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.
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.
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.
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."
This research was funded, in part, by the National Science Foundation, the Army Research Office, the U.S. Department of Energy, and the MIT Undergraduate Research Opportunities Program (UROP).
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Whether or not women think beards are sexy has to do with "moral disgust"
- A new study found that women perceive men with facial hair to be more attractive as well as physically and socially dominant.
- Women tend to associate more masculine faces with physical strength, social assertiveness, and formidability.
- Women who display higher levels of "moral disgust," or feelings of repugnance toward taboo behaviors, are more likely to prefer hairy faces.
Beards and perceptions of masculinity<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjU5OTg0MC9vcmlnaW4uanBnIiwiZXhwaXJlc19hdCI6MTY0NzkxMjM3N30.cH-GqNwP5GVqvstgJWAhBPn1B_lYpVEAI0I7iax7EQw/img.jpg?width=1245&coordinates=0%2C1900%2C0%2C849&height=700" id="caae6" class="rm-shortcode" data-rm-shortcode-id="cb0a355a4e8e1899789bc45f3f7aef56" data-rm-shortcode-name="rebelmouse-image" />
Photo Credit: Wikimedia<p>The study used 919 American (mostly white) women ages 18-70 who rated 30 pictures of men they were shown with various stages of facial hair growth. The photographs depicted men with faces that had been digitally altered to look more feminine or more masculine, with a beard and without a beard. The women rated the men according to perceived attractiveness for long-term and short-term relationships. The study found that the more facial hair the men had, the higher the men were rated on their attractiveness, particularly for their suitability for a long-term relationship.</p><p>Part of this might be attributed to facial masculinity — i.e. protruding brow ridge, wide cheekbones, thick jawline, and deeply set narrow eyes — which conveys information to a woman about a man's underlying health and formidability. Women tend to associate more masculine faces with physical strength and social assertiveness. It can also indicate a man with a superior immune response. The researchers suggested that their findings favoring bearded men could be due to the fact that facial hair enhances the masculine facial features on a man's face, like creating the illusion of a thicker jaw line. This could communicate direct benefits to women like resources and protection that would enhance survival among mothers and their infants. In other words, while a beard doesn't mean superior genetics in and of itself, it might be a primitive, ornamental way of saying, "Hey girl, I'm a testosterone-fueled lean, mean, pathogen fighting machine." <br></p><p>It could also be that a beard becomes its own destiny. The researchers in this study cite prior research that found that by growing a beard, men felt more masculine and had higher levels of serum testosterone, which was linked to a higher level of social dominance. They also tended to subscribe to more old-school beliefs about gender roles in their relationships with women as compared to men with clean-shaven faces.<span></span><br></p>
What does disgust have to do with beard preference?<p>Obviously, not all women dig beards. The researchers were particularly interested in what traits make a women prefer bearded men over clean-shaven faces. They looked into several factors including a woman's disgust levels on various concepts, her desire to become pregnant, and her exposure to facial hair in her personal life. </p><p>According to the study, women who were not into facial hair were turned-off by potential parasites or other critters they imagined could be in the hair or skin. Women ranking high on this "ectoparasite disgust" scale might have viewed beards as a sign of poor grooming habits. However, women who ranked higher in levels of "pathogen" did find the bearded men to be desirable, possibly because they perceived beards as a signal of good health and immune function. An intriguing discovery in the study was links to morality. Women who displayed higher levels of "moral disgust," or feelings of repugnance toward taboo behaviors, were more likely to prefer hairy faces. The authors opined that this could reflect a link between beardedness, politically conservative outlooks, and traditional views regarding performances of masculinity in heterosexual relationships.</p>
Additional findings<img type="lazy-image" data-runner-src="https://assets.rebelmouse.io/eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpbWFnZSI6Imh0dHBzOi8vYXNzZXRzLnJibC5tcy8yMjU5OTg1My9vcmlnaW4uZ2lmIiwiZXhwaXJlc19hdCI6MTYyNDI1NjUyOX0.P9B8WbmJR0q4nfzYZKbuNSA-2SAigVWJgrQE-_Gxlds/img.gif?width=980" id="49143" class="rm-shortcode" data-rm-shortcode-id="2ed3b1d6f20fc170bf2974646e565e8d" data-rm-shortcode-name="rebelmouse-image" />Giphy<p>The correlations that existed between married and single women's rating on the attractiveness of beards were not particularly clear, although the researchers noted that single and married women who wanted children tended to find beards more attractive than the women who didn't want children. They also found that women with bearded husbands found beards to be more attractive, which might indicate that social exposure to beards influences how desirable they are perceived of as being. Or it could be that men with wives who like beards grow beards.</p><p>It's important to note that culture plays a huge role in how attractive women perceive certain male characteristics as being. This study looked at a small, culturally specific group of American women, so no big, universal claims should be made about masculinity, facial hair, and male desirability to women. However, research like this is important in highlighting how human grooming decisions are driven by much more than fashion trends. Sociobiological, economic, and ecological factors all play a part in the way we choose to present ourselves.</p>
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