1. Problema De Monty Hall 21 Blackjack 2
2. Problema De Monty Hall 21 Blackjack De

Monty Hall Simulation Online. Play the Monty Hall game or run the simulation many times to better understand one of the most famous math riddles.

• Blackjack is a French deck game for up to 7 players where the players face the house. The goal is to get 21 with our cards or a higher value than the dealer, without exceeding the number. If we exceed 21 or add a lower value than the dealer we’ll automatically lose our bet.
• The Monty Hall Problem 1. The Monty Hall Problem Presented by Irvin Snider 2. Let’s Make a Deal There are 3 curtains on stage Behind 2 curtains are goats Behind one curtain is a Cadillac Monty knows what’s behind each curtain.
• Apunts sobre 'Probabilitat' (INS Valldigna) Fitxa resum 'Probabilitat' Atzar Monedes (cara i creu) El Problema de Monty Hall (Black Jack).

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 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.

Plot[edit]

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 successfully. 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 lifestyle 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. Meanwhile, 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). Furthermore, 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 past 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. However, as Ben is leaving with his earnings, 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. However, 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 now 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 entire tale to the dazzled and dumbfounded scholarship director.

Cast[edit]

• 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

Production[edit]

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.

Reception[edit]

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]

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[edit]

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.

Problema De Monty Hall 21 Blackjack 2

See also[edit]

References[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'. chasingthefrog.com. Retrieved March 31, 2013.
7. ^Janusonis, Michael. 'Movies: 21 star Jim Sturgess got a crash course in card counting'. projo.com. 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''. manaa.org. Archived from the original on 2013-10-04. Retrieved March 31, 2013.
13. ^'21 (Single-Disc Edition) (2008)'. Amazon.com. Retrieved March 31, 2013.
14. ^ ^abBrown, Marisa. '21 [Original Soundtrack]'. AllMusic. Retrieved 2008-04-02.

External links[edit]

• 21 on 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

©

Leandro Castelluccio

Image obtained from Wikipedia (see in: link)

We seldom notice how our ability to separate, divide or segment things interferes with the ability to see facts as they are: simple, and that are presented to our senses directly. Here I will raise this question in relation to a probability game.

There is an interesting statistical problem that deals with contingencies, where intuitively it seems that one thing is true but the opposite is the case. I consider the topic relevant because our propensity to think of multiple possibilities based on separation and segmentation, on the elaborate intellect trying to see something difficult in the simple, can deviate us from the simple and correct solutions. To see an example of it, with the suggested solution, you can enter the following link.

Problema De Monty Hall 21 Blackjack De

What is the matter here? Well we have 3 doors, two of which contain a goat and a third that has the prize: a car. We have the opportunity to select a door at the beginning. After this, the person in charge of the test, or the presenter of the program, opens one of the remaining doors showing one of the goats, at that moment it gives us the option of staying with the door we have chosen or changing it to the remaining door. According to the proposals regarding the solution of the problem, the correct strategy is always to change the door and not keep the one we had selected. Why is this? Well, the odds would be against us otherwise. Let’s consider:

If we select the first door we have a third chance that the car is behind it. Now, the remaining two doors, together, represent the remaining two thirds. So when the presenter eliminates one of these two possibilities from the right, taking into account the initial situation, the probability that the car is in the remaining door on the right is greater, so that the optimal strategy would be to change the door:

Now, let’s see what happens when we think of other possibilities. It could be considered that there is a cognitive bias in the matter, and this refers to the group of doors that we assign the remaining probability. Keep in mind that any combination of two doors, including or not the one that was selected at the beginning, would contain 2/3 of the probability of containing the car:

As we can see in the previous examples, we could consider that the first and last door represent the 2/3 probability of containing the car and the remaining one of the middle the 1/3. Or in the second example, we could consider that the first and second doors contain the 2/3 probability of containing the car, and the third door the remaining 1/3.

So, consider that the 2/3 probability of finding the car behind one of the doors two or three (the middle and the third to the right) would seem in principle a bias or error in our reasoning, taking into account that any combination of two doors would contain 2/3 probability.

Now consider this taking into account that the rules are maintained and the subject chooses the first door. The subject who chooses the first door may be thinking that either the first or the second contains the car, between them there is 2/3 probabilities, and the third one remaining contains the one third. So when the presenter eliminates the option of the middle, the subject would say that there would be more probability that the car is in the first chosen door, since the first and the second contained 2/3, in which case the optimal strategy would be stay with the chosen door, under that perspective and that line of thought. Now, if the subject was with the idea that both the first and the last door contain 2/3, by eliminating the option of the meddle, which was the remaining third, the subject has still uncertainty, as the first plus the last option contains 2/3 of the probability of containing the car, under such a perspective. But if we add the first perspective of the 2/3 in the first and second door, here we could also say that the strategy is to maintain the choice. We must take into account the fact that the presenter has knowledge of which is the door that contains the car, and that when he eliminates one of the options, he can only do so with respect to a door that contains a goat and not the prize of the car, but under the previous perspectives the strategies seem to change, it is true that taking into account that the 2/3 are in the second and third door the strategy would be to change, but not under the previous perspectives as a whole, so in the face of the same situation we would have contradictory strategies depending on the point of view we adopt. In itself we have a strategy that tells us to keep the election, another to change it, and a third of uncertainty that according to which position we adopt, we can take the strategy of maintaining or changing.

The same would happen if the person chooses door two or three. Consider that in the previous case the door you chose, the first one, was the one that contained the car. Now consider that the first door is still the one that contains the car, but the subject chooses door two, even though door one and two represent 2/3. In that case if the presenter eliminates door 3 (which is the only one that can eliminate), then the person remains in the same position of uncertainty mentioned above, but adding the other perspective, that the 2/3 represent the door 2 and 3, then when the presenter eliminates the door 3, then the strategy would be to keep the election, and again under the consideration that the 2/3 are the door 1 and 3, then the subject should change, we have again contradictory strategies according to what 2/3 we consider, but both would be feasible according to the intellect, when we carry out the work of segmenting and dividing.

Under the above, one could conclude that any strategy is valid. But if we consider the third possibility, to choose the third door when the first one contains the car, although the contradictory strategies arise again, we can see a pattern when taking into account the previous possibilities. In the first case, the strategy was to stay in order to get the car, in the second to change to get the car, and in the third case he also get the car if we change. So 2 out of 3 times the car is obtained if one changes its initial choice, even considering that any 2/3 of combinations of doors is valid and throws us contradictory or uncertain strategies. These speculations leave aside the simple fact that when one chooses at the beginning, one has only 1/3 of possibilities of choosing the car, the rest are conjectures and thoughts, that is the basic fact, so changing will always have more chances of success because the remaining option contains a car 2 out of 3 times.

In general, many times we fool ourselves into our own thoughts, divide, classify, segment things, and this plays against the observation of concrete, simple facts. In fact many people continue to argue other possibilities regarding this problem, obviating this simple fact. And it happens in many areas of people’s work, perhaps the conclusion of all this is to observe the facts, and consider the simplicity of things, where usually the truth and solutions are.

In the following link you can perform a simulation of the problem and see the different probabilities.