In this week’s 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, there’s a theorem called the Law of Large Numbers. It teaches that you can’t win in the long run at casino games. Period. The law of large numbers is a mathematical truth. It’s a law as serious as the law of gravity. It’s 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 there’s also a chance you will get hit by falling space debris while juggling.”

He adds, for good measure, “I tell people it’s better if you give your money to me and I’ll 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.

Before we get started: Note: Robert J. Marks, a Distinguished Professor of Computer and Electrical Engineering, Engineering at Baylor University, has a new book, coming out Non-Computable You (June, 2022), on the need for realism in another area as well — the capabilities of artificial intelligence. Stay tuned.

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 one’s 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 you’re not really going against the rules of how to actually play your hands or anything. So I’ve really not looked much into the techniques of cheating because I just didn’t 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 can’t do that in Las Vegas anymore, right?

Sal Cordova: Not anymore. They actually passed a law. It’s 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 couldn’t dice slide. But then on top of that, the casinos began to put down felt [on the tables] so that the dice wouldn’t 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 it’s 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 you’re really well practiced at this, you only needed to tilt the odds. Even you didn’t 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: It’s not that I sat down one day and decided I wanted to cheat. It’s 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. It’s 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,” it’s the card that the players aren’t supposed to see.

So the player will make playing decisions based on knowledge he’s not supposed to have. He has a huge advantage. In blackjack, the dealer has what they call a whole card (the card you can’t see). And after you’ve finalized your decision as a player, then he’s going to reveal it. And then you find out whether you’re going to win or lose.

Robert J. Marks: And probably he didn’t 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. What’s a false shuffle?

Sal Cordova: A false shuffle is where you’re you look like you have actually shuffled the cards, but you didn’t… There’s a technique where you can make it look like you shuffled the cards, but you didn’t. 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 card’s going to be?

All they had to do is take note of what the cards were. I don’t 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 that’s 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. What’s 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 doesn’t 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 it’s 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 it’s faster. And it can randomize the cards to the standards that the casino would want.

Because some people are just savants, they’ll 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 they’re able to predict.

Robert J. Marks: Do you ever watch the movie Rain Man (1988) with Dustin Hoffman? Well, he’s a savant. And he goes in and they’re playing 21 and he keeps on saying “Hit” or “Skip” or something like that. So he knows what’s going on.

Sal Cordova: People that can do that are called shuffle trackers. They’re 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 can’t beat it so they join it.

Note 1: 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:

Note 2: This information is intended for math nerds and people entertained by statistics. It is not directed at anyone who has a gambling addiction. For help, see Gamblers Anonymous.

Here are the writeups (with partial transcripts, notes, and links) of all the podcasts with gambling maven Sal Cordova:

Gambling: WHY the house always wins in the long run… The casinos are not cheating. They rely on the Law of Large Numbers, part of the mathematical structure underlying our universe. Robert J. Marks and fellow engineer and mathematician Sal Cordova look at the many creative methods gamblers use to improve their odds.

Casinos: How nerds gamble and win, using the Law of Large Numbers The American Physical Society created Las Vegas’s worst week in history and Don Johnson cleaned out Atlantic City. How? Sal Cordova explains to Robert J. Marks how nerd gamble and win, mainly by deciding whether to play at all and, if so, how to manipulate the house’s strategies.

The struggle between casinos and advantage players The scene is enlivened by assorted other characters who use romance to help in the struggle for a big win. Sal Cordova explains. Often the advantage player, who astounds us by seemingly beating probability, is taking advantage of the casino’s upper management’s weaknesses.

Can casinos ban would-be customers who might get TOO “lucky”? Sal Cordova was good enough at card counting that his photo was circulated and the casino nabbed his driver’s licence… But as casinos slowly eliminate loopholes, “math whiz” advantage players seem to find others.

Can you really be a card counter without resorting to magic? Math nerd (and successful gambler) Salvador Cordova explains how card counters improve their odds in blackjack. Successful card counting strategy originated in a theory out of Bell Labs and also found its way into hedge fund management.

Probability: Now for the basic arithmetic of card counting… The advantage player who dresses like a bum (or worse) has it all worked out, in part with the help of a computer at home. Sal Cordova tells Robert J. Marks that mathy pro gamblers could retire after a year, using the Exponential Growth Law, but casinos spot them and kick them out.

Gambling: And when advantage players team up, dealer beware! On the other hand, the movie industry has made a good thing from films of the legendary exploits. Sal Cordova details for Robert J. Marks odd strategies he and other advantage players use to win via the Law of Large Numbers — until they’re found and ejected.

and

The Holy Rollers: Christians who gamble for God. Not only have many successful players been Christians, probability theory was developed in part by a philosopher who became a devout Christian. Strange as it might seem, the successful Rollers were not really “gambling”; they followed the Law of Large Numbers — and the computer — obediently.

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.

Show Notes

• 01:06 | Introducing Sal Cordova
• 03:11 | The Famous Team: Claude Shannon and Edward Oakley Thorp
• 06:58 | Is There a Good Way to Cheat in a Casino?
• 14:31 | Shuffle Trackers
• 19:51 | Is There Such a Thing as a Winning Streak?
• 21:27 | Don Johnson the Whale

Additional Resources

• Thorp, Edward. “A favorable strategy for twenty-one.” Proceedings of the National Academy of Sciences of the United States of America 47.1 (1961): 110.
• “The Man Who Broke Atlantic City” at The Atlantic (more information about Don Johnson)
• More information about Claude Shannon
• More information about Edward Oakley Thorp

Podcast Transcript Download