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Games possess been intertwined together with the earliest developments throughout computation, game theory, and artificial intelligence (AI). At the particular very conception involving computing, Babbage got detailed plans for an? automaton? competent of playing tic-tac-toe and dreamt associated with his Analytical Motor playing chess (1). Both Turing (2) and Shannon (3)? on paper plus in hardware, correspondingly? developed programs to be able to play chess as a means of validating early on ideas in computation and AI. For more than a half century, games have carried on to act as testbeds for fresh ideas and the resulting successes have marked important breakthrough in the progress of AI. Examples include the checkers-playing personal computer program Chinook turning into the first to be able to win a global championship itle against human beings (4), Deep Orange defeating Kasparov within chess (5), and Watson defeating Jennings and Rutter upon Jeopardy! (6). On the other hand, defeating top individual players is not typically the same as? dealing with? a? that will be, computing a game-theoretically optimal solution of which is incapable associated with losing against any opponent in the fair game. Significant milestones inside the advancement of AI have been achieved by way of solving games such as Connect Four (7) and checkers (8). Every nontrivial sport played competitively simply by humans that has been solved to date i Des Neumann? s statement hints at the quintessential game involving imperfect-information: the ame of poker. Poker involves each gamer being dealt exclusive cards, with gamers taking structured converts making bets in getting the strongest palm (possibly bluffing), contacting opponents? bets, or folding to provide up the hand. Poker played an essential role in earlier developments in the field of game theory. Borel? s i9000 (12) and von Neumann? s (13, 14) foundational gets results were motivated simply by designing a mathematical rationale for bluffing throughout poker, and smaller synthetic poker games (15) were very common in many earlier papers (12, 16, 16, 17). Holdem poker is also arguably the most popular card video game on earth, with extra than 150 , 000, 000 players worldwide (18). The most well-known variant of holdem poker today is The state of texas hold? em. When it is enjoyed with ju Within this paper, many of us announce that heads-up limit Texas hold? em poker is essentially weakly solved. Moreover, we bound the game-theoretic value of the sport, proving of which the game is definitely a winning game for the seller.