Quantum Blackjack
August 4, 2020
Study finds quantum entanglement could, in principle, give a slight advantage
in the game of blackjack
In some versions of the game blackjack, one way to win against the house is for
players at the table to work as a team to keep track of and covertly communicate
amongst each other the cards they have been dealt. With that knowledge, they 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.
This calculating strategy, known as cardcounting, 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 cardcounting and other
techniques to successfully beat casinos at blackjack around the world  a story
that later inspired the book "Bringing Down the House."
Now researchers at MIT and Caltech have shown that the weird, quantum effects of
entanglement could theoretically give blackjack players even more of an edge,
albeit a small one, when playing against the house.
In a paper published this week in the journal Physical Review A, the researchers
lay out 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 in forms convenient for any practical use in casinos. In their study, the
authors nevertheless explore the theoretical possibilities for how a quantum
system might influence outcomes in blackjack.
They found that such quantum communication would give the players a slight
advantage compared to classical cardcounting 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 first author Joseph Lin, a former graduate student at MIT. "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."
Lin's MIT coauthors on the paper are professor of physics Joseph Formaggio,
associate professor of physics Aram Harrow, and Anand Natarajan of Caltech, who
will start at MIT in September as assistant professor of electrical engineering
and computer science.
Quantum dealings
Entanglement is a phenomenon described by the rules of quantum mechanics, which
states that 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.
In 1964, physicist John Bell proved mathematically that quantum entanglement
could exist, and also devised a test  known a Bell test  that scientists
have since applied to many scenarios to ascertain if certain spatially remote
particles or systems behave according to classical, realworld physics, or
whether they may exhibit some quantum, entangled states.
"One motivation for this work was as a concrete realization of the Bell test,"
says Harrow of the team's new paper. "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."
After casually entertaining the idea during a regular poker night with friends,
Formaggio decided to explore the possibility of quantum blackjack more formally
with his MIT colleagues.
"I was grateful to them for not laughing and closing the door on me when I
brought up the idea," Formaggio recalls.
Correlated cards
In blackjack, the dealer deals herself and each player a faceup card that is
public to all, and a facedown card. With this information, each player decides
whether to "hit," and be dealt another card, or "stand," and stay with the cards
they have. The goal after one round is to have a hand with a total that is
closer to 21, without going over, than the dealer and the other players at the
table.
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 cardcounting scenario without communication; a
bestcase scenario in which Alice simply shows Bob her facedown card,
demonstrating the best that a team can do in playing against the dealer; and
lastly, 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 instance, if Alice's facedown 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 facedown 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 cardcounting 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, the fact that you know a little bit more through
this quantum process actually gets diluted," Formaggio explains.
Nevertheless, Harrow notes that "it was surprising that these problems even
matched, that it even made sense to consider entangled strategy in blackjack."
Do these results mean that future blackjack teams might use quantum strategies
to their advantage?
"It would require a very large investor, and my guess is, carrying a quantum
computer in your backpack will probably tip the house," Formaggio says. "We
think casinos are safe right now from this particular threat."
