Analysis of casino scene in On Her Majesty’s Secret Service
In this week’s newsletter we shall look at the casino scene in On Her Majesty’s Secret Service. Here is the YouTube clip I shall refer to. At the 0:55 point, we start to see Bond play. He is banking one-on-one against a player to high right. The player acting on the Player Hand asks to draw a card. Bond reveals his own two-card four-point hand and delivers a 9 to the Player Hand.
What I assume happens next, but isn’t shown, is Bond chooses to stand on his total of four. The scene then cuts to the man in the white coat acting on the Player Hand, revealing his initial two cards – two face cards, giving him a total of nine. Bond made the right play, mathematically. It is also possible he was forced to stand, if playing the version of Chemin de Fer described in Scarne’s New Complete Guide to Gambling, where there are only three situations with free will, this not being one of them.
Per the rules of chemin de fer, Bond had to give up his turn as the banker, because he lost the previous hand. What seems to be happening next is the new banker wagers more than anyone is comfortable with. Then a woman in a white dress, Tracy, walks up to the table and says “banco.” This means she wishes to bet the limit established by the banker by herself and play alone. At the 1:42 point, she says “carte,” indicating she wants to draw. The banker reveals his own two-card total of 0 and deals a 5 to Tracy. Then the banker draws a third card. The dealer (not to be confused with the banker) announces “neuf,” which means nine in French. It’s not shown, but the banker drew a 9 for a total of nine points. Tracy reveals her two-card total of five. The third five gives her a 0-point hand, losing to the banker.
Then what happens is Tracy asks for credit to pay the bet she just lost. The man she asks says “C’est impossible.” It would seem Tracy can’t honor the losing bet. Then Bond comes to the rescue and pays the losing wager for her. I am not sure why the casino let her play without bringing money to the table or approving credit, but this is necessary to advance the story, so I’ll let it go. That she is the daughter of the leader of a wealthy organized crime family may explain why she got credit so easily.
Then Tracy walks away as Bond follows her. They find a table to chat where Bond says, at the 2:53 point, “Next time, play it safe and stand on five.”
Pause. This is the kind of statement I must analyze. I assume they were playing the form of chemin in fer where both sides have free will in taking a third card, as long as neither side starts with a natural 8 or 9. Under this assumption, the strategy in some borderline hands, including a Player Hand total of five, should be determined randomly, much like in rock-paper-scissors. I go into all the math in my page on chemin de fer. The bottom line is that if we assume both sides per perfect logicians, then Tracy should have hit with 78.91% probability. If they are playing the Scarne version, with limited free will, she definitely should have hit on five.
Bond’s advice to play it safe and stand on five is bad advice either way. If she must always play a five one way or the other, it’s better to hit. However, as I mentioned, assuming the version that allows more free will, it’s better to mix it up, hitting 79% of the time and standing 21%. There is nothing safe or risky about hitting or standing. The important thing is to be unpredictable and keep your opponent on his toes by mixing it up. Any good poker player will understand the concept of the value of randomizing some hands, like bluffing with garbage. If you always play the same way your opponents will catch on to it and punish you for it.
So, shame on Bond for giving Tracy bad advice.
Next week we will finally change games and look at the craps scene in Diamonds are Forever.