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 — why the odds are stacked against the gambler — or, depending on a gambler’s skill and knowledge of the circumstances, maybe they aren’t…
This portion begins at approximately 00:31 min. A partial transcript and notes, Show Notes, and Additional Resources follow below.
Sal Cordova: He was very good at his craft.
Robert J. Marks: … he used comps in order to offset his probability of loss and was able to turn that to his advantage and won tens of millions of dollars. They had to have found him out because if I was him, I would keep on going until somebody kicked me out.
(Note: Comps are free games, kickbacks, etc., intended to keep players gambling.)
Sal Cordova: Well, probably even before they found him out, it was just… they were losing so much money. They said “We can’t afford to keep this guy here.” And I can’t believe that this is such obvious, basic math. So the comps that he was offered was a loss rebate. So he was playing a losing game of blackjack. But again, going back to the Law of Large Numbers, his loss rate was only half a percent. And they’re giving him loss rebates of 10 to 20%.
Robert J. Marks: Was he card counting?
Sal Cordova: No, no. He was doing what they call basic strategy, which going back to Edward Oakley Thorp and his predecessors.
Note: Edward Oakley Thorp is a retired math professor who has also beat the numbers in casinos and offered investment strategies. A book has been written about his exploits, A Man for All Markets (2017). In the following video, he explains the view that Wall Street is “the biggest casino in the world.”
Sal Cordova: They figured out that if you play your hands just a certain way — if the dealer has a certain card and you have your set of cards. In 21, it’s what they call “hit” or “stand.” “Hit” means you draw another card and you hope you don’t go over 21 (what we call “busting”). Or you “stand” — where you just say, “I’m not going to take any cards.” In fact, the casinos will even give you the playbook… It’s just like a little index card with all the proper plays.
Robert J. Marks: Do they give you probabilities with them?
Sal Cordova: No, they’ll just say this is the optimal way: If the dealer has this card, you play it.
And I said, “That’s really nice of them.” But you see that’s that’s…
Robert J. Marks: So you still end up losing. If I remember right from a freshly shuffled deck, your loss is what in blackjack?
Sal Cordova: It’s on average about half a percent if you use this optimal strategy that even the casinos will give you. Now, you think that they’re being nice…
There’s an old saying, you can shear the sheep many, many times. You can only skin him once.
Robert J. Marks: I’d never heard that. That’s a good one. Okay.
Sal Cordova: They realize that they could get repeat customers if you don’t hurt them too bad. You let them have some good times, they’ll keep coming… it’ll add to the atmosphere of the casino.
So what Don Johnson was doing, he was just playing basic strategy… Now he was a very good con artist. He would look like he was a loser. He did things that he made him look like a degenerate, all the girls and stuff surrounding him and just, kind of, his mannerisms. But he was hiring actors, so he …
Robert J. Marks: He hired actors?
Sal Cordova: Adult movie actresses. That’s the reports I read.
Sal Cordova: So he looked like a real degenerate and he acted the part real well. But he was playing just basic strategy. It was another department that they weren’t monitoring that was giving him all these loss rebates and so he cleaned them out.
Robert J. Marks: So let me ask you this, casinos learn from their mistakes and they fix them. I understand today, they have to very carefully balance the roulette wheel. There’s no more tilts. We talked about shooting craps last time and how you have to shoot craps right now where you can do no dice sliding. How did they get rid of this thing that let Don Johnson win all these big bucks?
Sal Cordova: I think they had to lose enough money and they came to their senses. But, like a lot of organizations, you have pockets of total incompetence in one department, and it’s going to negate all the skill and diligence in another. And so this is what happened. The marketing department was out of sync with quality controls and the accounting and was just managing expectation values. And Don Johnson somehow sniffed that out.
The marketing department was not really looking after the bottom line like they should have and someone was asleep at the wheel… But the funny thing is, multiple casinos began to compete [by offering similar incentives]. I guess they figured, “Oh, they’re doing it so we ought to do it too.” And apparently they weren’t too sharp, so…
Robert J. Marks: I’m wondering, do they still offer comps? I think they would’ve gotten rid of that.
Sal Cordova: Well, unfortunately for advantage players, Don Johnson decided to keep making some more bucks, so he started to become a consultant to these casinos. How not to do stuff like that. And so his fellow advantage players were kind of mad at him for that.
Robert J. Marks: It’s like a hacker that gets caught, goes to work for the NSA or the FBI.
Sal Cordova: Exactly. Again, like a lot of organizations, they’ll have pockets of competence and little pockets of incompetence and this is where it hurt the casino. An advantage player is always looking for that — where someone probably in the higher-ups made a really dumb mistake.
Robert J. Marks: Looking for the weakest link. I used to think that the game of poker involved skill until an artificial intelligent program named Pluribus beat the world champions at Texas hold’em, which really surprised me.
I thought there was so much psychology in the game of poker. But the fact that an algorithm could beat the world champions in Texas hold’em … really fascinated me that there was really minimal contribution to psychological aspects of the game.
Sal Cordova: Because I don’t have a poker face, people can read me really easily. I’ve never touched that realm at all, but there are some people that are very good at reading other people, the reactions to the hands that they’ve been dealt and their bluffing patterns.
Robert J. Marks: Does that surprise you too, that an algorithm…
Sal Cordova: That actually does surprise me a lot. So I could only assume that the algorithm was keeping track of bluffing patterns of its opponents.
Robert J. Marks:. I don’t know the details but anyway, they taught it to do it and that to me was just astonishing.
Let’s talk about gaming oversight … What are they looking for?
Sal Cordova: One of the first things is game protection, meaning the casinos want to make sure that their own employees are not stealing.
Robert J. Marks: Oh, you mentioned that to me, that their biggest fear is that the dealers for example, are going to stick a few bucks in their pocket, right?
Sal Cordova: Or up their sleeve. And there’s one casino in Tunica, Mississippi, where the boxman –- the head of the craps table — would take these thousand-dollars chips and put it in his sleeve or something very discreetly. And then somehow he would put it in his mouth and then kiss an employee and transfer the chip. His girlfriend employee. And so for a while, surveillance was having a hard time figuring out how he…
Also, they try to protect the patrons in case one patron is trying to steal money from another. I do have some stories about that. Some of these ladies would come up to you and if you have a big pile of chips, they’d start to be really cozy with you. I would have to put my hands around my chips because I didn’t want her stealing it. They call them “rail bandits.”
Sometimes they’ll cozy up or they’ll try to say, “Hey, can you spare a chip here or there?” And so surveillance will be watching some of this…
Robert J. Marks: And do the casinos discourage you from giving stuff to these ladies, to these rail bandits?
Sal Cordova: They try to discourage the women from being there if they figured out who they are.
Robert J. Marks: Do they have the ability to ban people from casinos?
Next: Can casinos ban would-be customers who might get TOO “lucky”?
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.
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.
- 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?
- 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