15 Jan 2025 Advanced This material is for experienced players blockers combinatorics One of the most advanced and essential skills in poker is understanding and applying combinatorics and blockers. This skill relies entirely on basic math, so if you can handle simple addition like 4+12, you're good to go! Knowing how to use poker combinatorics and blockers can help you find additional bluffing opportunities and thin value bets in every session. Let’s break down these concepts in simple terms. What Are Combinations in Poker? Combinations represent the number of ways a particular hand can be formed. For example, for AKs, there are 4 possible combinations: , , , If you’ve heard terms like "combos" or "combinatorics," they all refer to the same thing. What Are Blockers in Poker? Blockers are known cards (either in your hand or on the board) that reduce the number of possible combinations your opponent could have. Complete Blockers: Fully remove a hand from the opponent’s range. Partial Blockers: Reduce the total number of combinations of a hand. Example: If you hold , your opponent cannot have . However, this doesn’t eliminate all AA combinations; it just reduces them from 6 to 3 (, , ). Combinations and Blockers Preflop Blockers and combinatorics work differently depending on the stage of the hand. Let’s start with preflop. Key Points: Any pocket pair: 6 combinations Unpaired hands: 16 combinations (4 suited and 12 offsuited) For example, if you hold , you block: KK: Reduced from 6 to 3 (, , ) AK: Reduced from 16 to 12 (3 Kings × 4 Aces = 12) QTs: Reduced from 4 to 3. Total Preflop Combinations 169 starting hands (13x13 matrix). 1,326 total combos (including suited and offsuit hands). With your two hole cards, the maximum is 1,225 remaining combos. Combinations and Blockers Postflop On the flop, you can use blockers and board cards to narrow your opponent’s range. Counting Pocket Pair Combos Use the 6-3-1-0 Rule: No blockers: 6 combos 1 blocker: 3 combos 2 blockers: 1 combo 3 blockers: 0 combos Example: Board : 6 combos : 3 combos : 1 combo (if you don’t hold a ) If you hold , the opponent has 0 combos of . Counting Non-Pair Combos For hands like two pairs or top pair, use multiplication. Multiply the number of unseen cards of each rank. Example: Board 3 unseen × 3 unseen = 9 combos of . If your opponent plays only suited combos, adjust accordingly. The board is blocking 1 suited combo of KJs, leaving 3 suited combos in the opponent's range. Flush Draws and Blockers Flush draws often scare players unnecessarily. Understanding blockers can help you stay rational. Example: Board Maximum flush draw combos: 56 (assuming loose ranges). Realistically: Tight players have ~15-30 flush draw combos. What Are Action Blockers? In poker, not only do your hole cards and the board cards act as blockers, but the actions taken during the hand can also reduce the possible combinations your opponent might hold. For example, imagine the turn brings a potential flush: , and you’re concerned your opponent could have completed flushes such as , , or . But ask yourself: Wouldn't they have raised with such strong combo-draws on the flop? If you believe they likely would have, and they didn’t, you can safely remove these hands from their range. As a result, the number of flush combinations they could hold becomes even lower by the turn. The same logic applies to hands like . Would they have called or raised with this hand earlier in the hand? Many players overreact when a flush draw completes, but in reality, if you consider combinations, card blockers and action blockers, the number of potential flushes your opponent can have is often very small. By applying combinatorics and blockers, you’ll develop a more precise understanding of your opponent’s range and improve your decision-making.
