Poker equity calculator: hand vs range

What equity means

Your equity is the part of the pot that belongs to you if the rest of the cards were dealt with no more betting. It counts every way the hand can finish: the times you win, plus your share whenever the pot is split. With 60% equity in a 1,000-chip pot, your hand is worth 600 chips on average — you won’t get exactly 600 in any one hand, but that is what the spot pays over many.

Heads-up equity = win % + half of tie %
It is the number to compare with the price of a call. Facing a half-pot bet you need 25%; with more than that, calling makes money in the long run. The pot odds calculator does that comparison for any bet size.

Why you play against ranges, not hands

You almost never know an opponent’s exact cards. What you know is how they played: someone who re-raised before the flop holds a different set of hands from someone who just called. That set is their range, and your real equity is your average against all of it.

Here is the same hand, A♠K♠, against a single hand and against ranges of different widths:

Against pocket kings, ace-king is a big underdog (34.1%); against pocket queens it is a coin flip (46.1%). A tight top-5% range (77+, AJs+, AKo) mixes hands that crush ace-king, coin flips, other ace-kings that split the pot, and ace-queen and ace-jack suited, which ace-king dominates — so the answer lands in between at 47.6%. Widen the range to the top 20% and the weaker hands pull ace-king up to 64.9%; past that it barely moves (67.2% against half of all hands, 67.0% against any two cards).

Notice the combo counts, too. Holding the ace and king of spades leaves only 3 of the 6 combos of pocket aces and 3 of pocket kings — the cards in your hand are cards they can’t have. Players call this card removal or blockers, and the calculator applies it automatically to your hand and the board.

How to write a poker range

Range notation is a shorthand for sets of starting hands. Type it into the box under the grid and the grid follows; paint the grid and the text rewrites itself. Pairs are two ranks (QQ), unpaired hands add s for suited or o for offsuit, a plus sign means “and everything better”, and a dash marks a span.

The combo counts follow from the deck: a pocket pair can be made 6 ways, a suited hand 4 ways and an offsuit hand 12 ways. That is why AK (16 combos) is far more common than AA (6), and why the 13 pairs make up only 78 of the 1,326 combos. The grid’s diagonal holds the pairs, suited hands sit above it and offsuit hands below.

How the board moves your equity

Before the flop, A♠K♠ has 64.9% against the top 20% of hands. After the flop, the same hand against the same range can be anything from a big favourite to an underdog. Each figure below is exact: every combo of the range that’s still possible, against all 990 turn-and-river run-outs.

Three things decide the swing. What you hit: top pair on an ace-high flop is worth 86.0%, trips on a paired king board 92.5%. What the range hits: on 9-8-7 ace-king has only two overcards, while much of the range already has a pair — every pocket pair in it, plus A9, A8, A7, K9 and K8 — so the favourite becomes an underdog at 43.3%. Draws: on 5-4-2 with two spades ace-king has made nothing, yet the nut flush draw, the gutshot to a wheel and two overcards keep it at 78.2% — most of a top-20% range missed that flop too.

Even the nut straight isn’t 100%: on Q-J-T the range still holds other ace-king combos, so 13.7% of the time the pot is split. Put any of these boards into the calculator and switch to Equity by hand to see exactly which combos you’re ahead of.

How this equity calculator works

Before the flop the calculator runs 60,000 random deals: each picks one combo from the range — every combo equally likely, minus any that clash with your cards — and a random board, then scores both hands with the same evaluator that settles showdowns at FizzPoker tables. That keeps the result within about ±0.4% of the true value, and the status line shows the margin for your spot.

From the flop on it stops sampling. It takes every combo still possible and deals every run-out against it — 990 on the flop, 44 on the turn, one on the river — so the figure it settles on is exact. That is what powers the Equity by hand view: each hand in the range is colored by your equity against it, and a bar chart groups the range by what they hold on the board right now, from high card up.

The top-X% presets order all 169 starting hands by all-in equity against one random hand (100,000 deals each). That is a strength order, not advice on what to play from a given seat: real opening ranges also weigh position and how well a hand plays after the flop, which is why suited connectors appear in them earlier than this list would suggest. Every combo in a range counts equally; if you think an opponent plays a hand only some of the time, leave it in or out based on which is closer.

Thinking in ranges at the table

The quickest way to get better at ranges is to play hands and review them — or to start with the poker test, twelve graded 6-max decisions. FizzPoker deals free No-Limit Hold’em in the browser for 2–9 players; with a free account you can fill seats with bots from Level 1, a calling station whose range barely narrows, to Level 5. After the game, each of your decisions gets an advisory label from game-theory models in the Fizz Score — acceptable, inaccuracy, mistake or blunder — never during the hand.

For several known hands at once, use the poker calculator; for the theory behind balanced ranges, read GTO poker explained.

Questions people ask

Keep going

• Poker calculatorWin, tie and equity for up to nine hands.
• Starting hands chartAll 169 hands by equity, one to eight opponents.
• GTO pokerGame theory optimal, explained with a live chart.
• Pot odds calculatorThe equity you need to call, and whether you have it.