How poker AI works

Why poker is harder for computers than chess

Chess and Go are games of perfect information: both players see everything. A program can search the position in front of it and pick the best move. Poker hides the most important fact — the cards — and that breaks the usual approach in three ways.

• You play a range, not a hand. The right action with your actual cards depends on what you would do with every other hand you could hold in the same spot, because that’s what your opponent sees.
• The best play is often mixed. Always betting strong hands and checking weak ones tells opponents everything. Good strategies bluff and slow-play at set frequencies — see the river bluffing game for why.
• Spots can’t be analyzed alone. In chess an endgame is the same no matter how you got there. In poker, what a river bet means depends on how you played the flop and turn, so each part of the strategy depends on the rest.

And the game is enormous. Heads-up No-Limit Hold’em, the version used in AI research, has about 10¹⁶¹ decision points — far too many to list, let alone compute one by one.

Counterfactual regret minimization: how poker AI learns

The breakthrough idea is almost psychological. After every hand of self-play, the program asks at each decision: how much more would I have won if I had taken each other action? That difference is the regret. Regrets add up, and next time the program plays each action in proportion to its positive regret. This rule, regret matching, comes from economists Sergiu Hart and Andreu Mas-Colell (2000).

Counterfactual regret minimization (CFR), introduced by University of Alberta researchers in 2007, applies regret matching separately at every decision point of the game, weighting each by how likely the opponent’s play makes reaching it. In two-player zero-sum games like heads-up poker, the average of all the strategies played converges to an equilibrium. The strategy of the moment keeps swinging — it chases its own regrets — but the average settles, exactly as the demo shows.

Kuhn poker is small enough to finish in a blink: three cards and one bet, twelve decision points. Its equilibrium is known on paper, so you can check the program’s answer — player 2 should call a bet with the Queen and bluff with the Jack each exactly one time in three. Real bots like Libratus and Pluribus used Monte Carlo versions of CFR that sample cards instead of walking the whole game each time — the same trick the demo uses, sampling one deal per iteration.

Abstraction: shrinking the game to fit

CFR needs to visit every decision many times, so full No-Limit Hold’em is out of reach. Poker AIs compute on a simplified copy of the game called an abstraction:

• Card abstraction groups hands that play alike — say, similar flush draws on similar boards — into buckets that share one strategy.
• Action abstraction allows only a few bet sizes, such as half pot, pot and all-in, instead of every possible chip amount.

The result is called a blueprint: a strong strategy for the simplified game. Its weakness is the gaps. When an opponent bets a size the blueprint never considered, the bot has to treat it as a nearby size it knows — and a sharp human can look for exactly those seams.

Search: thinking during the hand

The 2017 bots fixed the gaps by computing during play. Libratus refined its strategy for the rest of each hand in real time on a supercomputer, using the blueprint as a starting point, and filled in gaps in its bet sizes overnight. DeepStack went further: it recomputed its strategy at every decision, looking only a few moves ahead and using neural networks to estimate what positions beyond that were worth.

Pluribus brought that depth-limited search to six players. Instead of assuming opponents play one fixed way at the edge of its look-ahead, it let them choose among several continuation strategies, which kept it robust. With three or more players, the equilibrium guarantees of two-player games no longer hold, and Pluribus doesn’t adapt to individual opponents — yet it still beat professionals.

DeepStack vs Libratus vs Pluribus

From the published Science papers. Win rates are in big blinds per 100 hands, each against different opponents, so they can’t be compared across bots.

Poker AI milestones, from Polaris to Pluribus

1. July 2007Heads-up limitPolaris vs Phil Laak and Ali Eslami

   At the first Man-Machine Poker Championship in Vancouver, the University of Alberta’s Polaris lost two sessions, won one and drew one against the two pros — overall, not a statistically significant difference.

2. December 2007ResearchCounterfactual regret minimization

   Zinkevich, Johanson, Bowling and Piccione introduce CFR and use it to compute strategies for simplified versions of limit hold’em with up to 10¹² game states.

3. July 2008Heads-up limitPolaris beats limit pros in Las Vegas

   In the second Man-Machine championship, Polaris won three of six duplicate matches against a team of limit hold’em professionals, lost two and drew one.

4. January 2015Heads-up limitCepheus

   Using CFR+ on 4,800 CPU cores for about 68 days, the Alberta team computed a strategy that a perfect opponent could exploit by less than one thousandth of a big blind per hand — too little to detect in a human lifetime of play. It also showed the dealer holds a small built-in edge.

5. April–May 2015Heads-up no-limitClaudico

   Carnegie Mellon’s bot played 80,000 hands against four top pros in Pittsburgh. The humans finished 732,713 chips ahead — a margin CMU described as a statistical tie.

6. Late 2016Heads-up no-limitDeepStack

   Built at Alberta with Charles University and the Czech Technical University, DeepStack played 44,852 hands online against 33 professional players from 17 countries and won about half a big blind per hand, beating 10 of the 11 who completed 3,000 hands by a statistically significant margin. The results appeared in Science in March 2017.

7. January 2017Heads-up no-limitLibratus

   Noam Brown and Tuomas Sandholm’s bot beat four top heads-up no-limit specialists — Dong Kim, Jason Les, Jimmy Chou and Daniel McAulay — over 120,000 hands in 20 days, finishing 1,766,250 chips ahead and ahead of each player individually.

8. July 2019Six-player no-limitPluribus

   Carnegie Mellon and Facebook AI’s bot won against elite professionals in six-handed games over 10,000 hands. Its core strategy was computed in eight days on a single 64-core server with no GPUs — a cloud bill the researchers put at about 144 dollars — and it played in real time on two CPUs.

9. 2020Heads-up no-limitReBeL

   Facebook AI combined self-play learning with search in one general method, and beat a top heads-up professional over 7,500 hands.

Chip totals are how these matches were scored — not cash that changed hands between the players and the bots.

What poker AI means for players

The same algorithms now power the study software serious players use away from the table. The lesson that filtered down is less about any single play than about approach: think in ranges, mix your actions, size bets on purpose, and review your decisions against a strong baseline instead of judging them by whether you won the pot.

It also changed what a practice partner can be. You don’t need a professional-grade bot to improve; you need opponents that play recognizable styles and a way to check your decisions afterwards.

FizzPoker’s bots and post-game review

Hosts can add bots to any open seat — one without an account, more with a free one — labeled clearly at the table. There are five levels, each a different personality rather than a handicapped copy of one bot:

• Level 1 — a calling station: loose and passive, rarely folds or raises.
• Level 2 — tight-passive: plays few hands and seldom bets them hard.
• Level 3 — “ABC” poker: position-aware opening, continuation bets, calls priced by pot odds.
• Level 4 — tight-aggressive: stack-depth aware, push-or-fold when short, semi-bluffs and varied bet sizes.
• Level 5 — plays from precomputed game-theory strategy tables where they exist, and falls back to Level 4 elsewhere.

They’re built for practice, not to beat professionals. After the game, the Fizz Score compares each decision a signed-in player made with game-theory models and labels it acceptable, inaccuracy, mistake or blunder by its estimated cost as a share of the pot — an advisory second opinion, never live advice. Start with poker against bots or build a routine with our poker practice plan.

Questions people ask

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• GTO pokerGame theory optimal, explained with a live chart.
• Poker against botsFive bot personalities, from calling station to GTO-guided.
• Rate my handWhat you have, what beats you, and your odds.
• Poker practiceA scored drill, bots and post-game review.