Quantum blackjack strategy helps players beat the dealer

Technology News | August 5, 2020

By Rich Pell

In their work, say the researchers, they have shown that the weird, quantum effects of entanglement could theoretically give blackjack players even more of an edge than “card counting” techniques where players at a table work as a team to keep track of and covertly communicate amongst each other the cards they have been dealt. With that knowledge, the players can then estimate the cards still in the deck, and those most likely to be dealt out next – all to help each player decide how to place their bets, and as a team, gain an advantage over the dealer.

The card counting strategy was made famous by the MIT Blackjack Team, a group of students from MIT, Harvard University, and Caltech, who for several decades starting in 1979, optimized card counting and other techniques to successfully beat casinos at blackjack around the world — a story that later inspired the book “Bringing Down the House.”

The edge achieved from card counting can be increased, say the researchers, in a theoretical scenario in which two players, playing cooperatively against the dealer, can better coordinate their strategies using a quantumly entangled pair of systems. Such systems exist now in the laboratory, although not currently in forms convenient for any practical use in casinos.

In their study, the researchers found that such quantum communication would give the players a slight advantage compared to classical card-counting strategies, though in limited situations where the number of cards left in the dealer’s deck is low.

“It’s pretty small in terms of the actual magnitude of the expected quantum advantage,” says Joseph Lin, a former graduate student at MIT and first author of the paper on the study. “But if you imagine the players are extremely rich, and the deck is really low in number, so that every card counts, these small advantages can be big. The exciting result is that there’s some advantage to quantum communication, regardless of how small it is.”

Quantum “entanglement” is a phenomenon described by the rules of quantum mechanics, in which two physically separate objects can be “entangled,” or correlated with each other, in such a way that the correlations between them are stronger than what would be predicted by the classical laws of physics and probability. To ascertain if certain spatially remote particles or systems behave according to classical, real-world physics, or whether they may exhibit some quantum, entangled states, scientists use a “Bell test” – a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein’s concept of local realism.

“One motivation for this work was as a concrete realization of the Bell test,” says associate professor of physics Aram Harrow and paper co-author. “People wrote the rules of blackjack not thinking of entanglement. But the players are dealt cards, and there are some correlations between the cards they get. So does entanglement work here? The answer to the question was not obvious going into it.”

In their paper, the researchers simulated a simple blackjack setup involving two players – Alice and Bob – playing cooperatively against the dealer. They programmed Alice to consistently bet low, with the main objective of helping Bob, who could “hit” or “stand” based on any information he gained from Alice.

The researchers considered how three different scenarios might help the players win over the dealer: a classical card-counting scenario without communication; a best-case scenario in which Alice simply shows Bob her face-down card, demonstrating the best that a team can do in playing against the dealer; and finally, a quantum entanglement scenario.

In the quantum scenario, the researchers formulated a mathematical model to represent a quantum system, which can be thought of abstractedly as a box with many “buttons,” or measurement choices, that is shared between Alice and Bob. For example, if Alice’s face-down card is a 5, she can push a particular button on the quantum box and use its output to inform her usual choice of whether to hit or stand.

Bob, in turn, looks at his face-down card when deciding which button to push on his quantum box, as well as whether to use the box at all. In the cases where Bob uses his quantum box, he can combine its output with his observation of Alice’s strategy to decide his own move. This extra information – not exactly the value of Alice’s card, but more information than a random guess – can help Bob decide whether to hit or stand.

The researchers ran all three scenarios, with many combinations of cards between each player and the dealer, and with increasing number of cards left in the dealer’s deck, to see how often Alice and Bob could win against the dealer. After running thousands of rounds for each of the three scenarios, they found that the players had a slight advantage over the dealer in the quantum entanglement scenario, compared with the classical card-counting strategy, though only when a handful of cards were left in the dealer’s deck.

“As you increase the deck and therefore increase all the possibilities of different cards coming to you,” says professor of physics Joseph Formaggio and a co-author of the paper, “the fact that you know a little bit more through this quantum process actually gets diluted.”

Nevertheless, says Harrow, “it was surprising that these problems even matched, that it even made sense to consider entangled strategy in blackjack.”

As far as whether it will ever become practical for future blackjack teams to use quantum strategies to their advantage, that is an open question.

“It would require a very large investor,” says Formaggio, “and my guess is, carrying a quantum computer in your backpack will probably tip the house. We think casinos are safe right now from this particular threat.”

For more, see “Quantum blackjack: Advantages offered by quantum strategies in communication-limited games.”