23 Jul 2025 Advanced This material is for experienced players combinatorics probabilities Combinatorics may sound complicated, but in poker, it’s just a way to count the different possible hand combos your opponents could have. In this article, we’ll go through the basics of counting combos in poker and see why it’s so useful for your decision-making. In this article we’ll use “combinatorics,” “combos,” and “hand combinations” to mean the same thing. What Is Poker Combinatorics? Poker combinatorics is the process of calculating how many combinations of specific hands are possible in a given situation. For example: How many ways can you be dealt ? How many combos of pocket exist? How many combos are possible on a board? How many straight draw combos can be on an flop? If you can quickly answer these questions, you’ll have a much better sense of what hands your opponent might hold — and this makes your decisions much stronger. Starting Hands Combinatorics Any two unpaired cards (e.g., or ): 16 combos Pocket pairs (e.g., or ): 6 combos Example If you write down every way you can be dealt AK (, , , , etc.), you’ll end up with 16 different combos. If you do the same with a pocket pair like JJ (, , , etc.), you get 6 possible combos. In Texas Hold’em, there are 1,326 different possible starting hand combinations. Also, you’ll notice: Suited combos (e.g., AKs): 4 Offsuit combos (e.g., AKo): 12 This means you’ll get offsuit unpaired hands 3x more often than suited ones, and you’ll be dealt unpaired hands much more often than pairs. Calculating Combos Using Known Cards Let’s say you have on board . How many and combos could your opponent have? Unpaired hands (like AK): Combos = Free cards for first rank × Free cards for second rank So on , you see 1 king on board and you have 1 king, so there are 2 kings left. All 4 aces are left. Combos of AK = 4 × 2 = 8 combos Pocket pairs (like TT): Combos = [Free cards × (Free cards - 1)] / 2 On a KT4 flop, there are 3 tens left in the deck. Combos of TT = (3 × 2) / 2 = 3 combos Key Takeaways Unpaired hands: Just multiply the number of available cards for each rank. Pocket pairs: Multiply the number of available cards by one less, then divide by two. Why Counting Combos Matters Counting combos gives you much more info about your opponent’s range. For example, imagine someone 3-bets you with a super tight range: [, ] (about 2% of hands). You might think the hands are split evenly: AA: 33% KK: 33% AK: 33% But if you count the actual combos: AA: 6 KK: 6 AK: 16 Out of 28 possible combos, AK makes up 57% — meaning your opponent has AK way more often than AA or KK. Bottom Line Counting combos is easy: For unpaired hands, multiply the number of available cards for each. For pairs, multiply the number of available cards by one less, then divide by two. If you only think about ranges and ignore combinatorics, you’ll miss out on valuable information. You probably won’t count every combo during live play, but even just being familiar with how hands are distributed can improve your decisions. Over time, you’ll start to see which draws and made hands are more likely, and this knowledge will help you win more often.
