How many hands are in the top 40 percent?

The top 40 percent is 73 hands and 524 combos, which is 39.52% of the 1,326 two-card hands. It runs from AA down to T8s. K4o is the first hand left out, because 12 more combos would reach 40.42%.

Why is the top 40 percent really 39.52%?

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 40 percent, so it lands on 39.52%, 524 of 1,326 combos, rather than exactly 40.

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 524 combos, 37.8%. Holding one ace yourself leaves 473 combos of the range possible for an opponent.

Top 40% of Poker Hands: Range and Combos

Taking the best hands in rank order up to 40 percent gives 73 hands, 524 combos, or 39.52% of all 1,326 two-card hands. T8s is the last one in, and you are dealt something from the range about 1 time in 2.53.

The 73 hands in the top 40 percent

To build the range, add hands from strongest to weakest and stop before the total passes 40 percent of 1,326, which is 530.40 combos. K4o would add 12 and make 40.42%, so the page stops at 39.52%.

The top 40 percent on the 13 by 13 grid

AA AKs AQs AJs ATs A9s A8s A7s A6s A5s A4s A3s A2s AKo KK KQs KJs KTs K9s K8s K7s K6s K5s K4s K3s K2s AQo KQo QQ QJs QTs Q9s Q8s Q7s Q6s Q5s Q4s Q3s Q2s AJo KJo QJo JJ JTs J9s J8s J7s J6s J5s J4s J3s J2s ATo KTo QTo JTo TT T9s T8s T7s T6s T5s T4s T3s T2s A9o K9o Q9o J9o T9o 99 98s 97s 96s 95s 94s 93s 92s A8o K8o Q8o J8o T8o 98o 88 87s 86s 85s 84s 83s 82s A7o K7o Q7o J7o T7o 97o 87o 77 76s 75s 74s 73s 72s A6o K6o Q6o J6o T6o 96o 86o 76o 66 65s 64s 63s 62s A5o K5o Q5o J5o T5o 95o 85o 75o 65o 55 54s 53s 52s A4o K4o Q4o J4o T4o 94o 84o 74o 64o 54o 44 43s 42s A3o K3o Q3o J3o T3o 93o 83o 73o 63o 53o 43o 33 32s A2o K2o Q2o J2o T2o 92o 82o 72o 62o 52o 42o 32o 22

In the range
Not in the range

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.

How the combos split

Not every hand in the range counts the same. A pair has 6 combos, a suited hand 4 and an offsuit hand 12, and the table totals each kind separately.

The top 40 percent by kind of hand
Kind	Hands	Combos	Share of range
Pairs	12	72	13.74%
Suited hands	35	140	26.72%
Offsuit hands	26	312	59.54%

In the top 40 percent, offsuit hands supply the most combos, 59.5% of the total. The rest is 72 from pairs, 140 from suited hands and 312 from offsuit hands.

The range by top card

Reading the range by top card, rank by rank, shows how fast it thins out. Each row has the hands and combos for one high card.

The top 40 percent by higher card
Top card	Hands	Combos
Ace	25	198
King	20	146
Queen	12	82
Jack	6	42
Ten	3	14
Nine	1	6
Eight	1	6
Seven	1	6
Six	1	6
Five	1	6
Four	1	6
Three	1	6
Two	0	0

25 ace-high hands bring 198 combos, 37.8% of the range. Nothing with a top card below the three makes it in; that rank has 1 hand, 6 combos.

Hands worth knowing at the edge

At the bottom edge sits T8s (rank 73, 52.33% equity against a random hand), and right outside it is K4o (rank 74, 52.33%).

Compared with the top 35 percent, this range adds 9 hands and 62 combos: J8s, 33, Q6s, Q8o, K5o, J9o, K2s, Q5s, T8s.

How your cards shrink the range

Your cards block part of the range. The table shows how many of the 524 combos are still possible when you hold one card of each rank, and the second table does the same when you hold both cards of a named hand.

Combos of the top 40 percent left after one known card of each rank
Known card	Combos left	Combos removed
Ace	473	51
King	482	42
Queen	494	30
Jack	500	24
Ten	503	21
Nine	504	20
Eight	507	17
Seven	512	12
Six	512	12
Five	512	12
Four	516	8
Three	516	8
Two	519	5

Combos of the top 40 percent left when you hold both cards of a hand
You hold	Combos left
AA	423
KK	441
AKs	432
AKo	432
QQ	465
JTs	480
77	501
A5s	462
72o	507

One ace in your hand leaves 473 of 524 combos, 51 fewer, while a two leaves 519. Holding AA leaves 423, and holding 72o leaves 507.

A worked example

Say you hold AA against a top 40 percent range. Of its 524 combos, 423 remain, so 423 / 1,225 = 34.53% of the hands your opponent can hold are in the range. AKs would leave 432.

How strong the range is as a group

How strong is the range as a group? It has 59.85% equity against a random hand and 52.62% against the top 50 percent, weighted by live combos.

Questions about the top 40 percent

How many hands are in the top 40 percent?: The top 40 percent is 73 hands and 524 combos, which is 39.52% of the 1,326 two-card hands. It runs from AA down to T8s. K4o is the first hand left out, because 12 more combos would reach 40.42%.
Why is the top 40 percent really 39.52%?: 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 40 percent, so it lands on 39.52%, 524 of 1,326 combos, rather than exactly 40.
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 524 combos, 37.8%. Holding one ace yourself leaves 473 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 40 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.