by Audrey Smith
In the movie Casino Royale, the titular character has beaten Mads Mikkelsen’s antagonist in a game by getting a straight flush over his full house. Not to mention that it was a split straight flush.
By cinematic standards, the scene was amazing. But, when we count in math and psychology, it was just incredible. The chances of getting those cards are absurdly small and staying cool to check twice when you have it is even harder.
Quick math for the Casino Royale chances
- 00001539077169% chance of getting a straight flush
- 00000012825643% chance of getting a split straight flush 4-8
- 0% chance of staying cool with $115M in the pot
Well, unless you are the fabled agent 007 that is.
Poker is more than Math
Unlike most card games, you don’t only play poker against the house or the dealer; you play it mostly against other players at the table. Having four of a kind doesn’t help if you fold and you can bleed all of your cash away before you get a lucky stroke.
Especially when it comes to playing hold’em, it is essential to be able to read other players and have a general idea if they have a good hand or not. Then you have to figure out what having a good hand means to them.
Also, you can always stumble upon a player akin to a Swedish pensioner who plays with a smile win or bust. Those people will mess up your game big time.
Not to mention that in the end, you need to win hands to go home in the black. That requires luck as well.
Offline Poker vs. Online Games
Ironically, the AI algorithm in online games is leagues more forgiving than playing actual IRL cards. For instance, odds on online pokies are such that you have 3 times bigger chances of winning the biggest jackpot there is than having a split straight flush.
Not to mention that the hand Bond had was not the strongest in the game. Chances for a royal flush are even slimmer and in hold’em, the signs would be more apparent.
Also, you can always win something in online games and you rarely exit quickly and with nothing. Even live casino games have stacked better chances to make the game more interesting as there is no psychological interaction.
Getting a Straight Flush
In the movie, the main antagonist Le Chiffre has a full house with aces over eights. The chances for that are roughly 1:100, making that hand exceptionally strong. The next closest chance was four aces, which he knew was impossible as he had an ace.
In many ways, expecting that Bond would have a straight flush was unreasonable.
Especially, because the row on the table was split into two places, having those exact cards would require 1:100.000.000 chances, or a million times better than a full house.
With that in mind, the torture scene that follows is, while gruesome, somewhat to be expected.
Dealer vs. Player
When playing against the AI or a dealer, you know that the person in front of you has nothing to gain by cheating or fooling you. In those cases, it is all a matter of luck, RNG, and RTP if you have a strategy.
But, playing against other humans who have something to lose is a whole different animal. You aren’t splitting the pot or winning in your own game. You can have a great hand and go home with nothing if the other person had a better one.
Hopefully, someday, we will know how it feels to stake millions on a single hand of cards. But, if we do the math, we are more likely to get there by winning a jackpot on online slots than we are playing poker against international criminals.
