What Is Range Equity in Poker?
Range equity is your hand's win share against every hand an opponent can hold, not just one. Here's how to weight combos and read it correctly.
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Range equity is your hand’s win share against every hand an opponent could hold, weighted by how likely each one is — not just your equity against a single guessed holding. Since you almost never see your opponent’s exact cards, this is the number that actually governs your decisions. You calculate it by taking your equity against each hand in their range and averaging those results, weighted by how many combinations of each hand exist.
From one hand to a whole range
Basic equity compares your hand to a specific opponent hand — say your kings versus their aces. Useful, but incomplete: your opponent doesn’t have a fixed hand, they have a range of possible hands, each with a probability.
Range equity collapses that whole distribution into one number: your average win share across every hand they can hold, weighted by frequency. It’s the honest version of “how am I doing in this spot.”
Weighting by combinations
The key mechanic is that different hands have different numbers of combinations, and the more common a hand is, the more it should count. From combinatorics:
| Hand type | Combinations |
|---|---|
| A specific pocket pair (e.g. AA) | 6 |
| A specific suited hand (e.g. AKs) | 4 |
| A specific offsuit hand (e.g. AKo) | 12 |
| Any specific unpaired hand (both) | 16 |
So an unpaired hand like ace-king is far more common than any single pair. When you average your equity across a range, ace-king’s result carries more weight than aces’ — because there are more ways to be dealt it. Skipping this weighting is the most common range-equity mistake.
Worked example: QQ against a tight 3-bet range
You hold Q♣ Q♦ and face a tight opponent whose 3-bet range you read as {AA, KK, AKs, AKo}. What’s your equity against that whole range?
First, your equity against each piece (verified by simulation) and its weight:
| Villain hand | Combos | QQ equity vs it |
|---|---|---|
| AA | 6 | ~18% |
| KK | 6 | ~18% |
| AKs | 4 | ~54% |
| AKo | 12 | ~57% |
Now weight and average. Total combos = 6 + 6 + 4 + 12 = 28.
- AA: 6 × 18 = 108
- KK: 6 × 18 = 108
- AKs: 4 × 54 = 216
- AKo: 12 × 57 = 684
- Sum = 1,116 → divide by 28 → ~40%
So QQ has about 40% equity against this range — a full-range simulation confirms it. Notice the surprise: against a single ace-king you’d be a 54-57% favorite, but against the range you’re a 40% underdog, because the two pair hands (AA and KK) crush you and drag the average down. That’s the entire value of range thinking: it stops you from anchoring on the one matchup you’d like to picture.
How range width changes everything
The same hand can be a favorite or a dog depending purely on how wide you put the opponent:
- Tight range (only premiums): your medium-strong hands do poorly, because you’re only ever up against hands that beat you.
- Wide range (many speculative hands): your medium-strong hands do well, because most of the range is weaker than you.
This is why position matters so much — players in late position can enter with wider ranges, which changes the range equity every one of their hands carries. Reading range width accurately is more than half the battle.
Polarized vs linear ranges
Two ranges with the same average equity can play very differently:
- A linear range (top-down: all the best hands) gives smooth, predictable equity — you’re a bit ahead or a bit behind.
- A polarized range (strong value hands plus bluffs, little in the middle) produces a bimodal outcome: you’re either crushing the bluffs or crushed by the value. The 50% average hides the fact that almost no hand is actually close.
Against a polarized range, don’t trust the average alone — think about which half you’re likely facing after action goes in.
Using range equity at the table
You won’t average combos by hand mid-session, but you can reason with the concept:
- Build the range. What hands would villain actually play this way, given position and action?
- Weight it roughly. More offsuit combos than pairs; more of the hands they’d routinely play than the rare traps.
- Estimate your share. Are you ahead of most of that range, or only ahead of the bluffs?
- Decide. Compare your range equity to the price, just as you would hand-vs-hand — this is what powers sound preflop all-in calls.
The takeaway
Range equity is real-world equity: your win share against everything an opponent can have, weighted by how often they have it. It’s why QQ can beat a lone ace-king yet lose to a tight range containing it — the combos of the hands that crush you outweigh the combos you crush. Master the combinatorics of counting combos, ground it in single-hand equity, and read position to gauge range width. Bring it all together in the poker odds & math hub.
Frequently asked
What is range equity in poker?
Range equity is how often your hand wins against the entire set of hands an opponent could be holding, weighted by how likely each one is. Instead of your equity versus one hand, it's your average equity across their whole range.
How is range equity calculated?
Take your equity against each hand in the opponent's range, weight each by its number of combinations, and average them. Hands with more combos count more, so an unpaired hand like ace-king pulls the average more than a specific pocket pair.
Why is range equity better than hand-vs-hand equity?
You almost never know your opponent's exact two cards. Range equity reflects the reality of the decision — you're up against a distribution of possible hands, and your average result against all of them is what actually matters.
What is a polarized range?
A polarized range contains strong value hands and bluffs but few medium hands. Your equity against a polarized range can be misleading — you're either well ahead or well behind, so the average hides a bimodal outcome.