In a recent podcast, “When the house can’t win the game, it will change the rules” (June 9, 2022), Walter Bradley Center director Robert J. Marks continued his discussion with mathematician, computer scientist, and engineer Salvador Cordova on the mathematics of gambling — who wins, who loses, and why. Last week, we looked at the struggle between the casino and the “advantage player” who knows very well how the system works and spots its weaknesses. But now, what about banning a suspiciously “lucky” would-be customer outright? Here’s what happened to Sal Cordova:

This portion begins at roughly 11:10 min. A partial transcript and notes, Show Notes, and Additional Resources follow.

Sal Cordova: One of the better things is that they ban addicted gamblers. Some of these gamblers that enter a program to kind of be in recovery, the casinos will cooperate with each other to say, “We’re going to make sure this guy doesn’t get in.” Unfortunately the casinos would love them to come back, but sometimes the city or state laws say, “Okay, you can’t set up a casino here unless you have a gambler’s recovery type program to help them with their addictions.”

So the casinos will comply. It’s like, “Okay, we want that license, so we’ll do it even though we’d really like to just get these guys, we’re going to meet them halfway.” Because advocacy groups will insist.

Robert J. Marks: But how do they monitor people? Like maybe a card counter or a gambling addict gets expelled. Do they do face recognition? Do they have a guy at the door that has memorized all these mugshots?

Sal Cordova: They use facial recognition now. And sometimes now you have to present your ID… Also, if you’re a frequent patron, the dealers would recognize you, the staff, so…

Robert J. Marks: But just like a card counter, you could casino hop, it seems to me.

Here’s how Sal Cordova got caught being an advantage player

Sal Cordova: Until they photograph you really well and then they circulate your photo — which they did to me. It’s called the surveillance information network; the acronym is SIN. So my photograph was circulated in the SIN network and one time I was in a casino in Michigan and got axed.

I drove 300 miles and I said, “They’re not going to get me there.”

Robert J. Marks: And they got you.

Sal Cordova: I walked in, I played a little bit. And they said, “Oh, well done, Mr. Cordova.”

Robert J. Marks: So what do they do, do they come up and tap you on the back?

Sal Cordova: Sometimes they’ll be subtle like that where they don’t want a physical confrontation. But if they really want you out, they’ll bring security and say, “Sir, may we have a word with you? We’ve determined that your action is too strong,” or they won’t even say anything but“Sir, may we have a word with you? Please step away from the table. You can cash your chips, but you’re not welcome to come in the casino anymore.” Or sometimes they’ll be half nice, they’ll say you’re welcome to play any other game, but you can’t play blackjack anymore.

Now, they have these tribal casinos around the land that are run by Indian reservations. And so they’re not subject to federal and state law. I mean, I’m sure that there’s some things that the states can do, but in those cases… one time I was taken aside by the casino security and then detained. And they said, “Well, it’s up to the tribal elders to decide your fate.”

Robert J. Marks: Oh my gosh. Because you’re not on US land, technically.

Sal Cordova: Exactly. I’m on the reservation. They let me go after they just kind of tried to intimidate me.

Robert J. Marks: Did it work? Oh yeah, I would imagine. I’d be fully intimidated.

Sal Cordova: It worried me for a little bit. B as long as they’re not going to draw their guns if I try to run away… what they did is they took my driver’s license and wouldn’t return it.

Robert J. Marks: Are you serious?

Sal Cordova: Yeah. They said, “Can I have your ID?” And then he just ran off with it. And I said, “Okay, I could walk out the casino, but I can’t drive my car back home.”

Robert J. Marks: So how’d you get your license back?

Sal Cordova: They came back 15 minutes later and said, “Okay, we’ll let you come back to the casino, but you can’t play blackjack the way you’re playing it.” When you bet you have to bet… Your starting bet has to be this… You can’t veer your bet.”

Because that’s how you beat it is when you’ve calculated the odds are favorable to you, then you raise your bet. So sometimes it’s very obvious if you’re a card counter you start off-betting $5.

Now there’s one guy, I saw it in Las Vegas, this was not on the tribal casino, but this is the ideal way to play it is you’re just betting the minimal amount or better yet, you’re just kind of standing at the table and watching the other players bet. And when what they call the “shoe” is hot, meaning it has a very high density of ACEs and tens.

Robert J. Marks: Okay. So you got all the bad cards out of the way.

Sal Cordova: Exactly. It’s independent trials, but in blackjack, the information you gather from the cards that are dealt out is telling you what’s remaining. So if it’s a “hot shoe,” meaning it’s rich in tens and ACEs, that’s the time to bet. This guy, he started betting $5 at a time. By the end of the deck, he was betting $1500. He knew the odds were in his favor. It was fun to watch him play.

So the countermeasure [the casino uses] is, “Well, we’re going to be nice. We’ll let you play blackjack, but you can’t veer your bet.” They call it “flat betting.” Whatever you start off with, you just got to keep betting that amount.

Robert J. Marks: Now what do they do to discourage card counting other than surveillance? …

How casinos change the rules to discourage advantage players

Sal Cordova: They’ve changed the rules, the payouts in the game. So it used to be, if you got a blackjack, it would pay three to two. You’d basically get 50%. So if you had a $10 bet, if you won, you’d normally get $10. But if you happen to have a blackjack, they’ll give you $15.

Robert J. Marks: I see. Okay.

Sal Cordova: The first thing they did is change the payouts in some games to six–five. You can’t beat that game with ordinary card-counting techniques. The other thing is tthese continuous shuffle machines where, after the dealer deals out the hands, they’ll put it right back in the shuffler.

Robert J. Marks: Oh, so the cards are returned and there’s an automatic shuffle and it’s just like a fresh deck all the time. And you can’t card count that.

Sal Cordova: Unless you have a full table where you might get a little bit of an advantage because you’ve seen some of the cards, you don’t have a very large advantage… The only time that I’ve known that the continuous shuffle machines were beaten is, again, because the casino made a marketing mistake. Like the loss rebates… The coupons were too generous. And somehow the advantage players got hold of all these coupons and they cleaned the casinos out for millions in Macau.

Robert J. Marks: That’s fascinating. They also use multiple decks now. They used to not use multiple decks, is that right?

Sal Cordova: You can count down multiple decks, I’ve done it.

Robert J. Marks: So how many decks can you count down?

Sal Cordova: I’ve counted down eight.

Robert J. Marks: Oh my gosh. And they also do surveillance. How does that work? They watch how you play and…?

Sal Cordova: They can watch how you play or they have a videotape of how you play and then they’ll put it through a computer and say, “Okay, these are the cards that were dealt out. This is how the player is betting and the way he’s playing his hand,” and the computer will do an evaluation. They’ll watch you play like through three shuffles, three shoes or three decks. And then they’ll say, “Okay, the odds of him doing this randomly are like that.” Otherwise…

Robert J. Marks: And they do this in real time, is that right?

Sal Cordova: No, no. Sometimes they’ll just do it just through video surveillance tape. That’s what they did to me when the tribal elders had… They reviewed the tapes and said, “This guy’s too good.”

Robert J. Marks: Tell us about the interesting players.

Top advantage players are a natural for the stock market

Sal Cordova: I think one of the most influential would be Bill Gross. He ran a gigantic hedge fund. I think he had an injury and so during his convalescence, he learned how to card count. And he went to Las Vegas for a year. They kicked him out, which probably was the best thing for his career. He went on to be a trading in bonds and he had the largest bond hedge fund. I think it managed, like, a trillion dollars.

And his saying was “The way we run our hedge fund is like playing blackjack every day. We’re always looking for advantages.”

There’s Russell Sands, who is a blackjack player and a backgammon player. He teamed up with Richard Dennis. Dennis started out with $400 or $1,400 and turned it into 400 million using mathematical techniques, I think he teamed up with a mathematician named [William] Eckhardt and they just made a killing. So there was a bet between him and someone else to say, “Can we actually make good futures trader or is it something that just is intuitive?”

He [Dennis, along with Eckhardt in 1983] formed what was called the Turtles. experiment. He gave volunteers this program of how to do futures trading, just very simple rules. And they obeyed it and they made a killing. Russell Sands was one of these Turtles.

Note: Hollywood has noticed. The film 21 (2008) “is the fact-based story about six MIT students who were trained to become experts in card counting and subsequently took Vegas casinos for millions in winnings.” – IMDB

Sal Cordova: Another one was Alan Woods. He made $2 billion in horse racing. He had computer analysis and he just made a killing off of it. During the crash of 2008, he had all these options bets on the NASDAQ market and he pulled out six weeks too early. He would’ve owned the NASDAQ figuratively speaking. They apply their casino skills to financial enterprises and some of them are quite successful.

Robert J. Marks: Let me ask you this, is there still an opening for an advantage player in Vegas? If a person is smart enough, could they go in and there’s still these loopholes where they could do be advantage players?

Sal Cordova: That’s a good question and I don’t know the answer. It’s been now about 10 years since I was kicked out. After I was kicked out, I went on to other things. The last time I went into a casino was just to use the restroom on my way to one of the conferences you and I attended actually out and there in West Virginia.

Online and live gaming vs. advantage players: It’s more difficult than formerly to be a successful advantage player, according to Michael Stevens in Casino & Gaming (July 10, 2020) because the computers that control online gambling are programmed “to stamp out any type of advantage play, such as card counting.” However, he suggests, “As with any other type of casino, you stand a better chance of winning with live gaming when choosing games with lower house edges. Baccarat, blackjack, and French roulette are your best bets in this regard. Baccarat features a 1.06% house edge when you bet on the banker hand winning. You can also enjoy a 1.24% house advantage when wagering on the player hand. French roulette offers a 1.35% house advantage. ”

That said, at Sydney News Today (December 22, 2021), Jack Martin writes, “Online casinos face a particular challenge in dealing with advantage players, as they can exploit a loophole in the system of random number generators to predict which cards will be dealt next. Online casinos have a lot less control over their games than land-based casinos, as they rely on third-party software to provide the rigged games that players have come to expect from casino gaming.”

It would appear that somewhere out there is still a nerd who will game the system.

Robert J. Marks: Well, we’ve been talking to Sal Cordova and next time I want to ask you about your career in card counting and I want a tutorial on how to card count, okay?

Next: Can you really be a card counter without resorting to magic?

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

• 00:31 | Recapping How Don Johnson Cleaned Out Atlantic City
• 02:48 | You Can Only Skin A Sheep Once
• 05:54 | What Happened to Don Johnson?
• 06:40 | How Does a Robot Win a Game of Poker?
• 08:25 | A Casino’s Greatest Fear
• 11:13 | When and Why Casinos Will Ban Someone or Throw Them Out
• 17:04 | Methods Casinos Use Beyond Surveillance
• 21:04 | Interesting Players
• 25:53 | Is There A Place For Advantage Players In Vegas?

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)
• Read More About The Robot Who Won A Game of Poker

Podcast Transcript Download