Top 50 percent of poker hands

The 90 hands in the top 50 percent

A budget of 663.00 combos (50 percent of 1,326) decides the range. Classes go in from the top of the ranking until the next one, T8o with 12 combos, would carry the total to 50.53%. It stays out, and the range sits at 49.62%.

In order, the hands are AA, KK, QQ, JJ, TT, 99, 88, AKs, 77, AQs, AJs, AKo, ATs, AQo, AJo, KQs, 66, A9s, ATo, KJs, A8s, KTs, KQo, A7s, A9o, KJo, 55, QJs, K9s, A5s, A6s, A8o, KTo, QTs, A4s, A7o, K8s, A3s, QJo, K9o, A5o, A6o, Q9s, K7s, JTs, A2s, QTo, 44, A4o, K6s, K8o, Q8s, A3o, K5s, J9s, Q9o, JTo, K7o, A2o, K4s, Q7s, K6o, K3s, T9s, J8s, 33, Q6s, Q8o, K5o, J9o, K2s, Q5s, T8s, K4o, J7s, Q4s, Q7o, T9o, J8o, K3o, Q6o, Q3s, 98s, T7s, J6s, K2o, 22, Q2s, Q5o, J5s.

How the combos split

Pairs, suited hands and offsuit hands each add to the range in their own way. The table gives the hand count and the combo count for each kind.

13 pairs make 78 combos, 43 suited hands make 172 and 34 offsuit hands make 408. The largest share is offsuit hands, at 62.0% of the range.

The range by top card

Count the range by its higher card and the weight of each rank is clear. Hands and combos for every top card are in the table.

The ace row alone is 198 combos, 30.1% of 658. The range ends at the two row, which has 1 hand and 6 combos.

Hands worth knowing at the edge

J5s (number 90, 49.99% equity) is the weakest hand that fits, and T8o (number 91, 49.72%) is the strongest that does not.

Compared with the top 45 percent, this range adds 10 hands and 66 combos: Q6o, Q3s, 98s, T7s, J6s, K2o, 22, Q2s, Q5o, J5s.

How your cards shrink the range

Each card you hold removes combos that need it. Below is the range after one known card of each rank, and after you hold both cards of some common starting hands.

An ace is the biggest blocker, removing 51 combos and leaving 607. A two removes 12. Two aces cut the range to 557, and 72o to 629.

A worked example

Worked example: you look down at AKs and an opponent's range is the top 50 percent, 658 combos before you look. Your cards remove some, leaving 557. Of the 1,225 hands left in the deck, 45.47% are in the range.

How strong the range is as a group

Put the range against two opponents. A random hand gives it 58.08%; the top 50 percent gives 50.00%. Weights are the combos that can be dealt together.

Neighboring ranges and hands

Questions about the top 50 percent

How many hands are in the top 50 percent?

The top 50 percent is 90 hands and 658 combos, which is 49.62% of the 1,326 two-card hands. It runs from AA down to J5s. T8o is the first hand left out, because 12 more combos would reach 50.53%.

Why is the top 50 percent really 49.62%?

Hands go in as whole classes, in rank order, and a class is never split. The range stops at the last class that keeps the total at or under 50 percent, so it lands on 49.62%, 658 of 1,326 combos, rather than exactly 50.

How many of the combos have an ace in them?

25 hands in the range have an ace as the higher card, adding up to 198 of 658 combos, 30.1%. Holding one ace yourself leaves 607 combos of the range possible for an opponent.

How this was computed

The range comes from our ranking of all 169 starting hands by equity against a random hand. Hands are added in that order while the total of their combos (6 for a pair, 4 for a suited hand, 12 for an offsuit hand) stays within 50 percent of 1,326, and a hand that would go over is left out whole.

Blocker counts list every combo of every hand in the range and remove the ones that use a known card. Group equity comes from our table of all 169 by 169 preflop matchups, counted over every one of the 1,712,304 boards with no sampling, and weighted by the pairs of hands that can be dealt together.

Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.