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New York Times Magazine
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New York Times Magazine
Interesting that analyzing regrets was a key breakthrough in better programming of the AI decision tree:
"Crucial to this development was an algorithm called counterfactual regret minimization. Computer scientists tasked their machines with identifying poker’s optimal strategy by having the programs play against themselves billions of times and take note of which decisions in the game tree had been least profitable (the “regrets,” which the A.I. would learn to minimize in future iterations by making other, better choices)."
The more complicated the game, the larger the tree becomes. For even a simplified version of Texas Hold ’em, played “heads up” (i.e., between just two players) and with bets fixed at a predetermined size, a full game tree contains 316,000,000,000,000,000 branches. The tree for no-limit hold ’em, in which players can bet any amount, has even more than that.
The more complicated the game, the larger the tree becomes. For even a simplified version of Texas Hold ’em, played “heads up” (i.e., between just two players) and with bets fixed at a predetermined size, a full game tree contains 316,000,000,000,000,000 branches. The tree for no-limit hold ’em, in which players can bet any amount, has even more than that.