Walter Bradley Center director Robert J. Marks is back withSalvador Cordova, mathematician, engineer — and gambling ace. In previous episodes, they discussed why most players lose and how “advantage players” — those who understand the game, the players, the management, and the mathematical probabilities — sometimes clean out casinos. Of course, they also sometimes get kicked out, as has happened to Cordova, and new rules and precautions ensue. And, doubtless, new ways are found around them.
In this new podcast episode, “Can a good hustler count cards like a computer?”, Cordova says a bit more about how the pros improve their odds from pure chance by card counting. He made his living, inpart, that way from about 2005 through 2014.
This portion begins at 00:36 min. A partial transcript and notes, Show Notes, and Additional Resources follow.
Sal Cordova: On the weekends, I would go to the casinos. My father had passed away and it was a chance for me to just decompress, driving the long distances, my way of coping. It really wasn’t that profitable; it was more or less a side hustle. The professionals, they have to be good con artists. I was not.
Robert J. Marks: They have to be actors, I guess. Right?
Sal Cordova: Very good actors. Persuading the casinos that they’re degenerate gamblers. I would walk in there and I think people knew right away. I kind of stood out. I looked like a scholar and I spoke like one.
If you wander in there and you look like you have brains, it’s like, yeah you’re automatically under suspicion.
Robert J. Marks: I want you to give us a tutorial in card counting, but before I do… how difficult is it? We talked before and you said, “It’s just like playing the piano. You just got to figure out which keys to touch at what time.” But you don’t get to be a concert pianist grand master by figuring out which keys to touch at the right time. It’s not as simple as that.
Sal Cordova: That’s correct. It’s like saying, “Playing tennis is just returning the ball that’s hit to you.”
I’m exaggerating obviously, but if one wanted to card count, there are computer simulations out there that will teach you, examine your ability and grade you…
Robert J. Marks: So they use computers to generate card counting… I thought Thorp did it in 1961 just by looking at the math.
Sal Cordova: Correct. And that counting system was brutally difficult… Now, one of the major roles of the computer was to find an estimation system that a human could actually execute.
Robert J. Marks: You have to have a good short term and maybe even long term memory in order to do this. Is that right?
Sal Cordova: A good short term memory. [You] actually have to be reasonable at arithmetic.
So I’m going to give you the counting system that I used. But this was developed by the computer. It’ll estimate the optimality of your heuristic. Maybe, since you’re a computer guy, you could explain what heuristics are.
Robert J. Marks: It’s just an intuitive algorithm. It’s one you make up by the seat of your pants and your experience, your life experience.
Sal Cordova: Right. So it was just an estimation system. In terms of what would be the optimal bet to put forward, it’s 99% accurate. In terms of the optimal play of your hands, it’s 75%. …
Again, with the Law of Large Numbers, and expectation value, if the theoretical advantage were, say 2%, you could get 1.5% percent, which is enough to put the casinos on their knees if they let you play long enough.
Because what ends up happening is, as you keep winning money, you have an exponential growth law. And so that’s why they want to nip it in the bud. You could start out with $10,000 in what they call your bankroll… They’re not worried if you’re still at the small scale, but some of these guys will grow their bankrolls from like $10,000 to millions. And then they start to become a real threat to the casinos.
Robert J. Marks: One of the challenges is if you have a bankroll, you have to be very careful in the way that you bet it. For example, you don’t want to put your entire bankroll down on one bet. And I learned this… I was in a business called Financial Neural networks, and there’s this risk, security trade off. You have a balance between the risk that you take and the amount of money you make. And the risk was a big choppy curve. It went up, but it shot up, it shot down, it shot up, it shot down and you made lots of money with lots of risk. Whereas if you erred on the side of security, it went up very gradually, but not as much.
And one of the things I found out, which is obvious once you know it, is that if you’re jumping up and down and that curve hits zero, you’re done.
Sal Cordova: Right. That’s called Gambler’s Ruin.
Sal Cordova: And actually this was an important theoretical result by John Kelly who also worked with Bell Labs — an MIT guy, so there must have been some connection in that era between Bell Labs and MIT.
This was an achievement. And it’s actually very simple. If your advantage is, say, 1%, approximately the most you should bet on any one bet is 1%. Beyond that you start to lose efficiency. And if you double it, you’ll go to ruin. So we call it not overbetting.
And preferably, if you wanted to limit that variability, you would only do fractions of what they call “the Kelly.” So when they say “full Kelly,” you’re at your maximum amount of growth but you’re going to have too much variance.
Sal Cordova: So the professionals will often operate at quarter Kelly or one eighth Kelly. Then hedge fund managers realized they could actually import those ideas into management of their hedge funds. This is why it’s really nice to see the casino math play out like that … Just Google Kelly criterion.
And another way of framing it, in terms of just raw metrics, is the expected value versus the variance. They call that the sharp ratio: You divide the expected value by the variance or vice versa…
So back to the actual card counting, they formulated using the computers all these various counting methods, but I’ll give you the one that I used.
Robert J. Marks: So there’s a number of ways to card count, right? And probably some are more difficult and require more memory than others.
Sal Cordova: Right. The simpler ones are just a single count. And I’ll explain how that 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 that I’ve used.
Robert J. Marks: That’s the card counting system you use, Omega II?
Sal Cordova: Right. If you see an ace or an eight, you just add zero to your running total…
Next: With basic theory out of the way, the arithmetic of card counting
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.
You may also wish to read: 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.
Here are the writeups (with partial transcripts, notes, and links) of the previous 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.
- 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
- 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.
- Read more about the robot who won a game of poker
- The Theory of Blackjack by Peter A. Griffin at Amazon.com
- Blackjack for Blood by Bryce Carlson at Amazon.com