In this weeks podcast, The house always wins in the long run (June 2, 2022), Walter Bradley Center director Robert J. Marks interviews mathematician, computer scientist, and engineer Salvador Cordova on a subject on which he has strong views: gambling.
Marks tells us, I teach a graduate course on probability and stochastic processes. There I teach the stupidity of casino gambling. In statistics, theres a theorem called the Law of Large Numbers. It teaches that you cant win in the long run at casino games. Period. The law of large numbers is a mathematical truth. Its a law as serious as the law of gravity. Its why casinos always get rich and the gambler always gets poor. There is a chance that you will win the lottery or win a million dollars jackpot in the casino, but theres also a chance you will get hit by falling space debris while juggling.
He adds, for good measure, I tell people its better if you give your money to me and Ill decide whether or not to give it back. You have a better chance of walking away with money in your pocket.
Cordova is, as it happens, a specialist in the Law of Large Numbers. Enjoy.
This portion begins at roughly 7:00 min. A partial transcript and notes, Show Notes, and Additional Resources follow.
Are there legitimate ways to improve ones odds in a casino?
Sal Cordova: There are laws in Las Vegas. If you actually now bring computers in and use them to beat the games, you could be prosecuted. I mean, stuff that is done now is only called cheating by law. but in my book youre not really going against the rules of how to actually play your hands or anything. So Ive really not looked much into the techniques of cheating because I just didnt want to get prosecuted
Robert J. Marks: Well, I read a book called Race Horse [whose author] maintained that he could throw dice in order to get a high probability of a seven. He literally knew how to throw the dice, but it had to do with something like sliding the dice. And you cant do that in Las Vegas anymore, right?
Sal Cordova: Not anymore. They actually passed a law. Its kind of like how gyroscopes work; you have a lot of angular momentum. It resists certain motions. So these dice sliders would throw the dice like when you throw football. You try to throw it with spin because that helps stabilize it.
And so they were throwing the dice with a lot of spin and then sliding it across the table. So it never tumbled. So whatever you set the dice, you just have like a seven on top, basically, with your two dice. If you could slide the dice, there was no randomizing.
And Las Vegas realized these people were so good at it, that they were changing the odds. First, they passed laws and then they started to pass rules within the casino.
Then you couldnt dice slide. But then on top of that, the casinos began to put down felt [on the tables] so that the dice wouldnt slide. And then they put these little pyramids on the ends and then they forced you to throw the dice in a certain fashion. So it
Robert J. Marks: Has to bounce against the back wall, at least in the movies.
Sal Cordova: So then they started to put arresting wires so that if you tried to slide it across from where you are, it would hit the arresting wire. So they forced you to basically lob it.
Robert J. Marks: So its like jumping a hurdle.
Sal Cordova: And then they made very sharp corners on the dice. They got some good physics to count as a countermeasure. But those must have been the glory days of being a crafts player. Because if youre really well practiced at this, you only needed to tilt the odds. Even you didnt even need to do it all the time, if you could just get like maybe a few percent in your favor, you could beat the game.
Cheater: Its not that I sat down one day and decided I wanted to cheat. Its just that I realized that cheating would raise my odds:
Sal Cordova: But now I do recall some instances of cheating where it was prosecuted. Its when the dealer had colluded with the players in games like blackjack or baccarat. So if the dealer reveals what they call the whole card, its the card that the players arent supposed to see.
So the player will make playing decisions based on knowledge hes not supposed to have. He has a huge advantage. In blackjack, the dealer has what they call a whole card (the card you cant see). And after youve finalized your decision as a player, then hes going to reveal it. And then you find out whether youre going to win or lose.
Robert J. Marks: And probably he didnt actually reveal it. He probably gave signs like a third base coach in baseball, touching the bureau or something.
Sal Cordova: Well actually he could subtly reveal it with his hands. He could bend the card a little bit so the player could actually peek and see it.
And in one case, it was really funny. The casino surveillance noticed that the dealer was dealing out the exact same set of cards each time. He had used the false shuffle. So somewhere
Robert J. Marks: Okay. Tell me about the false shuffle. Whats a false shuffle?
Sal Cordova: A false shuffle is where youre you look like you have actually shuffled the cards, but you didnt Theres a technique where you can make it look like you shuffled the cards, but you didnt. And so he was dealing out the same set of cards each time. Then they were realizing, why are the players so good at predicting what the next cards going to be?
All they had to do is take note of what the cards were. I dont know how they did that. And then the dealer would do a false shuffle and deal out the exact same sequence the next time. And when thats done, the player has huge advantage.
Sal Cordova: So the casino bosses began to be suspicious why a particular player was winning so well. Like he knew what the next card was going to be. They had casino surveillance and video cameras and they realized, oh wow, this is how it was being done. And the FBI came in and prosecuted the guys.
Sal Cordova: So those are the two big instances I know. And this is kind of interest to me because it starts to deal with issues of probability and kind of my areas of interest. Whats the chances that you could deal the same decor cards, the same way each time. And this relates to things in some of our interest in biology and stuff. And so I was just fascinated.
Robert J. Marks: So if I know Vegas, they had to come up with some sort of rule where the dealer doesnt shuffle or something like that. Is that true today? How are the decks shuffled for blackjack? Does the dealer shuffle them?
Sal Cordova: It depends on the casino. And in some places he would shuffle the deck and then put it in something called a shoe. And its dealt out from there There are all sorts of devices they can use to shuffle, or it can be hand shuffled. The preferred method, I think, would be machine shuffling because its faster. And it can randomize the cards to the standards that the casino would want.
Because some people are just savants, theyll actually memorize the sequence. And if they have a good understanding of the shuffling techniques they can start to in interleave it in their own brain. And then theyre able to predict.
Robert J. Marks: Do you ever watch the movie Rain Man (1988) with Dustin Hoffman? Well, hes a savant. And he goes in and theyre playing 21 and he keeps on saying Hit or Skip or something like that. So he knows whats going on.
Sal Cordova: People that can do that are called shuffle trackers. Theyre ACE trackers or card counters. And sometimes you would have teams. There are all these techniques
Sal Cordova: You mentioned the Law of Large Numbers and the casino always wins with the Law of Large Numbers. These players that are able to beat the game legally, we call advantage players. They actually turn the tables, figuratively speaking, and use the Law of Large Numbers in their favor.
Next: How advantage players at casinos use the Law of Large Numbers in their favor. They cant beat it so they join it.
Note: There is a history of mathematicians and physicists trying to beat the odds at Las Vegas casinos, perhaps largely for the fun of working with numbers. Sometimes they beat the dealer and even changed things in the long run. Watch for Claude Shannon (1916 2001), father of information theory, and probability theorist Edward Thorp (1932 ) to come up in this short account:
You may also wish to read: Does AI really get poker? Why that matters. Science journalist Maria Konnikova, also a professional poker player, explores the human side of poker and efforts to automate it. Those who hope that an algorithm can come along and solve the basic problem of uncertainty in life are kidding themselves.
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