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Gambling, Movies, Odds, And Misrepresentation 1: Casino Royale

Updated: Apr 12, 2021

In this series of gambling in movies blog, I discuss the gambling scenes and the mathematics behind them. Follow my social media if you are interested in discussing the misrepresentation of gambling in movies.

Gambling in Movies

For a lot of people, gambling is something more relevant to the silver screen as opposed to the late nights spent in casinos or horse racing tracks. And why not, given the entertainment industries’ attraction to the bright lights of Las Vegas. However, it is not just colourful lights and stunning visuals that attract directors and producers to these locations. The prospect of including gambling gives the film industry a chance to exploit characters to a rollercoaster of emotions. Writers show a long history of using turmoil in gambling to string together an exciting narrative of loss or recovery. Some movies that deal with gambling stick to reality, others create suspense by putting characters in unlikely situations, and others can walk the line of reality and fantasy.

There are countless examples of each of these situations. This list of films that delve into the genre of gambling is long: Casino Royale, 21, The Hangover, Uncut Gems, Molly’s Game, The Gambler, and Snatch to name a few. We can look at some of these movies to see how Hollywood takes the real gambling world and turns it into something that serves as a plot device that often discards the consequences and risks of gambling.

James Bond and His Unbelievable Poker Hand in the Casino Royale

The first study is Casino Royale, a 2006 James Bond movie directed by Martin Campbell. Originally adapted from a 1953 novel, James Bond (Daniel Craig) heads to Madagascar, where he uncovers a link to Le Chiffre (Mads Mikkelsen), a man who finances terrorist organizations. Learning that Le Chiffre plans to raise money in a high-stakes poker game, MI6 sends Bond to play against him, gambling that their newest "00" operative will topple the man's organization. During the movie’s most famous scene, tensions begin to build over a poker game gathering momentum. The players at the table gradually start to lose out, with some players losing millions, until it is the turn of Mr. Bond. His $10 million buy-ins is taken from him with an unusual draw of cards, and he is forced to be bankrolled back into the game. With a $5 million investment, he is able to ‘buy in’ to the game again in an attempt to win his money back.

The emotional turmoil James is put through is heightened with poisoning by his nemesis- Le Chiffre. However, after recovering and returning to the game, Mr. Bond manages to win the final hand, with a near-impossible run of cards. The poker game is used as a device to hold the rising tension and emotion between the protagonist and antagonist. Every card that falls is followed by close-up shots that dramatize the situation. While the clashing of ego and calculating probability is reflective of the emotion that can be found in gambling, the story does not show the story of our antagonist- a tale of loss and destruction.

The Reality was...

The reality was that James should have lost that hand. The chance of him losing $130 million was at 97.4%. His winning hand of a straight flush to the eight had a 0.027% chance of coming up - showing the reality of gambling- that it is really all down to luck and chance. So, although the movie does show a fair representation of the emotion and turmoil a player can go through, it does not reflect the risk and chance that the players go through. It only shows the dramatized tension and excitement and overlooks the consequences of the lives it can destroy in a split-second decision.

The Basic Probability of Poker Hands

Going deeper into these numbers, the argument around Casino Royale misrepresenting risk becomes easier to understand. Firstly, we must look at how those numbers even come about in the first place. They are found by looking at all the possibilities of cards that could be in each player's hand, and what ‘hands’ can be made alongside the cards that are on the table. In poker, a hand is a set of cards that have a ranked value. The highest-ranked hand is a royal flush- which is a run of the top 5 cards (Ace-Ten) all of the same suit. This is incredibly rare, as it requires a perfect run and matching suits. In fact, it is so rare that there is just a 0.000154% chance of getting that hand.

This can be found out by knowing that the chance of getting all of those cards would be 1/52 each time. Because the order in which the cards come up does not matter, we can use the formula for combinations and see that there are 2,598,960 possible distinct hands, with four ways of achieving a straight flush (one for each suit). This formula for combinations is a whole area of study that cannot be covered here, but generally, these combination possibilities can be found online. They are set statistical models that represent the possibility of certain positive outcomes within the context of all the potential outcomes.

The probability of being dealt a royal flush is the number of royal flushes divided by the total number of poker hands. We now carry out the division and see that a royal flush is rare indeed. There is only a probability of 4/2,598,960 = 1/649,740 = 0.000154% of being dealt this hand.

Even if we use the same logic to work out the probability of James’s hand coming up, the chances are just 0.027%. Although this is nearly 200X higher chance, the possibility of this hand coming up is tiny. It is therefore important that when watching gambling movies, we understand the space it is taking place in. One of heightened feeling, with the reality of consequence taken away. Similar patterns can be seen in other movies, for example- the comedy classic- The Hangover.

Next Blog: Hangover

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