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I recently started a new newsletter focus on AI education. TheSequence is a no-BS( meaning no hype, no news etc) AI-focused newsletter that takes 5 minutes to read. The goal is to keep you up to date with machine learning projects, research papers and concepts. Please give it a try by subscribing below:

I had a long conversation with one of my colleagues about imperfect information games and deep learning this weekend and reminded me of an article I wrote last year so I decided to republish it.

Poker has remained as one of the most challenging games to master in the fields of artificial intelligence(AI) and game theory. From the game theory-creator John Von Neumann writing about poker in his 1928 essay “Theory of Parlor Games, to Edward Thorp masterful book “Beat the Dealer” to the MIT Blackjack Team, poker strategies has been an obsession to mathematicians for decades. In recent years, AI has made some progress in poker environments with systems such as Libratus, defeating human pros in two-player no-limit Hold’em in 2017. Last year, a team of AI researchers from Facebook in collaboration with Carnegie Mellon University achieved a major milestone in the conquest of Poker by creating Pluribus, an AI agent that beat elite human professional players in the most popular and widely played poker format in the world: six-player no-limit Texas Hold’em poker.

The reasons why Pluribus represents a major breakthrough in AI systems might result confusing to many readers. After all, in recent years AI researchers have made tremendous progress across different complex games such as checkers, chess, Go, two-player poker, StarCraft 2, and Dota 2. All those games are constrained to only two players and are zero-sum games (meaning that whatever one player wins, the other player loses). Other AI strategies based on reinforcement learning have been able to master multi-player games Dota 2 Five and Quake III. However, six-player, no-limit Texas Hold’em still remains one of the most elusive challenges for AI systems.

Mastering the Most Difficult Poker Game in the World

The challenge with six-player, no-limit Texas Hold’em poker can be summarized in three main aspects:

1. Dealing with incomplete information.
2. Difficulty to achieve a Nash equilibrium.
3. Success requires psychological skills like bluffing.

In AI theory, poker is classified as an imperfect-information environment which means that players never have a complete picture of the game. No other game embodies the challenge of hidden information quite like poker, where each player has information (his or her cards) that the others lack. Additionally, an action in poker in highly dependent of the chosen strategy. In perfect-information games like chess, it is possible to solve a state of the game (ex: end game) without knowing about the previous strategy (ex: opening). In poker, it is impossible to disentangle the optimal strategy of a specific situation from the overall strategy of poker.

The second challenge of poker relies on the difficulty of achieving a Nash equilibrium. Named after legendary mathematician John Nash, the Nash equilibrium describes a strategy in a zero-sum game in which a player in guarantee to win regardless of the moves chosen by its opponent. In the classic rock-paper-scissors game, the Nash equilibrium strategy is to randomly pick rock, paper, or scissors with equal probability. The challenge with the Nash equilibrium is that its complexity increases with the number of players in the game to a level in which is not feasible to pursue that strategy. In the case of six-player poker, achieving a Nash equilibrium is computationally impossible many times.

The third challenge of six-player, no-limit Texas Hold’em is related to its dependence on human psychology. The success in poker relies on effectively reasoning about hidden information, picking good action and ensuring that a strategy remains unpredictable. A successful poker player should know how to bluff, but bluffing too often reveals a strategy that can be beaten. This type of skills has remained challenging to master by AI systems throughout history.

Pluribus

Like many other recent AI-game breakthroughs, Pluribus relied on reinforcement learning models to master the game of poker. The core of Pluribus’s strategy was computed via self-play, in which the AI plays against copies of itself, without any data of human or prior AI play used as input. The AI starts from scratch by playing randomly, and gradually improves as it determines which actions, and which probability distribution over those actions, lead to better outcomes against earlier versions of its strategy.

Differently from other multi-player games, any given position in six-player, no-limit Texas Hold’em can have too many decision points to reason about individually. Pluribus uses a technique called abstraction to group similar actions together and eliminate others reducing the scope of the decision. The current version of Pluribus uses two types of abstractions:

• Action Abstraction: This type of abstraction reduces the number of different actions the AI needs to consider. For instance, betting $150 or $151 might not make a difference from the strategy standpoint. To balance that, Pluribus only considers a handful of bet sizes at any decision point.
• Information Abstraction: This type of abstraction groups decision points based on the information that has been revealed. For instance, a ten-high straight and a nine-high straight are distinct hands, but are nevertheless strategically similar. Pluribus uses information abstraction only to reason about situations on future betting rounds, never the betting round it is actually in.

To automate self-play training, the Pluribus team used a version of the of the iterative Monte Carlo CFR (MCCFR) algorithm. On each iteration of the algorithm, MCCFR designates one player as the “traverser” whose current strategy is updated on the iteration. At the start of the iteration, MCCFR simulates a hand of poker based on the current strategy of all players (which is initially completely random). Once the simulated hand is completed, the algorithm reviews each decision the traverser made and investigates how much better or worse it would have done by choosing the other available actions instead. Next, the AI assesses the merits of each hypothetical decision that would have been made following those other available actions, and so on.The difference between what the traverser would have received for choosing an action versus what the traverser actually achieved (in expectation) on the iteration is added to the counterfactual regret for the action. At the end of the iteration, the traverser’s strategy is updated so that actions with higher counterfactual regret are chosen with higher probability.

The outputs of the MCCFR training are known as the blueprint strategy. Using that strategy, Pluribus was able to master poker in eight days on a 64-core server and required less than 512 GB of RAM. No GPUs were used.
The blueprint strategy is too expensive to use real time in a poker game. During actual play, Pluribus improves upon the blueprint strategy by conducting real-time search to determine a better, finer-grained strategy for its particular situation. Traditional search strategies are very challenging to implement in imperfect information games in which the players can change strategies at any time. Pluribus instead uses an approach in which the searcher explicitly considers that any or all players may shift to different strategies beyond the leaf nodes of a subgame. Specifically, rather than assuming all players play according to a single fixed strategy beyond the leaf nodes, Pluribus assumes that each player may choose among four different strategies to play for the remainder of the game when a leaf node is reached. This technique results in the searcher finding a more balanced strategy that produces stronger overall performance.

Pluribus in Action

Facebook evaluated Pluribus by playing against an elite group of players that included several World Series of Poker and World Poker Tour champions. In one experiment, Pluribus played 10,000 hands of poker against five human players selected randomly from the pool. Pluribus’s win rate was estimated to be about 5 big blinds per 100 hands (5 bb/100), which is considered a very strong victory over its elite human opponents (profitable with a p-value of 0.021). If each chip was worth a dollar, Pluribus would have won an average of about $5 per hand and would have made about $1,000/hour.

The following figure illustrates Pluribus’ performance. On the top chart, the solid lines show the win rate plus or minus the standard error. The bottom chart shows the number of chips won over the course of the games.

Pluribus represents one of the major breakthroughs in modern AI systems. Even though Pluribus was initially implemented for poker, the general techniques can be applied to many other multi-agent systems that require both AI and human skills. Just like AlphaZero is helping to improve professional chess, its interesting to see how poker players can improve their strategies based on the lessons learned from Pluribus.

Original. Reposted with permission.

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Looking for the best Facebook games to play with your friends or when you are bored? This list is all you need.

This list doesn't feature every single Facebook game under the sun. Instead, it focuses on the best Facebook games to play in 2020.

You can play these games with your friends and when you are alone. All you need is an internet connection, a browser, and the time to get on a new adventure.

This list of Facebook games includes only free-to-play games, because you don't need to spend anything to have some good fun — if you know where to look for it.

Don't miss our top choices!

1. WSOP Poker App is the official poker app of the World Series of Poker where you play real poker games with other people and start with a no deposit bonus of 1,000,000 free chips.
2. Slotomania is the world's most downloaded collection of 'social' slot machine with exciting multi-player tournaments, missions, and more.
3. House of Fun is exactly what the name says: a place where you find lots of exclusive games that are a lot of fun to play alone or with friends.

Some of the games you see on this page have reached millions of Facebook users already and continue to attract players with quality graphics and gameplay.

Many of them require logic, some rely on reflexes and quick decision making. Others, like you would expect from a site like PokerNews involve playing cards and are a great way to learn how to play poker.

Like our top choice...

1. WSOP Poker app

On a site like PokerNews, starting this list with the official World Series of Poker (WSOP) app is almost an obvious choice.

Start the game and choose between the very best poker games you can find on Facebook.

Got time to play? Work your way through the app and battle at the tables to win a real WSOP bracelet in the only online game allowed to give them away.

And if you like more fast-paced action, head to the site's free cash games to play Texas hold'em and Omaha. With more than 3.4 million users registered to the game's Facebook page alone, there's always someone ready to play with you.

2020 Update: Now Play with Your Friends!

What's great about the WSOP poker Facebook game is that you can also use it to play with your friends online!

To start a 'virtual home game' for free, just sit at a cash game table and click on the '+' sign next to the empty seat.

After that, you and your friends can play poker together on this fun, entertaining, and surprisingly realistic Facebook game.

When you register to play WSOP Poker on Facebook you also have daily missions to complete, with each of those bringing you more chips to conquer the tables later.

The game features special Multipliers, Momentum, Active Effects, and even more exciting elements that contribute to make it the most action-packed poker game we have seen on Facebook in a long time.

You can take advantage of Total Recalls for added chips while joining a Club serves as a leaderboard in the game. Upon reaching Grand Masters status, you'd be ready to take on WSOP events for real!

You can play on WSOP Poker via Facebook (on this page) or you can download their apps if you want to bring them to your mobile device.

In that case, the correct links are:

You receive a massive welcome bonus (i.e. no deposit free chips) as soon as you register — and there are new bonuses every day to refill your bankroll without spending any money.

2. Slotomania

The next one on our list of the top Facebook games to play in 2020 is Slotomania, a true icon in the world of free slots.

This popular Facebook game and comprehensive free-to-play mobile app by Playtika gathers titles with an array of different themes.

Be it fairytale-themed slots like Despicable Wolf or classic all-timers in the face of Rapid Fire, you'll definitely find your match.

There are daily quests, level-ups, and a ton of content to unlock as you play, so this app is never boring.

You will constantly receive free chips from various sources – even if you like to bet on the big side, you'd still have enough to go on.

Slotomania runs smoothly on the desktop via Facebook and mobile via its own dedicated mobile apps, making it among the finest additions to the list of Facebook games to play this year.

3. House of Fun

To conclude the podium, let's look at House of Fun, another massive hit coming from the Playtika's kitchens.

Available on Facebook and mobile devices, House of Fun is a collection of slot machines that features only exclusive games you won't find anywhere else on the internet.

Rather than giving you the same old Vegas slots, this game focuses on a totally different experience that, as the name says it's a lot of fun.

Just like Slotomania, there are quests and milestones to reach. Each of them boosts your account's volume, and let's face it – it's incredibly fun to spin and gather collectibles all the time.

You can even invite your Facebook friends and compete on who gets ahead faster!

All the action is free, so there's no need to spend any money on this game. You can buy additional coins if you want to, but we found that the amount of daily freebies is more than sufficient to stay busy for ages.

4. Clash of Clans

This Facebook game is as simple as it is addictive: you build a village, gather a clan, and enter glorious clan wars with other players.

With 10 million monthly users on average, you'll never run out of opponents to beat.

Fighting other clans, reinforcing your fortress, or simply gaining allies – all of that is presented with great graphics and smooth gameplay on one of the best Facebook games ever created.

5. Throne Rush

An easy to play massive multiplayer online role-playing game (MMROPG) title with friendly and intuitive gameplay.

If you are into strategy games and you like to take your time to think about every single move you take, Throne Rush is a great one to consider.

Labeled as one of the best Facebook games ever for strategy enthusiasts, this game sees you build a town center and various other buildings, train an army, and then fight against opponents from around the globe.

The visuals are very well well-designed and the battle simulations are super entertaining.

6. Zynga Poker

Going back to card games and casino-related content, Zynga's Hold 'em is one the most advanced poker games on Facebook.

Be it to test your skills or just rumble for chips, the app is designed to offer a good variety of games and a fair poker action.

You can complete quests and milestones, sit at High Roller tables, and measure your expertise with lots of other players.

Zynga Poker v WSOP Poker: What is the Best Game?

If you have been on Facebook for 15+ years, you know what Zynga poker is. This title pioneered the world of Facebook games brining free poker to the masses.

Back in the days, the glory and diffusion of Zynga poker made everyone feel it could disrupt the industry so much that the days of sites like PokerStars and partypoker were almost counted.

Then - the future turned out to be different.

Today's Zynga Poker is a much lesser ambitious Facebook game with a solid fans base, but not much more than that.

Compared to the WSOP Poker app and Facebook game, the Zynga one is inferior in terms of software and offer. Zynga's games are less realistic and Zynga players can't access any of the goodies (WSOP bracelets and WSOP rings) available on the WSOP Poker game.

7. Criminal Case

Criminal Case brings crime solving closer to online users with a terrific and popular Facebook game.

If you always guess who the murder is while watching a thriller on TV, this title might be your new favorite.

Following CIA and FBI-like onvestigations, this Facebook game allows you to slip into your detective self and catch bad guys without leaving your chair.

There are some in-game purchases but none of them is crucial to the game. Also, you you can gather in-game currency and upgrade your tools as you play.

8. NCIS: Hidden Crimes

Another crime puzzle game, NCIS: Hidden Crimes relies on your sharp mind to keep moving.

The game is serious, with realistic graphics and incredibly hard cases once you reach the higher levels.

Compared to Criminal Case, the NCIS game is a little bit more complex to solve, meaning you might not love it if you want some casual fun.

Otherwise, it's a brilliant Facebook game that will keep your brain seriously busy!

9. 8 Ball Pool

Drifting away from the casino and crime-solving genres for a bit, 8 Ball Pool is arguably the best pool game on Facebook at the moment.

Aside from the 10 million monthly users, the game packs amazing graphics and play-style. Playing is super simple as you can choose to aim at the balls using your skills... or rely on the helping indicator for guaranteed precision.

Even if you haven't played pool in your life, the rules are well explained and easy to follow.

You can level up, challenge random opponents, or gather some friends and launch the app for a friendly competition. Either way, the title comes highly recommended!

10. Trivia Crack

Trivia Crack is simply an all-around question-and-answer Facebook game. You can challenge your Facebook friends and dive into a pool of endless knowledge.

Like the famous board game, this Facebook trivia game offers six sections to play in – Arts and Literature, Entertainment, History and Geography, Sports, Science, and Technology.

Be it for fun or to truly decide which one is the smartest between you and your friends, the game deserves a try.

11. Top 11 Football Manager

Sports, strategy, and countless efforts to become the best. If those sound like your game preferences, Top 11 Football Manager is the right fit for a competitive game session.

Reaching the top of the leaderboard doesn't come easy with this one.

From acquiring and training players to playing against the toughest opponents in real time, the app will keep you occupied. Try it out if you've always wanted to lead a football team to the greatest of victories!

12. Glow Hockey

One of the most simplistic, yet satisfying, Facebook games ever.

Glow Hockey resembles the renowned Air Hockey game – you aim to score in your opponent's goal whilst defending from their advances.

It is the true definition of a time-killer game. Of course, you can challenge your friends and become the best glow hockey player in the neighborhood!

13. Hero Wars

Going back in action game history, Hero Wars is a remastered 2D fighting game for iOS and Android.

You are a noble hero, trying to save the so-called Guardians from evil demons and spirits. It is easy to play and advance in, so you won't spend hours just to beat a level.

If you love entering swift battles from hour to hour, this is a great pick to consider.

14. Global Strike

A classic example of first-person shooting game (FPS), Global Strike is a respectable option when you want to play games on Facebook.

Real-like weapons, detailed environment, and multiple game modes keep variety high in this one.

The app runs lightly and it can be launched directly through a browser.

There are app games with better graphics, but GS fits on all types of mobile devices, be it old or new.

15. Lies of Astaroth

We've reached a card-based app now – Lies of Astaroth combines sensible deck-building with strategic decisions during a fight.

Battling other players isn't as entertaining as Hearthstone, for example, but the game has its plus sides.

For instance, it runs so lightly, you could probably play it on a 10-year-old smartphone. In summary, check it out if you crave an old-school card game experience.

16. Agent Elf

Agent Elf is the sole definition of an endless runner to play on Facebook.

If you've ever played such a game (or have been left without an Internet connection), you'd know the aim of the game.

Run as fast as you can handle, go over obstacles, and gather multipliers for your progress.

The graphics are neat, you're wearing shades, and everything seems so light, you can almost feel yourself flying.

17. Subway Surfers

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Another endless runner game, Subway Surfers is an advanced version of Agent Elf.

You're a cool kid, running away from an inspector while jumping over trains and other obstacles. The animations are truly mesmerizing, and you can run in 3D, gathering coins and reaching harder levels.

One of the best Facebook games in the genre offers game-related events, taking place at different times – those grant you bonus features and added content.

18. Monster Legends

Monster Legends has become somewhat of a classic nowadays. It's a multiplayer RPG, where your only goal is to raise a monster strong enough to defeat your enemies.

Each creature has different abilities, and you are free to enhance them however you like.

Level up your toothy army in order to smash even the most powerful of opponents. Battles are turn-based, you can use items, and even return to a field after upgrading your creatures.

19. CSR Racing

When it comes to free games to play with friends, CSR Racing is a top-notch choice.

It features a series of drag races to explore alone or with opponents. The more you win, the more vehicles you add to your collection.

Upgrades are in place, such as nitrous oxide, massive engines, and better tires. Be it a story-related session or random PVP races, you'll have fun with this one.

20. SimCity BuildIt

SimCity BuildIt is a great Facebook game where you get an entire town to develop and make into yours. It looks like a classic SimCity title, but includes elements from Farmville and other popular Facebook games.

The main target for your characters is to gather resources and use them to build different constructions.

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Wood, steel, plastic, lumber, nails, and more are up for grabs for your factories, commercial stores, and residential buildings.

21. MMA Pro Fighter

MMA Pro Fighter is primal, intense, and aimed at a full-on fighting brawl for the Championship belts.

You can choose to play versus strangers or invite your friends to try it out. Fighting simulations in the app are realistic and extremely engaging. You are free to customize your character, train, and challenge more powerful opponents to test your progress.

22. Bejeweled Blitz

A more advanced version of Candy Crush, this one hits players with harder puzzles and shorter time frames.

It's perfect for short gameplay sessions, but prolonged play may make you dizzy.

Nonetheless, this doesn't seem to stop over 120 million monthly users. You can battle all of them while chasing the highest possible score on each puzzle!

23. Mob Wars

Played by over 12 million users, Mob Wars opens the door to exciting mob-themed events on your smartphone.

Join a crime family, do dirty jobs, board airplanes, and engage in full-on crime boss battles. There are bounty rewards for valuable characters and players, as well.

Truly among the best Facebook games to master!

24. Farmville 2

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Although this is probably not the type of game you'd expect to find featured on PokerNews, it would be a surprise if you didn't know Farmville 2.

This 3D title became one of Facebook's most popular games already some years ago and has since then taken Facebook players by storm.

The game developers have ensured enough room to explore even for the most dedicated virtual farmers.

Around 5 million players engage in a Farmville 2 session monthly. You can raise animals, harvest crops, cook delicious meals, and much, much more.

Being a free game lets users of all ages around the world play it seriously – the improved graphics and added quests make it a worthy ancestor of the original Farmville!

25. Candy Crush Saga

Last, but not least, a true legend in the world of Facebook games.

With over 50 million monthly users, Candy Crush Saga packs nearly 1000 levels to face and complete.

Solving various puzzles requires a sharp mind and quick fingers. You have access to the first few levels for free – defusing bombs and matching candies don't come funnier than that.

Once you invite friends to join you, you'll be able to continue on your quest to the higher levels.