Combinations of an opponent range

Practice with exercises

Content by Tools of Poker Methodology and calculation assumptions

A range is a sum of hand combinations

We do not know the opponent’s exact hand. We assign a range: a set of hands they could have, based on their position and action. Each hand class contributes its own combos.

We will follow one example. The opponent range contains TT, JJ, QQ, KK, AA and AKs. Count only these hands; AKo and other hands are outside our starting range.

Perceived range

TTJJQQKKAAAKs

Your cards

As 7d

board

Kh 9c 2s
Review exercise 4.2: known-card blockers

1. Add the original combos in the range

The five pairs contribute 6 combos each, and AKs contributes 4. Six highlighted hand classes therefore represent more than six combos.

5 × 6 + 4 = 34

This is the original perceived range: the starting total before removing any cards.

2. Count blocked combos in each hand class

Your As removes three AA combos. The Kh on the board removes three KK combos. AKs loses AsKs and AhKh. TT, JJ and QQ are unaffected by these known cards.

3 + 3 + 2 = 8

Count each physical combo only once. A blocked AA combo and a blocked AKs combo are different hands, even if both contain As.

3. Subtract to find the available range

Remove the blocked combos from the original total. The remaining combos are the possibilities the opponent can still hold within the range we assigned.

34 − 8 = 26

The hand labels AA, KK and AKs stay in the range, but with fewer combos. Only a hand with no available combos would disappear completely.

4. Compare what remains with the original range

We started with 34 combos and 26 remain possible. To express the part that survives as a percentage, divide the available count by the original count and multiply by 100.

Perceived range
34
Blocked combos
8
Available range
26
Available range (%)
76.47%

26 ÷ 34 × 100 = 76.47%

26 of the 34 original combos remain available: 76.47% of the perceived range survives the blockers.

The denominator is the range we started with. Hands outside that range do not enter this calculation. Round only the final percentage to two decimal places.

Read the three counts in each range cell

Read each highlighted cell from left to right: original combos / blocked combos / available combos.

  • AA shows 6/3/3: 6 combos originally, 3 blocked by As and 3 still possible.
  • AKs shows 4/2/2: 2 of its 4 suited combos are blocked, leaving 2.

Open a highlighted hand to see its exact card combinations. Crossed-out cards explain the blocked count; checks show the combos that remain. Yellow cells are partly blocked, not incorrect answers.

We assign the 3-bet range to the opponent in BB (30 BB). Against BTN.

View source chart

Hand combinations reference

Counts for one starting hand when all 52 cards are available.
Hand type Example Combos
PairAA6
Suited handsAKs4
Offsuit handsAKo12
Any suits (suited + offsuit)AK16

Next: find what the available combos form

Here we counted how many combos survive the blockers. In lesson 4.4, we use those same available combos to find how many have top pair, a set or a draw on the board.

4.4 · Range composition on the board

Questions about range combinations

It is the set of hands we assign to an opponent from their position and action. It is an estimate, not a revealed hand.

It is the share of the original perceived range that survives the known-card blockers. It is not equity or the chance that the opponent holds that range.

Only identified cards can remove specific combos. In a multiway pot, analyse the selected opponent using your cards and the board; do not subtract the unknown hands of other players.

No. Without blockers, AA represents 6 physical combos, AKs represents 4 and AKo represents 12. Add physical combos rather than counting highlighted cells.

We are measuring how much of our starting range is still possible. In this example, 26 of 34 combos remain, so the calculation is 26 divided by 34.