New poker combinatorics exercises: count combos and analyse ranges

How many combinations of AA can your opponent hold when you already have an ace? And how much of their range connects with a flop? To practise these questions, Tools of Poker introduces five combinatorics and range-analysis exercises, each with its own tutorial.

The new section follows a progression: count specific hands, remove impossible combinations and understand the range that remains.

First, understand what you are counting

A combo is a specific pair of cards, including their suits. A♠K♠ and A♥K♥ both belong to AKs, but they are different combos. Hand classes do not all carry the same weight: with all 52 cards available, a pair has 6 combos, a suited hand has 4 and an offsuit hand has 12.

🎯 From hands to blockers

Hand combinations trains that initial count. The aim is to understand where each number comes from, rather than memorise figures without context. The hand-combinations tutorial explains it visually.

Known-card blockers then introduces your cards and the board. Every known card removes opponent combos containing that card. You work with three counts: original, blocked and available. The blockers tutorial helps you avoid removing the same combo twice.

An example to get started

Without known cards, AA has six combos. If you hold A♠ and no other ace is known, your opponent can only pair A♥, A♦ and A♣. That leaves 3 AA combos: A♥A♦, A♥A♣ and A♦A♣. One ace has blocked three combinations, not one.

🔎 Count the range and find out what it contains

Range combinations applies the count to every marked hand in a matrix. Add the original combos, subtract blockers and calculate the percentage still available relative to the original range. Follow the process in the range-combinations tutorial.

Range composition on the board asks a different question: how many available combos form the requested hand or draw? Examples include top pair, a set or a flush draw. The range-composition tutorial explains why the denominator is now the available range. This percentage describes the range’s contents; it is not your equity.

From counting combos to estimating equity

The progression ends with Hand vs range equity. Compare your hand with the opponent’s possible combos and include ties. On the river, against one opponent and with equal weight for each combo, equity is wins plus half the ties, divided by all available combos.

The initial levels guide you through river calculations. Hard and nightmare introduce turn or flop situations, where the remaining cards also matter. The hand-vs-range equity tutorial develops this distinction.

Practise in a useful order

Start with combinations of one hand and move on when you understand what you are removing and why. Use the tutorials for support before returning to exercises with different situations. The goal is to see an opponent’s range as concrete hands you can count and compare, rather than just marked squares.

Start with the new combinatorics exercises on Tools of Poker.