.
    7. ^Janusonis, Michael. 'Movies: 21 star Jim Sturgess got a crash course in card counting'. Archived from the original on April 11, 2008. Retrieved 29 May 2015.
    8. ^Justin Berton (2008-03-27). 'Hollywood deals Jeff Ma a good hand with '21''. San Francisco Chronicle. Archived from the original on 29 March 2008. Retrieved 2008-03-29.
    9. ^Berry, Jillian A. (March 14, 2008). 'INTERVIEW MIT, Vegas, Hollywood'. The Tech. Retrieved March 31, 2013.
    10. ^Bowles, Scott (2008-03-26). 'New film '21' counts on the real deal for inspiration'. USA Today. Retrieved 2010-04-23.
    11. ^Nick Rogers (2008-03-26). 'When the stakes are high, '21' folds'. The Enterprise. Archived from the original on 2008-04-01. Retrieved 2008-03-29.
    12. ^'CONTROVERSY STILL SURROUNDS DVD RELEASE OF MOVIE '21''. Archived from the original on 2013-10-04. Retrieved March 31, 2013.
    13. ^'21 (Single-Disc Edition) (2008)'. Retrieved March 31, 2013.
    14. ^ abBrown, Marisa. '21 [Original Soundtrack]'. AllMusic. Retrieved 2008-04-02.

    External links[edit]

    Mit Students Counting Cards Movie
    • 21 at IMDb
    • 21 at Rotten Tomatoes
    • 21 at Metacritic
    • 21 at Box Office Mojo
    • 21 at AllMovie
    • Photos of the filming of 21 near the campus of MIT: 123456
    • Official world wide release dates with links to different national sites
    Retrieved from ''