Blackjack: Can a quantum strategy help bring down the house?
Study finds quantum entanglement could, in principle, give a slight
advantage in the game of blackjack

Date:
August 3, 2020
Source:
Massachusetts Institute of Technology
Summary:
Now researchers 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.



FULL STORY ==========================================================================
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 card-counting, 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."
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 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 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 co-authors 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, real-world 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 face-up card that is public to all, and a face-down 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 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 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 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, 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."

========================================================================== Story Source: Materials provided by
Massachusetts_Institute_of_Technology. Original written by Jennifer
Chu. Note: Content may be edited for style and length.


========================================================================== Journal Reference:
1. Joseph X. Lin, Joseph A. Formaggio, Aram W. Harrow, Anand
V. Natarajan.

Quantum blackjack: Advantages offered by quantum strategies in
communication-limited games. Physical Review A, 2020; 102 (1)
DOI: 10.1103/PhysRevA.102.012425 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/08/200803105235.htm

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