Walter Bradley Center director Robert J. Marks is back with Salvador Cordova, a mathematician, engineer and gambling ace. which include gambling, players, management and mathematical probabilities – sometimes clean up casinos. Of course, they are also sometimes expelled, as happened in Cordoba, and new rules and precautions ensue. And, no doubt, new paths lie around them.
In this new podcast episode, “Can a Good Scammer Count Cards Like a Computer?”, Cordova talks a bit more about how pros improve their odds by sheer luck counting cards. He made his living, in part, this way from around 2005 to 2014.
This game starts at 00:36 min. A partial transcript and notes, View Notes and additional resources follow.
Sal Cordoba: On weekends, I went to the casino. My father had passed away and it was a chance for me to just decompress, by running the long distances, my way of coping. It really wasn’t that profitable; it was more or less a side hustle. Professionals, they must be good crooks. I was not.
Robert J. Marks: They must be actors, I guess. Right?
Sal Cordoba: Very good actors. Persuading the casinos that they are degenerate gamblers. I was walking into it and I think people knew right away. I stood out a bit. I looked like a scholar and spoke like one.
If you walk around in there and look like you have a brain, it’s like you’re automatically under suspicion.
Robert J. Marks: I want you to give us a tutorial on card counting, but before I do… is it hard? We talked before and you said, “It’s like playing the piano. You just need to figure out which keys to hit when. But you don’t become a grand piano master by determining which keys to hit at the right time. It’s not as simple as that.
Sal Cordoba: It’s correct. It’s like saying, “Playing tennis is just returning the ball that hit you.”
I’m obviously exaggerating, but if one wanted to count cards, there are computer simulations that will teach you, test your abilities, and grade you…
Robert J. Marks: So they use computers to generate the card count… I thought Thorp did it in 1961 just by looking at the calculations.
Sal Cordoba: To correct. And this counting system was brutally difficult… Now, one of the major roles of the computer was to come up with an estimation system that a human could actually run.
Robert J. Marks: To do this, you need to have good short-term and maybe even long-term memory. Is it correct?
Sal Cordoba: A good short-term memory. [You] must in fact be reasonable in arithmetic.
So I’m going to give you the counting system I used. But it was developed by the computer. It will estimate the optimality of your heuristic. Since you are a computer scientist, maybe you could explain what heuristics are.
Robert J. Marks: It’s just an intuitive algorithm. It’s the one you create through the bottom of your pants and your experience, your life experience.
Sal Cordoba: Right. So it was just an estimation system. As for the optimal bet to offer, that’s 99% accurate. In terms of your optimal hand play, it’s 75%. …
Again, with the law of large numbers and the value of expectation, if the theoretical edge was, say, 2%, you could get 1.5%, which is enough to bring casinos to their knees. they let you play long enough.
Because what ends up happening is that when you keep making money, you have a law of exponential growth. And that’s why they want to nip it in the bud. You could start with $10,000 in what they call your bankroll… They’re not worried if you’re still small scale, but some of these guys will take their bankroll from $10,000 to millions. And then they start to become a real threat to casinos.
Robert J. Marks: One of the challenges is that if you have a bankroll, you have to be very careful in how you stake it. For example, you don’t want to put your entire bankroll on a single bet. And I learned this… I was at a company called Financial Neural networks, and there’s this risk, this security trade-off. You have a balance between the risk you take and the amount of money you earn. And the risk was a big choppy curve. It went up, but it went up, it went down, it went up, it went down and you made a lot of money with a lot of risk. Whereas if you made a mistake on the security side, it increased very gradually, but not as much.
And one of the things that I found out, which is obvious once you know this, is that if you jump up and down and that curve hits zero, you’re done.
Sal Cordoba: Right. This is called player ruin.
Sal Cordoba: And in fact, it was an important theoretical result of John Kelly who was also working with Bell Labs – a guy from MIT, so there must have been a connection at that time between Bell Labs and MIT.
It was a feat. And it’s actually very simple. If your edge is, say, 1%, approximately the maximum you should bet on a bet is 1%. Beyond that, you start to lose efficiency. And if you double it, you will go to ruin. That’s why we call it not overbidding.
And preferably, if you wanted to limit that variability, you’d only do fractions of what they call “the Kelly.” So when they say “full Kelly” you’re at your maximum growth, but you’re going to have too much variance.
Sal Cordoba: Thus professionals will often operate at a quarter of a Kelly or an eighth of a Kelly. Then hedge fund managers realized they could actually import these ideas into managing their hedge funds. That’s why it’s really nice to see the casino math play out like this… Just Google Kelly’s criteria.
And another way to frame it, in terms of raw metrics only, is expected value versus variance. They call it the pointed ratio: you divide the expected value by the variance or vice versa…
So back to actual card counting, they formulated using computers all these different counting methods, but I’ll give you the one I used.
Robert J. Marks: So there are many ways to count cards, right? And probably some are more difficult and require more memory than others.
Sal Cordoba: Right. The simplest are just one account. And I will explain to you how it is. So let’s say you keep a running sum. So if you see a certain card, like an ace or an eight in the Advanced Omega II system… that’s the one I used.
Robert J. Marks: Is that the card counting system you use, Omega II?
Sal Cordoba: Right. If you see an ace or an eight, you simply add zero to your running total…
Next: With basic theory out of the way, card counting arithmetic
To note: This information is intended for math enthusiasts and people amused by probability theory and statistics. It is not for anyone with a gambling addiction. For help, see Gamblers Anonymous.
You can also read: Can casinos ban potential customers who might be TOO “lucky”? Sal Cordova was good enough at counting cards that his picture circulated and the casino nabbed his driver’s license… But as casinos slowly close loopholes, “mathematician” advantage gamblers seem to be finding others.
Here are the debriefs (with partial transcripts, notes, and links) from previous podcasts with gaming maven Sal Cordova:
Gambling: WHY the house always wins in the long run… Casinos don’t cheat. 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 examine the many creative methods players use to improve their odds.
Casinos: How Nerds Play and Win Using the Law of Large Numbers The American Physical Society created the worst week in Las Vegas history and Don Johnson cleaned up Atlantic City. How? Sal Cordova explains to Robert J. Marks how nerds gamble and win, primarily deciding whether or not to gamble and, if so, how to manipulate house strategies.
The fight between casinos and advantage players The scene is animated by various other characters who use romance to help in the fight for a big win. explains Sal Cordova. Often the advantage player, who surprises us by seemingly beating the odds, takes advantage of weaknesses in the casino’s upper management.
- 00:06 | Introducing Sal Cordova
- 00:36 | What does it take to be a good Hustler?
- 01:45 | A lesson in card counting
- 15:07 | You have to be a good actor
- 16:58 | How to use your teeth as a keyboard
- 19:28 | Blackjack Books
- 21:56 | If you try to beat the game, you could be arrested
Download the podcast transcript