PokerSkill: A Solver-Free Poker Strategy Framework

• PokerSkill is a framework that operationalizes measurable poker skills using probabilistic modeling, behavioral dynamics, and structured AI decision-making.
• It integrates quantitative analysis, legal classification, and computational methods to delineate skill versus chance in various poker formats.
• The approach combines a deterministic context engine with a layered human-authored skill library to enable competitive, solver-free play in heads-up no-limit Texas Hold’em.

PokerSkill denotes the formal study and operationalization of skill in poker across legal classification, probabilistic modeling, behavioral dynamics, and artificial intelligence, and more narrowly names a 2026 training-free, solver-free framework for heads-up no-limit Texas Hold’em that uses a deterministic context engine and a human-authored skill library to ground large-language-model decisions (Li et al., 28 May 2026). Across this literature, poker skill is not treated as a single primitive. It is variously represented as a player’s probability of winning raked cash-game rounds, rational decision-making in tournaments, leverage over stochastic decision trees, calibrated bluffing under incomplete information, persistent performance in online play, and bounded action selection in large imperfect-information games (Javarone, 2015).

1. Skill, chance, and the classification problem

A central research problem is whether poker should be classified as a skill game or as gambling. In the cash-game thermodynamic model, this distinction is presented as an open question with legal, regulatory, and healthcare implications that vary from country to country, and the paper explicitly limits itself to a simplified heads-up cash-game setting rather than claiming to settle the issue for all poker formats (Javarone, 2015). A parallel tournament-based agent model makes the classification explicitly behavioral: poker is treated as more skill-based when rational players systematically outperform irrational players, but the degree to which this occurs depends on the fraction of rational players, the tournament structure, and whether rational play degrades into irrational play under pressure (Javarone, 2014).

Format dependence is a recurring theme. The statistical-physics study of rational versus irrational behavior distinguishes between a full heads-up challenge, modeled as $n=\infty$, and a single-round interaction, modeled as $n=1$, and concludes that poker can behave like a skill game or like gambling depending on how the game is played (Javarone, 2015). Online-play evidence points in the same direction but from observational data rather than stylized dynamics: the paper reports a correlation coefficient of $0.904$ between poker win rates across December 2022 and January 2023 for users with at least 30 games in both months, interprets this as persistence of performance, and concludes that there is a preponderance of skills over chance to succeed in online poker, while also stating that there is no difference in online and offline poker from the perspective of requirement of skills (Kaur et al., 2023).

These lines of work converge on a narrow but important distinction. A game may reward better decisions in relative terms without guaranteeing that those decisions are sufficient for easy or stable profitability. This suggests that “poker skill” is best understood as a family of measurable edges whose practical expression depends on format, incentives, opponent ecology, and observation horizon.

2. Quantitative formalisms of poker skill

One of the sharpest quantitative definitions appears in the cash-game thermodynamic model. In a heads-up game with equal initial bankrolls $E_A(0)=E_B(0)$, fixed pot $\delta$, and rake $\epsilon$, player $A$’s bankroll evolves as

$$E_A(t) = E_A(0) - \Phi_{A,B}(t) + \Phi_{B,A}(t)\cdot (1-\epsilon).$$

Under the long-run break-even condition $\lim_{t\to\infty}E_A(t)=E_A(0)$, the minimum round-winning probability required to avoid losing money is

$P_a=\frac{1}{2-\epsilon}.$

With a rake of about $n=1$0, this gives $n=1$1, so a player must win about 51.28% of rounds just to break even in that stylized raked cash game (Javarone, 2015). In this formulation, skill is a probabilistic edge, but profitability requires that the edge exceed a transaction-cost threshold imposed by the poker room.

A broader cross-game formalization is the Skill–Luck Index

$n=1$2

where $n=1$3 is skill leverage and $n=1$4 is luck leverage. In that framework, poker is reported as

$n=1$5

The positive index places poker on the skill-dominant side, while the nontrivial $n=1$6 and the volatility $n=1$7 preserve the claim that short-run outcomes remain highly noisy (Silver, 3 Nov 2025).

A more local strategic formalism appears in the river-defense work on the “100--50--25 MIN rule.” There, the optimal defense frequency is approximated by

$n=1$8

with

$n=1$9

and range advantage defined as Player 1’s equity under the two private-card distributions. The point is not that bet size alone determines optimal calling frequency, but that defense should be discounted when the bettor’s range is stronger overall (Ganzfried et al., 2019).

A still more stripped-down game of incomplete information is the two-bet “poker-litigation game,” in which each player receives a private card $0.904$0, chooses a high bet $0.904$1 or low bet $0.904$2 with $0.904$3, and plays a threshold-with-randomization equilibrium. The derived strategy is

$0.904$4

meaning a player should always bet high with cards above $0.904$5, and with cards below $0.904$6 should bet high with probability $0.904$7 and low with probability $0.904$8 (Guerra-Pujol, 2015). In that model, poker skill is identified with calibrated mixed-strategy bluffing under incomplete information.

Taken together, these formalisms define poker skill through distinct but compatible quantities: round-win probability under rake, strategic leverage relative to luck leverage, range-level defense frequencies, and mixed-strategy thresholds under private information.

3. Behavioral, population, and multiplayer dynamics

Behavioral models emphasize that poker skill depends not only on rules but on who is playing and how they adjust. In the tournament study of rational versus irrational agents, a rational player’s single-match win probability against an irrational player is estimated as

$0.904$9

which yields $E_A(0)=E_B(0)$0 consecutive expected wins and a “minimum theoretical density” of rational agents

$E_A(0)=E_B(0)$1

Under increasing blinds $E_A(0)=E_B(0)$2, the probability that a rational agent wins the tournament exceeds $E_A(0)=E_B(0)$3 when $E_A(0)=E_B(0)$4, and approaches $E_A(0)=E_B(0)$5 as $E_A(0)=E_B(0)$6. Under constant blinds $E_A(0)=E_B(0)$7, rationality is even more dominant, with $E_A(0)=E_B(0)$8 already at $E_A(0)=E_B(0)$9. When rational agents are allowed to become irrational after losses according to

$\delta$0

the tournament win probability is well fit by

$\delta$1

This makes rationality a contingent rather than absolute source of skill (Javarone, 2014).

The statistical-physics cash-game model reaches a related conclusion from a different direction. In full heads-up challenges, a rational player facing an irrational player is assigned win probability $\delta$2, so the selection parameter

$\delta$3

favors rational behavior. In the single-round case, however, the paper reports the empirical fit

$\delta$4

and states that rational agents prevail with probability greater than $\delta$5 only if $\delta$6. The paper’s summary phrase is that few irrational players can turn poker into gambling (Javarone, 2015).

Multiplayer Kuhn-poker models complicate the notion of a single optimal style. In simplified three-player Kuhn poker, there is one equilibrium solution if

$\delta$7

and three distinct equilibrium solutions if $\delta$8; the accompanying third-order ODE model yields oscillatory dynamics rather than convergence to a fixed point (Billingham, 2017). In the full-street simplified three-player variant, the number of nontrivial betting frequencies is reduced from 23 to 11, there are three ranges of pot size with three coexisting equilibria, and none of the equilibrium solutions is asymptotically stable under the repeated-play ODE model; depending on pot size, the resulting trajectories can be periodic, close to periodic, or exhibit long chaotic transients (Billingham, 2017).

Observational online evidence aligns with these stylized models in a weaker but population-level sense. Average big blind amount won rises with experience, average big blind amount lost in losing sessions falls, more experienced users display greater tightness linked to VPIP, and the distributional analysis is interpreted as inconsistent with pure randomness (Kaur et al., 2023). This suggests that poker skill is not only a static equilibrium object. It also appears as behavioral stability, adaptation, and repeated-play control of frequencies in noisy environments.

4. Computational models of poker skill before solver-free grounding

Early computational systems operationalized poker skill as probabilistic inference and decision theory. The Bayesian Poker Program used a Bayesian network over nodes such as BPP Current, BPP Final, OPP Upcards, OPP Current, OPP Final, OPP Action, and BPP Win, combined with pot-odds thresholds

$\delta$9

and stochastic betting curves defined over $\epsilon$0. Its betting/raising, folding, and calling tendencies were parameterized by sigmoid and Gaussian-like functions, and the system was reported to outperform a simple rule-based system and a probability-only baseline, though not the better human opponents (Korb et al., 2013).

Pattern-learning approaches treated poker skill as structured recognition over cards and action history. Poker-CNN encoded cards as sparse $\epsilon$1 matrices padded to $\epsilon$2, built a five-card representation with one layer per card plus an aggregate layer, and in 2-7 triple draw expanded the full state to a $\epsilon$3 tensor. The best video-poker CNN achieved $\epsilon$4 for the heuristic player and $\epsilon$5 for the fully connected baseline; in triple draw, the final self-play-refined Poker-CNN significantly outperformed both the heuristic model and an earlier CNN trained on heuristic play (Yakovenko et al., 2015).

By 2015, the strongest no-limit systems were already built around approximate equilibrium computation. In the first man-versus-machine no-limit Texas Hold’em competition, Carnegie Mellon’s Claudico played 20,000 hands against each of four elite human specialists for a total of 80,000 duplicate-scored hands. The human team won by 732,713 chips, equivalent to 9.16 BB/100, statistically significant at the 90% confidence level but not at the 95% level. Claudico relied on action abstraction, information abstraction, scalable CFR, pseudo-harmonic action translation

$\epsilon$6

and river endgame solving, but the paper identifies the off-tree problem and blocker-sensitive bluff selection as major weaknesses (Ganzfried, 2015).

Later work examined whether AI systems actually exhibit bluffing. In extended Leduc Hold’em, both DQN and CFR agents were found to bluff, but with different styles and frequencies. Under the threshold-based detector, CFR’s bluff success rate was $\epsilon$7 and DQN’s was $\epsilon$8; under the statistics-based detector, CFR’s was $\epsilon$9 and DQN’s was $A$0. The paper’s interpretation is that bluffing is an essential aspect of the game, not of the algorithm (Zaciragic et al., 4 Sep 2025).

LLM-based poker systems initially exposed a gap between declarative knowledge and stable play. In a pre-flop raise-first-in analysis for 9-player no-limit hold’em, ChatGPT and GPT-4 displayed understanding of hand value and position, but neither matched GTO charts. ChatGPT was characterized as a nit, GPT-4 as a maniac, and GPT-4 under a GTO prompt was reported to raise 90% of hands from the Button, whereas the paper describes standard GTO Button play as folding about 50% of hands (Gupta, 2023). A more specialized LLM route is SpinGPT, trained by supervised fine-tuning on 320,000 high-stakes expert decisions and then refined with 270,000 solver-generated hands. The resulting model reaches 78% tolerant accuracy on held-out solver decisions and, with a simple deep-stack heuristic, achieves

$A$1

versus Slumbot in heads-up over 30,000 hands (Maugin et al., 26 Sep 2025).

5. “PokerSkill” as a solver-free LLM framework

The 2026 framework named PokerSkill is a training-free, solver-free system for heads-up no-limit Texas Hold’em that uses a large human-authored library of poker skills as a structured action-grounding interface for a frontier LLM. Its target domain is full HUNL with 200 big blind effective stacks, and its architecture consists of a layered skill library, a deterministic context engine, and an action-grounding and validation interface (Li et al., 28 May 2026).

The skill library is organized into five prompt layers. P1 contains always-active game rules, legal-action protocol, output schema, and general constraints. P2 provides preflop range-table guidance for one of 12 preflop scenarios. P3 encodes stable postflop principles. P4 supplies context-specific postflop skills keyed by board texture, hand class, action line, and role. P5 adds river blocker guidance. The deterministic context engine computes preflop scenario, board texture, hand class, draw class, action-line scenario ID, pot type, aggressor or defender role, and weighted betting pressure, and then derives remaining attack and defense budgets as

$A$2

The pressure weights come from a 46-entry piecewise lookup over bet size as a percentage of pot, with representative thresholds ranging from $A$3 up to $A$4.

The system then presents the LLM with only a small list of viable strategic options rather than the entire legal no-limit action space. Roughly 60% of postflop decisions present 2 viable actions, and the remaining 40% present 3–4 options. Output is forced through structured JSON, checked by a validator, and if validation fails the system defaults to the most conservative viable action; such fallbacks occur in fewer than 0.1% of hands. The framework reports approximately 60 action-line scenarios, 23 hand classes, and 46 bet-size pressure thresholds, and the paper’s central claim is that rules alone do not yield a strong strategy and raw LLMs alone do not play well, but their combination produces a competitive agent (Li et al., 28 May 2026).

Evaluation is against GTOWizard’s HUNL benchmark server using AIVAT-adjusted mbb/hand. The main reported results are: $A$5 for GPT-5.5 XHigh with PokerSkill,

$A$6

for Claude Opus 4.6, and

$A$7

for Claude Opus 4.7. These reduce losses by 49--61\% relative to default-prompt baselines and improve substantially over the rule-based (no LLM) ablation at

$A$8

The paper also reports default-prompt losses of $A$9 for GPT-5.5 XHigh and $$E_A(t) = E_A(0) - \Phi_{A,B}(t) + \Phi_{B,A}(t)\cdot (1-\epsilon).$$0 for Claude Opus 4.6, and notes that all three PokerSkill agents outperform the published Slumbot result of $$E_A(t) = E_A(0) - \Phi_{A,B}(t) + \Phi_{B,A}(t)\cdot (1-\epsilon).$$1 against GTOWizard (Li et al., 28 May 2026).

Within the literature surveyed here, PokerSkill is distinctive because it does not compute equilibrium online, does not fine-tune the model, and does not query a solver at inference time. Its competence is instead attributed to deterministic state grounding, selective symbolic retrieval, bounded viable-action presentation, and strict output validation.

6. Tooling, infrastructure, limitations, and open problems

Two infrastructure projects broaden the research space around poker skill. PokerKit is an open-source Python library for fine-grained multi-variant poker simulation and unified hand evaluation, intended to overcome the fact that many existing simulators are proprietary and many open-source evaluators have narrower hand-type support. The paper reports support for pre-defined and user-defined variants, customizable deck type, unit tests and doctests, replay of all 83 televised hands, and 99% code coverage (Kim, 2023). The Instruction-Driven Game Engine uses poker as a case study for Next State Prediction and Differential State Prediction with natural-language rule descriptions. Its curriculum combines core-function warmup and segment rephrasing, and the best configurations achieve 100% round-level success on ten in-domain poker variants while generalizing strongly to human-authored out-of-domain variants such as “Magic Dealer,” “6-card Draw,” and “Joker Hold’em” (Wu et al., 2024).

At the same time, the literature is explicit about what current formalisms do not capture. The Skill–Luck Index paper states that poker and werewolf are approximated “by averaging over hidden states, conflating epistemic and aleatoric uncertainty,” and adds that “true skill measurement requires information-set equilibria” (Silver, 3 Nov 2025). The pre-flop LLM study shows that even broad poker competence can be fragile with respect to notation order, temperature, and top-$$E_A(t) = E_A(0) - \Phi_{A,B}(t) + \Phi_{B,A}(t)\cdot (1-\epsilon).$$2, with prompts like A4s and 4As producing very different decision matrices (Gupta, 2023). The Claudico reflection identifies the off-tree problem as a structural weakness of abstraction-based no-limit play (Ganzfried, 2015). PokerSkill itself is training-free only in the sense of zero model fine-tuning and zero solver access during play; the library is entirely human-authored, the framework is HUNL-specific, and the paper does not provide exploitability bounds (Li et al., 28 May 2026).

A plausible synthesis is that poker skill research has moved from asking whether poker contains skill at all to specifying which kind of skill is being measured. The resulting objects are heterogeneous: break-even thresholds under rake, persistence of performance, rationality under tournament pressure, equilibrium multiplicity in multiplayer toy games, solver alignment, bluff success, and context-grounded action selection. This suggests that “PokerSkill” is best understood not as a single metric, but as a layered research program linking legal classification, stochastic control, strategic balance, behavioral adaptation, and increasingly modular AI systems.