This last instalment of the writeup of the podcasts with mathematician, computer scientist, engineer — and part-time gambler — Salvador Cordova looks at why and how Christians like himself gamble without cheating. Cordova was one of the crowdfunders of a film on the topic called Holy Rollers (2011).

The host is fellow engineer and Walter Bradley Center director Robert J. Marks in “Card Counting Strategies and Dangers” (podcast, June 23, 2022):

This portion begins at 15:47 min. A partial transcript and notes, Show Notes, and Additional Resources follow.

Robert J. Marks: First of all, tell us what the movie was about, and then your involvement.

Sal Cordova: It’s about one of the most successful card counting teams, blackjack teams. They took the casinos for multimillions of dollars.

Now they didn’t use the Big Player model. What they would do is they would just send players in there with a lot of cash. They’d be throwing down these $10,000 bets or whatever. And if they got burned out and got kicked out, so be it, they’d bring another. It was a different style of play. It was just kind of, “We’ll just keep playing until they kick us out” type thing.

The idea was, use the Law of Large Numbers. But to have a team like that be successful, they had to be very honest because you’re going to give a guy $100,000. You expect him to report that if he really lost $100,000 versus just pocketing it, if he was being honorable. And that’s why the team was so effective, because everyone trusted each other and they were honest. They were pastors and elders.

Robert J. Marks: Pastors and elders. And typically they were on, well typically you have to work a second job for many ministry positions. And so I think that they figured, “Well, let’s not work a second job and go out and toil, let’s go to Vegas and card count.” And that’s a way that they earn their money. Is that right?

Sal Cordova: Exactly. And again, it’s the Exponential Law. They’re able to leverage that. So they didn’t start out with a lot of money, but because they kept reinvesting their bank, the collective bankroll got bigger and bigger and bigger till the point they were… I think their total winnings at the time, and this was some years ago, was three and a half million. In today’s dollars, would that be like 10 million?

Robert J. Marks: Do you know what they started with?

Sal Cordova: The head of the team probably had $700.

Robert J. Marks: That is the power of the exponential.

Sal Cordova: Now he was really lucky because that’s kind of a smallish bankroll. But I think his story was he was on food stamps at the time, and that was the only thing he could do. And he had a baby to feed.

Robert J. Marks: And plus he had a Christian ministry.

Why Christians have an advantage in gambling (not prayer, exactly)

Sal Cordova: So they found me and I was just very moved by the story, because I’m a Christian, and it’s really funny that the Christians have had a long history in advantage play. Partly because I think it’s the discipline of following the book. And to be a good, successful gambler, you want to follow rules and play by the book, so to speak … But that form of discipline extends to other areas of life. You play by the rules and you’re disciplined and …

Robert J. Marks: We’re taught to submit to authority, and that’s following the rules.

Sal Cordova: So if the computer says, “This is the optimal mathematical play,” you do it. And so it was that mindset. You also live a clean life. You don’t drink. And the idea really, honestly, you don’t gamble. Meaning if you play by the rules, you’re not getting a thrill out of throwing the money in there and kind of taking the risk.

You’re there because it’s a job. You’re doing this for the honor and glory of God, just like Father Fahey…

Robert J. Marks: Repeat that story. It’s been a few years…

Sal Cordova: Oh, yeah. Father Fahey was a Catholic priest. He was an MIT graduate in economics and he taught mathematics and economics. And always in his last class — that was so popular — he would say, “Okay. Now I’m going to teach you how to card count.” Being a Catholic priest, you have a vow of chastity and poverty. So he gave all his winnings away and he was able to get computers for a particular school that he was a part of…

Note: Fr. Joseph R. Fahey (1937–2002) was a Jesuit priest and math genius: “Garbed in his single blue suit, Fahey played blackjack tables from Atlantic City to Las Vegas, in his words ‘all for the greater glory of God,’ until the casinos blacklisted him … “Many Jesuit missions owe a great debt to him and his abilities at the card table,” said John Dunn, who worked for Fahey at Boston College High School … As president of Boston College High from 1988 to 1998, Fahey boosted the school’s endowment by 500%, financing an athletic center, library and computer laboratory.” – Obituary, Los Angeles Times (January 21, 2002)

Sal Cordova: So Christians have done well. I mentioned in one of the episodes, Keith Taft, who had the wearable computer, he was a Christian. And there are other Christians like Kevin Blackwood, and others. I don’t know why that is, but then you have the Holy Rollers and their story…

And I could identify with these people. I mean, there are moral issues that you deal with. “Is this the right thing to do?” It’s stuff that I dealt with. But for some of us, we felt like we’re hurting the casinos and they’re the bad guys.

Robert J. Marks: Well, they are the bad guys. I think one of the people in Holy Rollers said, “You know, the casinos say, ‘Come in, have fun, get rich.’ But if you go in, you have fun and you get rich, they kick you out. Right? Even, even by their own rules. And that just isn’t consistent.”

I’ve been at a casino once and I went in and it struck me. All of these people were figuring out ways to game the system. And some of them were so stupid. One guy was there pumping, I don’t know if it was quarters or tokens or whatever, into a machine. And every time he did it, he pulled the one-arm bandit, and then he put his hand across the screen, like that would increase his chances of winning. And it was clear he was doing that for some reason…

Sal Cordova: Superstitions…

How 17th century mathematicians invented the concept of probability we use today

Sal Cordova: Well, one thing that this influenced me is, there’s a theological thing called Pascal’s Wager. And I began to conceive of life this way, at a personal level. And then also I realized everyday life also has… you’re wagering on things where you have incomplete information and it’s kind of the benefit to cost the reward-to-risk ratios.

Note: Pascal’s Wager: “Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.” – – Britannica

Sal Cordova: And I began to view things very differently in other realms of my personal life, because I’d done this kind of semi-professionally. And it did affect the way I looked at the world and how to live my everyday life, and how to invest time, et cetera, and money and resources and things. I would say it affected my personal life in a very positive way. Ironically…

Robert J. Marks: Blaise Pascal, by the way, was the guy that, well, the metric unit for pressure is named after: pascal. He invented one of the first computers called the Pascaline … That’s the reason there was a computer language called Pascal.

Sal Cordova: I actually program in that. Yeah, I’m giving away my age here. Now I used to program in Pascal. I think that BASIC was my first language. Pascal is my second.

Robert J. Marks: Well, the other thing he did, with Pierre de Fermat, was create the world of probability. There’s a famous book called The Unfinished Game.

A series of letters between the great mathematician Fermat and Pascal … came up with probability. In a few years they had things like actuaries. They had insurance, because people could forecast the future in a probabilistic sense. And it’s so obvious to us now. But back then, the idea of talking about the future was just kind of ridiculous until Pascal and Fermat did it.

Sal Cordova: And I would add one other thing. It was Pascal that actually formulated a lot of the gambling stuff. The concept of expected value, that was Pascal. It reverberated through all of physics because a lot of quantum mechanics is expressed in terms of expected value. You’ll just see that the idea of notion of expected value.

Robert J. Marks: But Pascal had, I guess, what a Baptist would call a born-again experience. In fact, on his deathbed, they found some letters on him. Have you heard this? It was called the Night of Fire where he became a Christian. He recognized who Christ was and decided to follow him. And he wrote down a lot of his feelings from the Night of Fire, and they’re preserved for history. We can go back and read them. So from that point on, he spent all of his time in apologetics. For example, in doing Pascal’s wager, and just an astonishing man. And he died when he was 39…

Why you shouldn’t gamble — not for money anyway

Well, let’s get back to the topic. Final question. Somebody hearing this might go, I want to learn card counting and I want to go out and make big bucks. Do you have any advice for those sort of people?

Sal Cordova: I’d say don’t do it. Don’t do it. Your time is better spent elsewhere. But if you just love it for the game, get on a computer simulator. Because in a computer simulator, you could bet a million dollars and…

Robert J. Marks: Nobody cares.

Sal Cordova: … that you could feel. So that’s the advice I would give. There are a lot of gambles in life, if you really like gambling, which I hope you don’t. But there are plenty of places you can take risks. And so I would say take risks for the things that are of value in your life…

I can’t tell you where to take risks, but for me, take risks for good causes. Take risks for other people, to care for them. That’s where if I had to do it all over again, that’s where I would say, okay, I might give money to this charity or that charity, and it could be squandered, but that’s a worthy risk…

Robert J. Marks: Are you ever going to card count again?

Sal Cordova: I haven’t, since I got kicked out… I’m on the SIN network now, the surveillance information.

Robert J. Marks: You’ve been blackballed.

Sal Cordova: I’d have to sneak in in my pimp outfit if I want to do that. So no.

Robert J. Marks: You need something else. It’s out there now that you dress up as a pimp. So thank you, Sal.

Note: This information is intended for math nerds and people entertained by probability theory and 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.

Show Notes

• 00:07 | Introducing Sal Cordova
• 00:23 | Team Play
• 09:47 | The Big Player Model
• 15:47 | Holy Rollers
• 22:47 | Pascal and Gambling
• 26:17 | Final Question: Should you count cards?

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.
• More information on Keith Taft
• More on the movie 21
• More on the movie Rounders
• Who was Blaise Pascal?
• More on the movie Holy Rollers: The True Story of Card Counting Christians

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