The single mental shift that separates recreational play from real study.
A beginner asks: what do I have? A studied player asks: what does my whole range look like here — and what does theirs?
You never hold just one hand in a spot. You hold every hand you'd play the same way. The grid on the home page is the map: 169 starting hands, coloured by what a solver does with each. Reading a board through ranges instead of your two cards is the whole game in one habit.
This is why poker shares an epistemic backbone with every other bet worth making — you act on the distribution of outcomes, never on a single certainty.
Range
The full set of hands a player can have in a given spot, weighted by how often each occurs.
Combo
One specific two-card holding. AKs is 4 combos; AKo is 12; a pair is 6.
Polarised
A range split into strong value and bluffs, with the middle checked or folded.
Range advantage
Whose range contains more strong hands on a given board — it dictates who can bet aggressively.
Alon analyses simplified Hold'em models where stronger players win at rates that can't be explained by chance alone. The Central Limit Theorem then implies that over enough hands, results converge toward skill — not toward 50/50.
One bad session proves nothing. Track decisions, not outcomes, until the sample is large enough for skill to surface.
Source — Alon (2013). Poker, Chance and Skill.
Fellows' abstraction work groups hands by strategic similarity on public boards — not by arbitrary colour. The range grid you train on is a compressed map of information structure, the same trick Billings et al. used to shrink full-scale Hold'em by 100 billion×.
When two hands share a colour on the matrix, the solver treats them similarly in that spot. That's a claim about strategy, not decoration.
Source — Fellows (2007). Pseudo-Optimal Hold'em Solutions. UCSD / AAAI Computer Poker Competition.
Poker, Chance and Skill
Alon (2013). Poker, Chance and Skill.
Toy models of Hold'em show skilled players beat weaker ones at rates variance can't explain away forever.
Pseudo-Optimal Solutions to Texas Hold'em with Improved Chance Node Abstraction
Fellows (2007). Pseudo-Optimal Hold'em Solutions. UCSD / AAAI Computer Poker Competition.
Board-card bucketing from empirical strategy structure — ranges aren't arbitrary, they're abstracted information.
Approximating Game-Theoretic Optimal Strategies for Full-scale Poker
Billings et al. (2003). Approximating GTO Strategies for Full-scale Poker. U. of Alberta.
Abstracted 10¹⁸-node Hold'em down 100 billion× while keeping strategic structure — the blueprint for modern solvers.
The board is A♠ K♦ 4♣. Who holds the range advantage: the preflop raiser or the caller?
The preflop raiser. Their range is dense with AK, AQ, AA, KK — the caller flatted these away preflop, so ace-king-high boards smash the raiser's range. They can bet small and often.
Stop asking 'is my hand good?' Ask 'how does my range interact with this board versus theirs?'