Ranges and combos
Before talking strategy, you need to be able to count. Almost every poker decision rests on one question: which hands can my opponent have, and how many of each? This lesson sets up the basic tool: the range, and combo counting.
A range is a set of hands
A range is the set of hands a player takes a given action with in a given spot. When someone says "he opens a middle-position range", they are not describing one hand: they are describing a list, for example "all pairs, suited aces, broadways".
Why think in ranges rather than hands? Because you never see your opponent's cards. The only thing you can honestly estimate is the set of hands he can hold given his action. The ranges in this lesson are teaching approximations, not certified solver output.
The 169 starting hands
There are many ways to be dealt two cards, but many of them are equivalent: A♠K♠ and A♥K♥ play exactly the same, since no suit outranks another. Group the equivalent hands together and 169 distinct starting hands remain:
- 13 pairs (AA, KK… 22);
- 78 suited hands, two cards of the same suit (AKs, T9s…);
- 78 offsuit hands, two cards of different suits (AKo, T9o…).
They are written with shorthand: AKs for suited ace-king, AKo for offsuit, TT+ for "pairs from TT up to AA", A2s-A5s for "from A2 suited to A5 suited".
Why 1,326 combos
Those 169 hands are not equally frequent. A specific hand is a combo: an exact choice of two cards from the deck, suits included. There are 1,326 combos in total, and they are unevenly spread:
| Hand type | Example | Combos per hand | Hands | Total combos |
|---|---|---|---|---|
| Pair | AA | 6 combos | 13 | 78 combos |
| Suited | AKs | 4 combos | 78 | 312 combos |
| Offsuit | AKo | 12 combos | 78 | 936 combos |
The logic is simple. There are four aces in the deck. For a pair of aces you pick two aces out of four: 6 ways. For AKs you need the ace and the king of the same suit: one way per suit, so 4 combos. For AKo the suits must differ: 12 combos. Altogether, AK (suited and offsuit) weighs 16 combos.
A direct consequence: pairs are rare, offsuit hands are common. You are dealt AA far less often than AKo, and that is exactly why counting is useful.
Counting a range
Counting a range means adding up the combos of every hand it contains. Example from the exercise series in the repository: a six-handed opening range from the first position, written 22+, ATs+, KTs+, QTs+, JTs, T9s, 98s, 87s, 76s, 65s, AJo+, KQo, contains 186 combos out of 1,326 combos possible combos.
Keep the method rather than the result: break the range into classes, multiply by the number of combos per class, add up, then compare with the total. Never guess a range size "in your head": an easy mistake is forgetting that an offsuit hand weighs much more than a suited one.
The blocker effect
The 1,326 combos assume you know no cards. As soon as you look at your own cards, you remove them from the deck, and so remove combos your opponent can hold. This is the blocker effect.
Example: you hold the ace of spades. Your opponent can no longer have that ace.
- AK goes from 16 combos to 12 combos;
- AA goes from 6 combos to 3 combos.
If you hold A♠K♥ yourself, only 9 combos of AK remain for your opponent: there are far fewer ways for him to hold the hands you block.
Why does it matter? Because a hand that blocks the strong part of your opponent's range makes that part less likely. Conversely, blocking his weak hands leaves his range stronger on average. We come back to this in the lessons on bluffing: for now, remember only that your own cards change the count.
Key points
- A range is a set of hands, not a single hand.
- There are 169 starting hands but 1,326 combos, and they are not evenly spread.
- A pair weighs 6 combos, a suited hand 4 combos, an offsuit hand 12 combos.
- Always count by class, add up, then compare with the total.
- Your own cards remove combos from your opponent.
This lesson describes a reasoning tool. It promises no result: counting correctly does not guarantee winning, it only keeps you from deciding on wrong numbers.