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Polished Poker is a 175-page book that covers everything from setting poker goals, diet, to the math behind poker, and reading your opponent. Although the book was written in 2014, it’s still one of the first resources I recommend to players who are just starting out with the game. GTO POKER STRATEGY IS THE BEST STARTING POINT YOU COULD HAVE When you know your opponents well or play with the same player all the time, you know their mistakes and can make some adjustments to exploit it. This includes any: non-relevant posts to poker, shilling your news site, shilling your YouTube channel,excessive shit-posting, and continuing to post content after you've been specifically warned not to by the mod team. Additionally, please do not advertise or promote your pppoker club or other 'social poker' clubs. Phillip Jerome Hellmuth Jr. (born July 16, 1964) is an American professional poker player who has won a record fifteen World Series of Poker bracelets.He is the winner of the Main Event of the 1989 World Series of Poker (WSOP) and the Main Event of the 2012 World Series of Poker Europe (WSOPE), and he is a 2007 inductee of the WSOP's Poker Hall of Fame.

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Presented by

Hansa Halim, Sanjana Rajendra Naik, Samka Marfua, Shawrupa Proshasty

Introduction

A super-intelligence is a hypothetical agent that possesses intelligence surpassing that of the brightest and most gifted human minds. In the past two decades, most of the superhuman AI that have been built were only able to beat human players in two-player zero-sum games, where the sum of the gains and losses always equals zero. They almost dominated most of the board games in these twenty years. The most popular AI in the board games are the chess AI deep blue and the go chess AI Alpha-go. The most common strategy that the AI uses to beat those games is to find the most optimal Nash equilibrium. A Nash equilibrium is a pair of strategies such that either single-player switching to any other choice of strategy (while the other player's strategy remains unchanged) will result in a lower payout for the switching player. Intuitively this is similar to a locally optimal strategy for the players but is (i) not guaranteed to exist and (ii) may not be the truly optimal strategy. An example of this is the Prisoner's dilemma, where two individuals each have the option to testify against the other or to remain silent. Although the optimal choice is to remain silent, the individuals have an incentive to act in their own self-interest which results in a less than optimal outcome.

More specifically, in the game of poker, we only have AI models that can beat human players in two-player settings. This means that developing a superhuman AI in multiplayer poker is the remaining great milestone in this field, because there is no polynomial-time algorithm that can find a Nash equilibrium in two-player non-zero-sum games. The discovery of such an algorithm would have surprising and profound implications in computational complexity theory.

In this paper, the AI which we call Pluribus is capable of defeating human professional poker players in Texas hold'em poker which is a six-player poker game and is the most commonly played format in the world. The algorithm that is used is not guaranteed to converge to a Nash algorithm outside of two-player zero-sum games. However, it uses a strong strategy that is capable of consistently defeating elite human professionals. This shows that despite not having strong theoretical guarantees on performance, they are capable of applying a wider class of superhuman strategies.

Knowing the basics of Texas hold'em poker may help to understand how the AI can play. Texas hold'em is played using a standard deck of 52 cards. For each hand, players are each dealt two cards, which only they can see. Once players receive their two cards, and prior to turning any other cards, players (in clockwise order) have the option to call, raise, fold, or check. Call means to match the highest bet so far, raise means to increase the bet, fold means the player wishes to leave the current hand, and check means to continue without betting any further. A player can only check if no one has bet yet this round or if they have already matched the highest bet. Once this round of betting is over three cards, called the Flop, are turned over, and the betting happens in a clockwise manner again. This is followed by revealing another card, the Turn, and then proceeding with another round of betting. Now, the final card, the River, is turned. There is one more round of betting before the players reveal their cards and determine the winner. The player with the best five-card hand (out of the 7 cards) wins the hand and the money in the pot. The following is a list of the Texas hold'em hands from best to worst:

Royal Flush (A,K,Q,J,10 all of the same suit)
Straight Flush(5 in a row from the same suit)
4 of a kind
Full house (3 of a kind + a pair)
Flush (5 cards of the same suit)
Straight (5 cards in a row)
3 of a kind
2 different pairs
A pair
Highest card

Nash Equilibrium in Multiplayer Games

Many AI has reached superhuman performance in games like checkers, chess, two-player limit poker, Go, and two-player no-limit poker. Nash equilibrium has been proven to exist in all finite games and numerous infinite games but the challenge is to find the equilibrium. It is the best possible strategy and is unbeatable in two-player zero-sum games since it guarantees to not lose in expectation regardless of what the opponent is