Hand vs range equity
Content by Tools of Poker Methodology and calculation assumptions
What share of the pot belongs to your hand?
Equity is your average share of the pot against all the opponent combos we consider possible. We will start on the river: the board is complete, so no more cards can change either hand.
Perceived range
Your cards
board
You have QQ on a board with a king. Some hands in the range beat you, some lose to you and some tie. We need to count their physical combos, not just their hand names.
Review exercise 4.4: range composition1. Find the available opponent combos
Our six hand classes start with 34 combos. Your two queens block five QQ combos. The Kh on the board blocks three KK combos and the AhKh combo from AKs. That removes nine combos in total.
We now compare your QQ with the 25 available opponent combos.
2. Count wins, ties and losses
Compare the best five-card hand for each available combo with your QQ on the completed board.
| Opponent hand | Combos | Result for Hero |
|---|---|---|
| TT | 6 | Win |
| JJ | 6 | Win |
| 1 | Tie | |
| KK | 3 | Loss |
| AA | 6 | Loss |
| AKs | 3 | Loss |
TT and JJ give you 12 winning combos. The remaining QQ combo ties with you. AA, KK and AKs give you 12 losing combos.
- Wins
- 12
- Ties
- 1
- Losses
- 12
3. Add half of each tie
A win gives you the whole pot and a tie against one opponent gives you half. The 12 winning combos therefore count as 12 pots, and the tied combo adds half a pot.
These are not extra opponent hands: 12.5 is the pot share represented by 12 wins and one tie. Now divide that amount by all 25 available combos.
4. Divide by all available combos
Your equity is 50%: across these possibilities, your average share is half the pot.
The chance of winning outright is 48%, and the chance of tying is 4%. Half of that 4% is added to the wins: 48% + 2% = 50% equity.
Check the same range in the grid
Each cell keeps the original / blocked / available combo counts. QQ shows 6/5/1: your cards leave just one opponent combo. AA shows 6/0/6: all six ace-pair combos remain.
Open QQ to see why only QhQc remains. The opponent’s exact suits matter when removing blockers, even when several combos would have the same hand strength.
We assign the 3-bet range to the opponent in BB (30 BB). Against BTN.
View source chartWhat changes on the turn and flop?
Before the river, a hand that is behind now may improve. Complete the board with the legal remaining cards, compare the final hands, and average the pot shares. Future cards cannot reuse your cards, the opponent combo or the existing board.
The first three levels use the river so you can count the combos by hand. Beginner and easy guide every calculation; intermediate starts with the available combos. Difficult and nightmare ask for a single equity estimate on the turn or flop.
Remember
Example: 12 winning combos + 1 tied combo ÷ 2 = 12.5. With 25 available combos, 12.5 ÷ 25 × 100 gives 50% equity.
On the river, count the combos you beat and add half the tied combos. Divide by every available opponent combo, then multiply by 100.
On the flop and turn, include the possible cards still to come. Every available physical combo has the same weight.
In guided river rounds, calculate equity to two decimal places. In difficult and nightmare, choose the closest estimate, rounded to five percentage points.