How many hands are in the top 45 percent?

The top 45 percent is 80 hands and 592 combos, which is 44.65% of the 1,326 two-card hands. It runs from AA down to K3o. Q6o is the first hand left out, because 12 more combos would reach 45.55%.

Why is the top 45 percent really 44.65%?

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 45 percent, so it lands on 44.65%, 592 of 1,326 combos, rather than exactly 45.

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 592 combos, 33.4%. Holding one ace yourself leaves 541 combos of the range possible for an opponent.

Top 45% of Poker Hands: Range and Combos

Count 592 combos for the top 45 percent: 80 hands, 44.65% of the 1,326 two-card hands, reaching down to K3o. A random deal falls in it about 1 time in 2.24.

The 80 hands in the top 45 percent

Start at the top of the ranking and keep going until adding the next hand would pass 45 percent of 1,326 (596.70 combos). Q6o is that hand: its 12 combos would make 45.55%, so the range stops short at 44.65%.

The top 45 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, K4o, J7s, Q4s, Q7o, T9o, J8o, K3o.

How the combos split

Here is how the range is made up. Each pair carries 6 combos, each suited hand 4 and each offsuit hand 12, so hands of one kind weigh more than hands of another.

The top 45 percent by kind of hand
Kind	Hands	Combos	Share of range
Pairs	12	72	12.16%
Suited hands	37	148	25.00%
Offsuit hands	31	372	62.84%

Pairs bring 72 combos from 12 hands, suited hands bring 148 from 37 and offsuit hands bring 372 from 31. Offsuit hands lead with 62.8%.

The range by top card

The top 45 percent does not spread evenly across ranks. The table counts hands and combos for each higher card.

The top 45 percent by higher card
Top card	Hands	Combos
Ace	25	198
King	22	170
Queen	14	98
Jack	8	58
Ten	4	26
Nine	1	6
Eight	1	6
Seven	1	6
Six	1	6
Five	1	6
Four	1	6
Three	1	6
Two	0	0

Ace-high hands supply 198 of the 592 combos (33.4%) from 25 hands. The range reaches down to a top card of three, where it holds 1 hand.

Hands worth knowing at the edge

Two hands mark the edge. K3o is the weakest hand inside, number 80 of 169 with 51.43% equity against a random hand. Q6o is the strongest hand left out, number 81 with 51.02%.

Compared with the top 40 percent, this range adds 7 hands and 68 combos: K4o, J7s, Q4s, Q7o, T9o, J8o, K3o.

How your cards shrink the range

Cards in your hand are out of an opponent's reach. These tables count the live combos of the range after one known card of each rank and after nine different two-card holdings.

Combos of the top 45 percent left after one known card of each rank
Known card	Combos left	Combos removed
Ace	541	51
King	544	48
Queen	558	34
Jack	564	28
Ten	568	24
Nine	569	23
Eight	572	20
Seven	576	16
Six	580	12
Five	580	12
Four	580	12
Three	581	11
Two	587	5

Combos of the top 45 percent left when you hold both cards of a hand
You hold	Combos left
AA	491
KK	497
AKs	494
AKo	494
QQ	525
JTs	541
77	561
A5s	530
72o	571

Compare the extremes: an ace leaves 541 combos and a two leaves 587; AA leaves 491 and 72o leaves 571, out of 592.

A worked example

With AA in your hand, 491 of the range's 592 combos are still possible, which is 40.08% of the 1,225 hands your opponent could hold. Hold AKs instead and 494 remain, 40.33%.

How strong the range is as a group

Every hand in the range is averaged here. The group has 58.92% equity against a random hand, falling to 51.16% against the top 50 percent.

Questions about the top 45 percent

How many hands are in the top 45 percent?: The top 45 percent is 80 hands and 592 combos, which is 44.65% of the 1,326 two-card hands. It runs from AA down to K3o. Q6o is the first hand left out, because 12 more combos would reach 45.55%.
Why is the top 45 percent really 44.65%?: 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 45 percent, so it lands on 44.65%, 592 of 1,326 combos, rather than exactly 45.
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 592 combos, 33.4%. Holding one ace yourself leaves 541 combos of the range possible for an opponent.

How this was computed

Ranking comes first: all 169 hand classes ordered by equity against a random hand. The range takes classes from the top for as long as their combos (6, 4 or 12 each) total no more than 45 percent of 1,326. The first class that would overshoot is left out entirely.

Known-card and two-card holdings are handled by removing every combo that uses one of those cards from the range. Equity for the whole range averages exact matchups, each counted over 1,712,304 boards, weighted by the pairs of hands that can coexist.

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