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One of the most important strategies in poker is the art of bluffing, in which a player makes or raises a bet without having the best hand, in order to fool an opponent into folding. "People often think about bluffing as being a psychological phenomenon," Sandholm said. But beyond psychology, "bluffing still emerges as a strategic phenomenon," he said.

Sandholm and his colleagues didn't pre-program Claudico's poker strategy. They wrote algorithms that automatically compute a strategy by trying to find the Nash equilibrium. This concept from game theory was developed by American mathematician John Nash, who was portrayed in the film "A Beautiful Mind." In a noncooperative game, players are said to be in Nash equilibrium if they are making the best decision possible, taking into account the decisions of the other players.

31/05/2023

"I am guessing [a poker-playing AI] will be stronger than the best humans in the world in one to five years," said Tuomas Sandholm, a computer scientist at�Carnegie Mellon University in Pittsburgh, who led the team that created Claudico. But even as AI ability gets closer and closer to that of the best human players, it will take many more poker hands in order to truly declare the program victorious, Sandholm said.

One of AI's best-known achievements occurred when IBM's chess-playing Deep Blue computer beat reigning world champion Garry Kasparov. But unlike chess, poker is a game of incomplete information; players do not have knowledge about the payoffs and strategies of the other players. "Poker is much more relevant for the real world than chess," Sandholm told Live Science.

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Its win also involved some surprising moves. For instance, AI was more likely than humans to make huge overbets — meaning that they would bet three, five or even 20 times the amount of chips in the pot. Interestingly, those overbets sometimes made mathematical sense in two very different situations.

"With a very strong hand and with the weakest hands, you want to make those big overbets," Sandholm said.

Libratus was also more likely than the humans to underbet in certain surprising situations, Sandholm said. And every night, it went home and adapted its strategy based on the hands it had played.

22/05/2023

For the "Brains vs. Artificial Intelligence" tournament, four of the world's best poker players faced off one-on-one against Libratus in 120,000 hands of poker. At stake was a $200,000 pot, which the human players received even if they lost.

"They are professionals, so they were fighting to the bitter end, really hard," Sandholm said. "They were studying really hard every night on their computers, trying to find holes in the AI."

In the end, it was no contest: The AI prevailed.

As part of the program, bluffing naturally emerged as a mathematically sound strategy, Sandholm noted.

20/05/2023

If you said black, you’d have won (the wheel eventually spun 26 blacks in a row).

If you said “red” you’ve have exhibited a behaviour known as the “gambler’s fallacy”, a phenomenon which, according to a paper published today in the Proceedings of the National Academy of Sciences (PNAS), can be narrowed down to a specific part of the brain – the insular cortex.

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The outcome of each spin of a roulette wheel is independent of the spin before it. The ball landing on red on one spin does not affect the probability of red on the next spin, or of black. Coin tosses are the same.

20/05/2023

You watch with interest the next spin of the wheel. It too lands on black, as does the next spin – and the next, and the next.

With 24 spins in a row landing on black you place your chips on the table. Where would you put your money? On the black, anticipating the next spin of the wheel will land a 25th black? Or on red, reasoning that the chances of the next spin landing on black are almost zero?