Poker Combination Calculator
Understanding hand combinations (or "combos") is fundamental to advanced poker strategy. This calculator helps you count the exact number of ways an opponent can hold specific hands, understand blocker effects, and master the mathematics behind card removal. Whether you're analyzing Texas Hold'em ranges or studying hand reading, knowing your combos transforms intuition into precise analysis.
Combination counting underlies concepts like range construction, blockers, and equity calculations. When you know there are only 6 ways to make pocket Aces but 16 ways to make AK, you can make more informed decisions about what opponents are likely to hold.
Select Calculation Mode
Select Hand Type
Click a hand type to see its combination count and breakdown.
AA Combinations
6 CombosAll Possible Combinations
Your Hole Cards (Blockers)
Enter your hole cards to see how they block opponent holdings.
Blocker Effects of A♠K♥
How Your Cards Block Opponent Hands
Remaining Combos Summary
Enter Board Cards
Add board cards to see how they affect opponent hand combinations.
Target Hand to Analyze
AA on A♠K♥T♦
3 CombosRemaining Combinations
Quick Reference: Starting Hand Combinations
Understanding Hand Combinations
Hand combinations, often called "combos," represent the number of different ways a specific hand can be dealt from a standard 52-card deck. This concept is fundamental to poker mathematics and directly influences how we construct and analyze opponent ranges. According to the Two Plus Two Publishing educational resources, understanding combos is essential for transitioning from recreational to serious poker play.
Why Combinations Matter
When you assign an opponent a range like "AA, KK, AK," knowing the exact combo count (6 + 6 + 16 = 28 combos) helps you calculate precise equities and make better decisions. A range of "just premium hands" isn't as narrow as it sounds when you count the combos.
The Mathematics of Poker Combos
Combination mathematics uses the binomial coefficient formula, often written as C(n,k) or "n choose k." For poker hands, this calculates how many ways we can select k cards from n available cards. Research published in mathematical journals and referenced by PokerStrategy's mathematics curriculum confirms these fundamental calculations.
| Hand Type | Formula | Combos | Probability | Example |
|---|---|---|---|---|
| Specific Pocket Pair | C(4,2) = 6 | 6 | 0.45% | AA, KK, QQ |
| Any Pocket Pair | 13 × 6 = 78 | 78 | 5.88% | 22 through AA |
| Specific Suited Hand | 4 suits available | 4 | 0.30% | AKs, QJs |
| Specific Offsuit Hand | 4 × 3 = 12 | 12 | 0.90% | AKo, QJo |
| Specific Non-Pair (s+o) | 4 + 12 = 16 | 16 | 1.21% | AK (all) |
| All Starting Hands | C(52,2) | 1,326 | 100% | Complete deck |
Understanding Blockers
Blockers (also called "card removal effects") describe how the cards you hold reduce the possible combinations of hands your opponents can have. This concept is critical for advanced strategies like bluffing with Ace-high or value betting thin. The Upswing Poker strategy guides emphasize blocker considerations as a key differentiator between intermediate and advanced players.
Blocker Impact Examples
Holding one Ace reduces opponent's AA combos from 6 to 3 (50% reduction). Holding AK removes 50% of opponent's AK combos (16 → 9). Understanding these reductions helps you bluff more effectively and call lighter when opponents could be bluffing.
Blocker Effects by Hand Type
- Holding one card of a rank: Reduces that rank's pocket pair combos from 6 to 3 (50%)
- Holding two cards of the same rank: Reduces that rank's pocket pair combos from 6 to 1 (83%)
- Holding one Ace: Reduces AK combos from 16 to 12 (25%), AA combos from 6 to 3 (50%)
- Holding AK: Reduces opponent's AK combos from 16 to 9 (44%), AA from 6 to 3, KK from 6 to 3
Practical Applications
Understanding combinations transforms your poker decision-making in several key areas:
1. Range Construction
When building opening ranges with our Hand Range Visualizer, knowing that AKo adds 12 combos while AKs adds only 4 helps you understand your actual range width. A "tight" range of AA-TT, AK-AQ is actually 66 combos (5% of hands).
2. Equity Calculations
Our Hand Equity Calculator and EV Calculator rely on combo counting to weight opponent ranges correctly. Knowing an opponent can have 6 combos of AA but 16 combos of AK means AK should be weighted more heavily in equity calculations.
3. Bluffing Decisions
Blockers inform optimal bluffing spots. Holding A♠ when the board is Q♠T♠8♠2♥3♣ means you block the nut flush, making your bluff more effective because opponents are less likely to call with the nuts. Learn more about integrating blockers into your bluffing strategy in our Complete Bluffing Guide.
4. Board Texture Analysis
As community cards are revealed, combo counts change. An Ace on the flop reduces opponent's AA combos from 6 to 3, and their AK combos from 16 to 12. This dynamic card removal is essential for hand reading throughout the hand.
Advanced Concepts
Combo Counting on Different Streets
Card removal compounds as more board cards appear. Preflop, an opponent has access to all 1,326 starting combinations. By the river, with 5 community cards known plus your 2 hole cards, only 45 cards remain unknown, significantly reducing possible opponent holdings.
Example: Flop Analysis
On a board of A♠K♥T♦, if you're considering whether your opponent has AK, remember: normally AK has 16 combos, but the A♠ and K♥ on board reduce this to 9 combos (the A and K in remaining suits combined with the three remaining K and A cards respectively).
The 169 Unique Hands
While there are 1,326 total two-card combinations, they group into 169 strategically distinct starting hands: 13 pocket pairs, 78 suited non-pairs, and 78 offsuit non-pairs. The Preflop Trainer helps you learn optimal decisions for all 169 unique hands.
Frequently Asked Questions
How many combinations are there for pocket pairs?
Each pocket pair has exactly 6 combinations. With 4 suits and needing 2 of the same rank, you have C(4,2) = 6 ways to make any specific pair. For example, AA can be made 6 ways: A♠A♥, A♠A♦, A♠A♣, A♥A♦, A♥A♣, A♦A♣. All 13 pocket pairs together account for 78 of the 1,326 total starting hand combinations.
What is the difference between suited and offsuit combinations?
Suited hands (same suit) have 4 combinations each - one for each suit (A♠K♠, A♥K♥, A♦K♦, A♣K♣). Offsuit hands (different suits) have 12 combinations - 4 choices for the first card's suit times 3 remaining suits for the second card. This 3:1 ratio explains why suited hands are significantly rarer than their offsuit counterparts.
What are blockers in poker and why do they matter?
Blockers are cards in your hand that reduce the combinations of hands your opponent can have. They matter because they affect the probability of opponents holding certain hands. For example, holding an Ace means opponents are less likely to have AA or AK. Skilled players use blocker information to make better bluffing decisions (bluff when blocking opponent's calling hands) and better calling decisions (call when blocking opponent's value hands).
How do I use combo counting in real-time during play?
Start with memorized baseline combos (6 for pairs, 4 for suited, 12 for offsuit, 16 for all). Then adjust based on known cards. Each card you see of a rank reduces pair combos by approximately half. Practice estimating rather than calculating exactly - knowing opponent has "about half" the combos is often sufficient for decision-making.
More Learning Resources
Expand your understanding of poker mathematics and strategy with these related tools and guides:
- Hand Range Visualizer - Build and analyze starting hand ranges
- Hand Equity Calculator - Calculate equity between specific hands
- Expected Value Calculator - Analyze decision profitability
- Pot Odds Calculator - Compare pot odds to equity
- Preflop Trainer - Practice opening decisions by position
- Poker Hand Rankings - Complete hand strength reference
- Position Guide - Understand positional advantages
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