Libratus Poker - Vielleicht hatte der Bot einfach nur eine Menge Glück?

Who knows. Perhaps that all they could do out of frustration with the ai super computer beating them down continuously.

Because these tournament poker players playing against Libratus were adaptive and winning online poker players and always used huds to win online themselves against other players.

They noticed a big hole in their abilities when they did not have a hud against Libratus to help guide them like they were used to using against other human players.

Yet Libratus is one giant poker player HUD in of itself. It analyzed its own play and found its own holes as well as collecting stats and information on the human Poker players it played against.

Therefore Poker Huds offer an unfair advantage to those that have and use them vs. If you play poker online you may have one already.

Next time you go to reload cash in your poker account think about What I Just Said. Especially so in the shark filled waters of sites like Poker Stars.

One of the subteams was playing in the open, while the other subteam was located in a separate room nicknamed 'The Dungeon' where no mobile phones or other external communications were allowed.

The Dungeon subteam got the same sequence of cards as was being dealt in the open, except that the sides were switched: The Dungeon humans got the cards that the AI got in the open and vice versa.

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 turns out this probability is very low: Somewhere between 0.

Meaning: It's very, very unlikely the general result of this challenge — the AI plays better than four humans — is due to the AI just getting lucky.

No bad luck. Basically the Libratus AI is just a huge set of strategies which define how to play in a certain situation.

Two examples of such strategies not necessarily related to the actual game play of Libratus :. It quickly becomes obvious that there are almost uncountably many different situations the AI can be in and for each and every situation the AI has a strategy.

The AI effectively rolls a dice to decide what to do but the probabilities and actions are pre-calculated and well balanced.

The computer played for many days against itself, accumulating billions, probably trillions of hands and tried randomly all kinds of different strategies.

Whenever a strategy worked, the likelihood to play this strategy increased; whenever a strategy didn't work, the likelihood decreased.

Basically, generating the strategies was a colossal trial and error run. Prior to this competition, it had only played poker against itself. It did not learn its strategy from human hand histories.

Libratus was well prepared for the challenge but the learning didn't stop there. Each day after the matches against its human counterparts it adjusted its strategies to exploit any weaknesses it found in the human strategies, increasing its leverage.

How can a computer beat seemingly strong poker players? Unlike Chess or Go, poker is a game with incomplete information and lots of randomness involved.

How can a computer excel at such a game? First, one needs to understand that while poker is a very complex game — much more complex than Chess or even Go — its complexity is limited.

There are only so many different ways the cards can be shuffled and only so many possible different distinguishable games to be played.

To put this in numbers: In Heads-Up Limit-Hold'em there are roughly ,,,,, different game situations. If you played out one of them per second, you'd need 10 billion years to finish them all.

That's a lot of game situations. For No-Limit the number is some orders of magnitude higher since you can bet almost arbitrarily large amounts, but the matter of fact is that the total number of different game situations is finite.

A Nash Equilibrium is a strategy which ensures that the player who is using it will, at the very least, not fare worse than a player using any other strategy.

In layman's terms: Playing the Nash equilibrium strategy means you cannot lose against any other player in the long run.

The existence of those equilibriums was proven by John Nash in and the proof earned him the Nobel Prize in Economics.

This Nash equilibrium means: Guts, reads and intuition don't matter in the end. There is perfect strategy for poker; we just have to find it.

All you need is a suitable computer which can handle quadrillions of different situations, works on millions of billions of terabyte of memory and is blazingly fast.

Then you put a team of sharp, clever humans in front of it, let them develop a method to utilize the computational power and you're there.

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.