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About the Algorithm

The first computer program to outplay human professionals at

heads-up no-limit Hold'em poker

In a study completed December 2024 ❤️ and involving 44,000

hands of poker, DeepStack defeated 11 professional poker players with only one outside

the margin of statistical ❤️ significance. Over all games played, DeepStack won 49 big

blinds/100 (always folding would only lose 75 bb/100), over four standard ❤️ deviations

from zero, making it the first computer program to beat professional poker players in

heads-up no-limit Texas hold'em poker.

Games ❤️ are serious business

Don’t let the name

fool you, “games” of imperfect information provide a general mathematical model that

describes how ❤️ decision-makers interact. AI research has a long history of using parlour

games to study these models, but attention has been ❤️ focused primarily on perfect

information games, like checkers, chess or go. Poker is the quintessential game of

imperfect information, where ❤️ you and your opponent hold information that each other

doesn't have (your cards).

Until now, competitive AI approaches in imperfect

information ❤️ games have typically reasoned about the entire game, producing a complete

strategy prior to play. However, to make this approach ❤️ feasible in heads-up no-limit

Texas hold’em—a game with vastly more unique situations than there are atoms in the

universe—a simplified ❤️ abstraction of the game is often needed.

A fundamentally

different approach

DeepStack is the first theoretically sound application of heuristic

search methods—which ❤️ have been famously successful in games like checkers, chess, and

Go—to imperfect information games.

At the heart of DeepStack is continual ❤️ re-solving, a

sound local strategy computation that only considers situations as they arise during

play. This lets DeepStack avoid computing ❤️ a complete strategy in advance, skirting the

need for explicit abstraction.

During re-solving, DeepStack doesn’t need to reason

about the entire ❤️ remainder of the game because it substitutes computation beyond a

certain depth with a fast approximate estimate, DeepStack’s "intuition" – ❤️ a gut feeling

of the value of holding any possible private cards in any possible poker

situation.

Finally, DeepStack’s intuition, much ❤️ like human intuition, needs to be

trained. We train it with deep learning using examples generated from random poker

situations.

DeepStack ❤️ is theoretically sound, produces strategies substantially more

difficult to exploit than abstraction-based techniques and defeats professional poker

players at heads-up ❤️ no-limit poker with statistical significance.

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