Poker school · lesson 3 of 7
Hands, ranges and combos
How players write hands down, why there are 1,326 starting hands but only 169 kinds, and why good players think about every hand an opponent could hold. 4 min read.
Writing hands down
Players use a short notation for starting hands. The ranks are A, K, Q, J, T, then 9 down to 2. T stands for ten, so every hand fits in two characters. Add s for suited, both cards of one suit, or o for offsuit.
- AKs: ace-king suited, such as ace of hearts, king of hearts.
- KQo: king-queen offsuit, such as king of spades, queen of diamonds.
- 77: a pair of sevens. Pairs need no s or o.
For groups of hands, a plus means “and better”, keeping the top card the same, and a dash gives a span.
- 22+: every pair, from twos to aces.
- 88+: 88, 99, TT, JJ, QQ, KK and AA.
- ATs+: ATs, AJs, AQs and AKs. The kicker rises to just below the ace.
- KTo+: KTo, KJo and KQo.
- A5s-A2s: A5s, A4s, A3s and A2s.
The 169 kinds of starting hand
Pairs, on the diagonal (6 combos each)Suited, above it: s (4 each)Offsuit, below it: o (12 each)
13 pairs, 78 suited and 78 offsuit hands
Combos: counting the ways
With 52 cards there are 52 × 51 ÷ 2 = 1,326 different two-card hands. They fall into 169 kinds: 13 pairs, 78 suited hands and 78 offsuit hands. The kinds aren’t equally likely, because each can be dealt a different number of ways, called combos.
- A pair: 6 combos, because four aces can be paired up 6 ways.
- A suited hand: 4 combos, one for each suit.
- An offsuit hand: 12 combos. There are 4 × 4 = 16 ways to pair an ace with a king, and 4 of them are suited.
So ace-king, suited and offsuit together, is 16 combos, while aces are only 6. A player who could have either is more than twice as likely to hold ace-king.
Every way to be dealt a hand
A pair of aces, AA: 6 combos
A♠A♥A♠A♦A♠A♣A♥A♦A♥A♣A♦A♣
Ace-king suited, AKs: 4 combos
A♠K♠A♥K♥A♦K♦A♣K♣
Ace-king offsuit, AKo: 12 combos
A♠K♥A♠K♦A♠K♣A♥K♠A♥K♦A♥K♣A♦K♠A♦K♥A♦K♣A♣K♠A♣K♥A♣K♦
Counting a range
- 22+: 13 pairs × 6 = 78 combos.
- ATs+: 4 hands × 4 = 16 combos.
- KQs: 4 combos.
- AJo+: 3 hands × 12 = 36 combos.
- In all: 134 combos out of 1,326, about 10% of hands.
22+, ATs+, KQs, AJo+: 134 combos
RaiseFold
134 combos · 10.1% of hands
22+ · ATs+ · KQs · AJo+
Cards you can see change the count
Every card you can see, in your hand or on the board, takes combos out of your opponent’s range. This is card removal, and the cards that do it are called blockers.
Blockers at work
- With no cards known, villain can hold ace-king 16 ways.
- You hold an ace: 3 aces × 4 kings = 12 ways.
- You hold ace of spades, king of diamonds: 3 × 3 = 9 ways.
- You hold ace of spades, king of diamonds and an ace is on the board: 2 × 3 = 6 ways.
Villain’s ace-king, as you see more cards
Villain can hold itGone: uses a card you can see
No cards known: 16 combos
K♠K♥K♦K♣A♠A♥A♦A♣You hold an ace, ace of spades: 12 combos
K♠K♥K♦K♣A♠××××A♥A♦A♣You hold ace of spades, king of diamonds: 9 combos
K♠K♥K♦K♣A♠××××A♥×A♦×A♣×You hold ace of spades, king of diamonds, and ace of hearts is on the board: 6 combos
K♠K♥K♦K♣A♠××××A♥××××A♦×A♣×
Blockers explain why a hand like A5s makes a good 3-bet bluff: with an ace in your hand, villain holds fewer of the aces they would fight back with.
Why think in ranges
You almost never know an opponent’s two cards. Saying “he has ace-king” is a guess that will usually be wrong. A range is every hand they could have, given what they have done, and it is a far better guess.
A range starts wide and narrows with each action. A player who raises first from the cutoff might have around 28% of hands. If you 3-bet and they 4-bet, most of the speculative hands are gone. If instead they check the flop and bet big on the river, it narrows another way. At each step, ask which hands would do this, and which would not.
Ranges change how you see your own hand, too. A pair of queens isn’t good or bad in itself: it is good against a range full of smaller pairs and missed draws, and bad against one made of aces, kings and sets.
The shape of a range
- Linear: the best hands down to a point, like most opening ranges.
- Polarised: very strong hands and bluffs, with little in between. Big bets usually come from these.
- Capped: missing its strongest hands, because the player would have raised them earlier. A player who just called before the flop rarely has aces.
Three shapes of range, from one spot
RaiseCall (outlined)Fold
Linear: the cutoff’s open
370 combos · 27.9% of hands
22+, A2s+, K5s+, Q8s+, J8s+, T8s+, 97s+, 86s+, 75s+, 65s, 54s, A8o+, KTo+, QTo+, JTo
Polarised: the big blind’s 3-bet against it
84 combos · 6.3% of hands
JJ+, AJs+, KQs, AQo+, A5s-A3s, 76s, 65s
Capped: the big blind’s call
370 combos · 27.9% of hands
TT-22, ATs-A6s, A2s, KJs-K5s, QJs-Q7s, JTs-J7s, T9s-T7s, 98s-96s, 87s-85s, 75s-74s, 64s, 54s-53s, 43s, AJo-A8o, KQo-K9o, QJo-Q9o, JTo-J9o, T9o
Player labels describe ranges too. A nit’s raise is narrow and strong; a maniac’s is wide and full of bluffs. VPIP, the share of hands a player puts money in with, and PFR, the share they raise, are the quickest ways to measure it.
In PokerIQ
The Ranges page shows every range PokerIQ uses as a 13 × 13 grid: pairs down the diagonal, suited hands above it, offsuit hands below. Raises are red, calls green and folds dark, and each range is given as a share of hands and a number of combos. The Balanced button open, for example, is 43.9% of hands, 582 combos.
In the Analyser, choose “A player type’s range” under “Villain holds”, then what they did before the flop. PokerIQ works out your equity against every combo in that range, with the cards you can see taken out, and marks the result vs assumed range, because the range is a read, not a fact.