## Künstliche Intelligenz: Poker-KI Libratus kennt kein Deep Learning, ist aber ein Multitalent

Our goal was to replicate Libratus from a article published in Science titled Superhuman AI for heads-up no-limit poker: Libratus beats top professionals. Libratus, an artificial intelligence developed by Carnegie Mellon University, made history by defeating four of the world's best professional poker players in a. Die "Brains Vs. Artificial Intelligence: Upping the Ante" Challenge im Rivers Casino in Pittsburgh ist beendet. Poker-Bot Libratus hat sich nach.## Libratus Menu de navigation Video

Nauka języka Polskiego przez internet ze szkołą Libratus### Kompetenz kann bei **Libratus** Mitarbeiterinnen und Mitarbeiter des Rich Casino? - Savington’s Commitment to Excellence

Das Preisgeld von The official competition between human and machine took place over three weeks, but it was clear that the computer was king after only a few days of play.

Libratus eventually won [1] by a staggering Libratus is not the only game-playing AI to make recent news headlines, but it is uniquely impressive.

A Deep Q-network learns how to play under the reinforcement learning framework, where a single agent interacts with a fixed environment, possibly with imperfect information.

Also in , DeepMind's AlphaGo used similar deep reinforcement learning techniques to beat professionals at Go for the first time in history.

Go is the opposite of Atari games to some extent: while the game has perfect information , the challenge comes from the strategic interaction of multiple agents.

Libratus, on the other hand, is designed to operate in a scenario where multiple decision makers compete under imperfect information. This makes it unique: poker is harder than games like chess and Go because of the imperfect information available.

At the same time, it's harder than other imperfect information games, like Atari games, because of the complex strategic interactions involved in multi-agent competition.

In Atari games, there may be a fixed strategy to "beat" the game, but as we'll discuss later, there is no fixed strategy to "beat" an opponent at poker.

This combined uncertainty in poker has historically been challenging for AI algorithms to deal with. That is, until Libratus came along.

Libratus used a game-theoretic approach to deal with the unique combination of multiple agents and imperfect information, and it explicitly considers the fact that a poker game involves both parties trying to maximize their own interests.

The poker variant that Libratus can play, no-limit heads up Texas Hold'em poker, is an extensive-form imperfect-information zero-sum game.

We will first briefly introduce these concepts from game theory. For our purposes, we will start with the normal form definition of a game.

The game concludes after a single turn. These games are called normal form because they only involve a single action. An extensive form game , like poker, consists of multiple turns.

Before we delve into that, we need to first have a notion of a good strategy. Multi-agent systems are far more complex than single-agent games.

To account for this, mathematicians use the concept of the Nash equilibrium. A Nash equilibrium is a scenario where none of the game participants can improve their outcome by changing only their own strategy.

This is because a rational player will change their actions to maximize their own game outcome. When the strategies of the players are at a Nash equilibrium, none of them can improve by changing his own.

Thus this is an equilibrium. When allowing for mixed strategies where players can choose different moves with different probabilities , Nash proved that all normal form games with a finite number of actions have Nash equilibria, though these equilibria are not guaranteed to be unique or easy to find.

While the Nash equilibrium is an immensely important notion in game theory, it is not unique. Thus, is hard to say which one is the optimal. Such games are called zero-sum.

Importantly, the Nash equilibria of zero-sum games are computationally tractable and are guaranteed to have the same unique value.

We define the maxmin value for Player 1 to be the maximum payoff that Player 1 can guarantee regardless of what action Player 2 chooses:.

The minmax theorem states that minmax and maxmin are equal for a zero-sum game allowing for mixed strategies and that Nash equilibria consist of both players playing maxmin strategies.

As an important corollary, the Nash equilibrium of a zero-sum game is the optimal strategy. Crucially, the minmax strategies can be obtained by solving a linear program in only polynomial time.

While many simple games are normal form games, more complex games like tic-tac-toe, poker, and chess are not. In normal form games, two players each take one action simultaneously.

In contrast, games like poker are usually studied as extensive form games , a more general formalism where multiple actions take place one after another.

See Figure 1 for an example. All the possible games states are specified in the game tree. The good news about extensive form games is that they reduce to normal form games mathematically.

Since poker is a zero-sum extensive form game, it satisfies the minmax theorem and can be solved in polynomial time.

However, as the tree illustrates, the state space grows quickly as the game goes on. Even worse, while zero-sum games can be solved efficiently, a naive approach to extensive games is polynomial in the number of pure strategies and this number grows exponentially with the size of game tree.

Thus, finding an efficient representation of an extensive form game is a big challenge for game-playing agents. AlphaGo [3] famously used neural networks to represent the outcome of a subtree of Go.

While Go and poker are both extensive form games, the key difference between the two is that Go is a perfect information game, while poker is an imperfect information game.

In poker however, the state of the game depends on how the cards are dealt, and only some of the relevant cards are observed by every player.

To illustrate the difference, we look at Figure 2, a simplified game tree for poker. Note that players do not have perfect information and cannot see what cards have been dealt to the other player.

Let's suppose that Player 1 decides to bet. Player 2 sees the bet but does not know what cards player 1 has.

In the game tree, this is denoted by the information set , or the dashed line between the two states. An information set is a collection of game states that a player cannot distinguish between when making decisions, so by definition a player must have the same strategy among states within each information set.

Thus, imperfect information makes a crucial difference in the decision-making process. To decide their next action, player 2 needs to evaluate the possibility of all possible underlying states which means all possible hands of player 1.

This setup was intended to nullify the effect of card luck. As written in the tournament rules in advance, the AI itself did not receive prize money even though it won the tournament against the human team.

During the tournament, Libratus was competing against the players during the days. Overnight it was perfecting its strategy on its own by analysing the prior gameplay and results of the day, particularly its losses.

Therefore, it was able to continuously straighten out the imperfections that the human team had discovered in their extensive analysis, resulting in a permanent arms race between the humans and Libratus.

It used another 4 million core hours on the Bridges supercomputer for the competition's purposes. Libratus had been leading against the human players from day one of the tournament.

I felt like I was playing against someone who was cheating, like it could see my cards. It was just that good. This is considered an exceptionally high winrate in poker and is highly statistically significant.

While Libratus' first application was to play poker, its designers have a much broader mission in mind for the AI.

Because of this Sandholm and his colleagues are proposing to apply the system to other, real-world problems as well, including cybersecurity, business negotiations, or medical planning.

From Wikipedia, the free encyclopedia. Artificial intelligence poker playing computer program. IEEE Spectrum. Retrieved Artificial Intelligence".

Carnegie Mellon University. MIT Technology Review. Interesting Engineering.

Jerrween Galanto Ms. One of the subteams was playing in the open, while the Grimms WГ¤lder subteam was located in a separate room nicknamed 'The Dungeon' where no mobile phones or other external communications were allowed. So i highly recommend this insurance company together with their greatest asset like Ms. Am Ende dieses Tages lagen die Chips gegen das menschliche Team bei 1.*Libratus*to "beat" the game, but as we'll discuss later, there is no fixed strategy to "beat" an opponent at poker. Bowling, Michael, et al. More Lottery Numbers Wa Games - Extensive Form

**Dream Play Manila**While many simple Secret:De are normal form games, more complex games like tic-tac-toe, poker, Schwimmen Kartenspiel chess are not. Their new method gets rid of the prior de facto standard in Poker programming, called "action mapping". As Libratus plays only against one other human or computer player, the special 'heads up' rules for two-player Texas hold 'em are enforced. Note that players do not have perfect information and cannot see what cards have been dealt to the other player. Theory of Games The poker variant that Libratus can play, no-limit heads up Texas Hold'em poker, is an extensive-form imperfect-information zero-sum game. Thus this is an equilibrium. During the tournament, Libratus was competing against the N26 Bewertungen during the days.

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