Combos of Every Hand Type

Assumptions: All examples use a 6-max online cash game at 100 big blinds effective with no rake, unless a different stack depth or format is stated in the example.

"He has aces or ace-king here." You've heard that read a thousand times, and most players treat the two holdings as a coin flip — half the time AA, half the time AK. They're not. Ace-king occurs almost three times as often, and the reason is the single most useful counting fact in poker: hands are not equally numerous. A "hand" like AK is really a bundle of specific two-card combinations, and the bundles come in different sizes. This lesson teaches you the sizes, how to add them up across a range, and how that one skill turns vague reads into numbers you can act on. No board cards yet — everything here is pure preflop counting.

What a combo actually is

A combo (combination) is one specific pair of cards: A♠K♦ is a combo. A♠K♥ is a different combo. "AK" is a label covering every ace paired with every king. When someone says "his range is QQ+ and AK," the label list is short, but the number of actual card pairs hiding behind it is what determines how often he shows up with each holding.

How many two-card combos exist in total? You're choosing 2 cards from 52, and order doesn't matter: 52 × 51 ÷ 2 = 1,326 possible starting hands. Every range you will ever assign is some slice of those 1,326. A range of 133 combos is "top 10% of hands" almost by definition.

The three base numbers

There are only three counts to memorize, because every starting hand falls into one of three structural types.

Pocket pairs: 6 combos each. Take 88. There are four eights — 8♠, 8♥, 8♦, 8♣ — and a pair is any two of them. Enumerate every pairing:

• 8♠8♥, 8♠8♦, 8♠8♣
• 8♥8♦, 8♥8♣
• 8♦8♣

That's 6, and the same enumeration works for any rank: with 4 cards available, the number of pairs is 4 × 3 ÷ 2 = 6. AA is 6 combos. 22 is 6 combos. Every pair in between is 6 combos.

Suited unpaired hands: 4 combos each. AKs means an ace and a king of the same suit, and there are exactly four suits to agree on: A♠K♠, A♥K♥, A♦K♦, A♣K♣. Four combos, no more. This is why suited hands are rare — and why "I always seem to get the offsuit version" isn't bad luck, it's arithmetic.

Offsuit unpaired hands: 12 combos each. AKo is any ace with any king of a different suit. Each of the 4 aces can pair with 3 kings that don't match its suit: 4 × 3 = 12. Or count it the other way: 4 aces × 4 kings = 16 total ace-king pairings, minus the 4 suited ones, leaves 12 offsuit.

Put suited and offsuit together and you get the third number worth engraving: any unpaired hand, suits unspecified, is 16 combos (4 suited + 12 offsuit). "He has AK" with no suit qualifier means 16 possible card pairs.

So the full cheat sheet is: pair = 6, suited = 4, offsuit = 12, unpaired total = 16. Notice the asymmetry that drives everything in this module: an unpaired hand is 16/6 ≈ 2.7 times as numerous as a pocket pair.

Turning range descriptions into totals

A range written in labels becomes a number by simple addition. Work these until the translation is automatic.

"QQ+ and AK." That's QQ, KK, AA, AKs, AKo: 6 + 6 + 6 + 4 + 12 = 34 combos. As a share of all starting hands, 34 of 1,326 is about 2.6% — the classic ultra-premium 4-betting range is one fortieth of the deck's possibilities.

"All suited connectors from 54s to T9s." Six labels — 54s, 65s, 76s, 87s, 98s, T9s — at 4 combos each: 6 × 4 = 24 combos, about 1.8% of hands. People drastically overestimate how often opponents hold these: an entire six-rung ladder of suited connectors is fewer combos than QQ+/AK.

A real opening range. Here is the site's standard UTG raise-first-in range:

AA

AKs

AQs

AJs

ATs

A9s

A8s

A7s

A6s

A5s

A4s

A3s

A2s

AKo

KK

KQs

KJs

Count it by type: 13 pocket pairs (13 × 6 = 78), 25 suited labels (25 × 4 = 100), and 4 offsuit labels (4 × 12 = 48). Total: 226 combos, which is 17% of all 1,326 starting hands. That decomposition tells you something charts hide: nearly half this range's combos are offsuit broadways and pairs even though suited labels dominate the label list. A range grid shows you labels; combos show you frequency. The 25 suited labels look like the bulk of the chart but contribute only 100 of 226 combos.

The habit to build: whenever you assign a range, silently tag it with its combo count. "He's opening 17% from UTG" and "he flats my 3-bet with about 100 combos" are statements you can do arithmetic with on later streets.

The cornerstone: AK outnumbers AA

Now the payoff. Your opponent 4-bet jams, and you're confident his range is exactly AA and AK — the classic nit read. How is that range composed?

• AA: 6 combos
• AK: 16 combos (4 suited + 12 offsuit)

Of his 22 total combos, 16 are AK: he holds ace-king 73% of the time and aces only 27%. The scary holding is the rare one. This single comparison — unpaired 16 versus paired 6 — is the cornerstone of combinatoric thinking, and it directly flips real decisions, because hands that are crushed by AA often do fine against AK.

Watch it play out with queens.

BTN

Q♠♠Q♠

Q♣♣Q♣

COunknown

1. 1.CO raises to $2.50
2. 2.BTN 3-bets to $11
3. 3.Blinds fold
4. 4.CO 4-bet jams to $50 total
5. 5.BTN must call $39 more into a $62.50 pot

Run the numbers. The pot at the decision point is $62.50 (his $50, your $11, plus $1.50 of blinds) and you must call $39, so you need 39 ÷ 101.5 = 38% equity to break even. Against AA alone, QQ has just 18% — fold in a heartbeat. Against AK alone, QQ is a small favorite at 56%. Blend them by combo weight — 73% of the time you're flipping, 27% you're crushed — and QQ's equity against the full {AA, AK} range comes out to 46%, comfortably above the 38% you need. The call profits only because ace-king is 2.7 times as common as aces. A player who mentally weights "AA or AK" at fifty-fifty computes a blended equity near 37% and finds a fold; the combo counter finds a call worth roughly 8 points of equity margin.

When counting says fold

The same arithmetic cuts the other way once the jamming range adds more pairs. Don't memorize "call jams with big pairs" — count the range every time.

CO

J♠♠J♠

J♦♦J♦

BTNunknown

1. 1.CO raises to $2.50
2. 2.BTN jams $25 total
3. 3.Blinds fold
4. 4.CO must call $22.50 more into a $29 pot

Analysis

This regular's jam range is QQ+ and AK: 34 combos, of which 16 (47%) are the AK flip and 18 are overpairs that dominate jacks. Jacks have about 36% equity against the full range but need 44% at this price — a clear fold. The interesting part is that AK is still the single most likely holding; it just isn't likely enough to pay off this price.

Here the read is a 34-combo range: QQ+ (18 combos of overpairs) plus AK (16 combos). Note that AK is still the most common single holding — 16 combos against 6 for any one pair. But the question isn't "what does he have most often"; it's "what's my equity against the whole bundle." Jacks hold 36% equity against {QQ+, AK}, and calling $22.50 to win a $29 pot requires 22.5 ÷ 51.5 = 44%. Fold. Compare the two examples and you see the method: identical logic, opposite answers, and the only inputs were combo counts and a price.

Counting shortcuts you'll use forever

A few patterns recur so often they're worth pre-computing:

• Each additional pocket pair adds 6. "TT+" is 5 pairs = 30 combos. "22+" is all 13 pairs = 78.
• Each unpaired label adds 16, 4, or 12 depending on the suit qualifier. "AQ+" (both AQ and AK, any suits) is 32 combos — almost as many as all of QQ+ (18).
• Broadway offsuit hands bloat ranges fast. Adding just AJo and KQo to a range adds 24 combos — the same as six suited-connector labels.
• Premium ranges are tiny. QQ+/AK at 34 combos is 2.6% of hands. When a tight player's line says "premiums only," you're fighting a 30-something combo range, and you know exactly which 16 of them are unpaired.

One warning before the next lesson: every count above assumed a fresh 52-card deck. The moment cards become visible — the flop, your own hole cards — some combos become impossible, and all of these numbers shrink in predictable ways. AA is 6 combos until an ace appears somewhere you can see. That shrinking, called card removal, is where combo counting starts winning you real pots, and it's the entire subject of the next lesson.

For now, drill the base translation until it's reflexive: pair 6, suited 4, offsuit 12, unpaired 16, deck 1,326. Then test any range description you encounter this week — a training video's "he arrives with JJ+, AQs+, AKo," a forum post's "flats all suited broadways" — by converting it to a combo total and a percentage. The players who do this stop saying "he could have aces" with dread and start saying "that's 6 combos out of his 60" with a shrug.