Top 35 percent of poker hands

The 64 hands in the top 35 percent

Hands are added in rank order while the running total is no more than 35 percent of 1,326, a budget of 464.10 combos. J8s comes next, and its 4 combos would push the total to 35.14%, past the limit, so the range ends at 34.84%.

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.

How the combos split

By kind, the range divides as the table shows. A pair is 6 combos, a suited hand is 4 and an offsuit hand is 12, which is why 64 hands are 462 combos and not a round multiple.

In the top 35 percent, offsuit hands supply the most combos, 59.7% of the total. The rest is 66 from pairs, 120 from suited hands and 276 from offsuit hands.

The range by top card

Which top cards does the range lean on? The table counts hands and combos by the higher card, from the ace down to the two.

25 ace-high hands bring 198 combos, 42.9% of the range. Nothing with a top card below the four makes it in; that rank has 1 hand, 6 combos.

Hands worth knowing at the edge

Range edge: T9s is the final hand in, ranked 64 with 54.03% equity against a random hand; J8s is the first hand out, ranked 65 with 54.02%.

Compared with the top 30 percent, this range adds 9 hands and 76 combos: Q9o, JTo, K7o, A2o, K4s, Q7s, K6o, K3s, T9s.

How your cards shrink the range

How much of the range can an opponent still hold once you look at your cards? The first table answers for one card of each rank; the second for nine named holdings.

One ace in your hand leaves 411 of 462 combos, 51 fewer, while a two leaves 458. Holding AA leaves 361, and holding 72o leaves 446.

A worked example

Say you hold AA against a top 35 percent range. Of its 462 combos, 361 remain, so 361 / 1,225 = 29.47% of the hands your opponent can hold are in the range. AKs would leave 374.

How strong the range is as a group

Averaged over all its hands, the range has 60.73% equity against a random opponent and 53.99% against the top 50 percent of hands.

Neighboring ranges and hands

Questions about the top 35 percent

How many hands are in the top 35 percent?

The top 35 percent is 64 hands and 462 combos, which is 34.84% of the 1,326 two-card hands. It runs from AA down to T9s. J8s is the first hand left out, because 4 more combos would reach 35.14%.

Why is the top 35 percent really 34.84%?

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 35 percent, so it lands on 34.84%, 462 of 1,326 combos, rather than exactly 35.

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 462 combos, 42.9%. Holding one ace yourself leaves 411 combos of the range possible for an opponent.

How this was computed

We ranked the 169 classes by equity against a random hand, then added them from the top while the combo total stayed within 35 percent of the 1,326 two-card hands. A class is never split, so the range stops at the last whole class that fits.

The blocker tables count live combos directly from the deck. The group equity figures read our exact preflop matchup table, in which each pair of classes was counted over all 1,712,304 boards, and weight each matchup by its card-compatible pairs of hands.

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