How many combos of 33 are there?

6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt 33 about 1 time in 221.0.

How many 33 combos are left if I hold a three?

3 combos of 33 remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.

Which hands rank next to 33?

J8s ranks number 65, just above 33, and 33 has 48.62% equity against it. Q6s ranks number 67, just below, and 33 has 50.91% equity against it.

33 Combos: Count, Blockers, Board Pairs

The answer is 6 combos. 33 covers 0.45% of the 1,326 starting hands and holds rank 66 of 169 on equity against a random hand, 53.69%.

33: the 6 combos

Each pairing of two threes is its own combo: 4 x 3 = 12 ordered picks, halved because order does not matter, gives 6.

Spelled out, 33 is these 6 holdings. The suits are what separate them from each other, and the ranks are the same in all.

How cards you can see change the count

A card in your hand or on the board takes combos away from your opponent's possible hands. This table counts what is left of 33 for each rank of card you can see.

33 combos left after one known card of each rank
Known card	33 combos left
Ace	6
King	6
Queen	6
Jack	6
Ten	6
Nine	6
Eight	6
Seven	6
Six	6
Five	6
Four	6
Three	3
Two	6

With a three in view, 3 of the 6 combos of 33 remain, which removes 50%. Any card of a different rank leaves all 6 combos in play.

When the board is paired

Two board cards of one rank are out of reach for your opponent. The table gives the 33 combos that remain for each paired rank.

33 combos left after a pair of each rank on the board
Board pair	33 combos left
Aces	6
Kings	6
Queens	6
Jacks	6
Tens	6
Nines	6
Eights	6
Sevens	6
Sixes	6
Fives	6
Fours	6
Threes	1
Twos	6

Only a board pair of threes matters here: 1 combo of 33 remain, against 6 for any other pair.

A worked example

Say your hole cards are a three and a two. That leaves 1,225 possible two-card hands for an opponent, and 3 of them are 33: a 0.24% chance, roughly 1 in 408. Without the three in your hand it would be 6 combos, 0.49%, roughly 1 in 204.

How strong is 33?

33 ranks number 66 of the 169 starting-hand classes, in the middle of the ranking. Against one random hand it has 53.69% equity, which counts a win as 1 and a tie as one half over every five-card board.

472 of the 1,326 starting hands are 33 or better by this ranking. That is 35.60% of deals.

33 against ranges of hands

Tighter ranges are harder to beat. 33 gets 24.92% against the top 5 percent (60 combos), 38.00% against the top 10 percent (130 combos), 44.13% against the top 20 percent (264 combos), 46.38% against the top 30 percent (386 combos) and 49.84% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.

33 equity against the strongest hands
Opponent range	Combos in range	33 equity
Top 5 percent	60	24.92%
Top 10 percent	130	38.00%
Top 20 percent	264	44.13%
Top 30 percent	386	46.38%
Top 50 percent	658	49.84%

33 is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.

Check what 33 does to the top 10 percent range of 130 combos: averaged over its 6, 130.00 remain for an opponent. That is no loss at all: 33 blocks none of those hands.

Hands next to 33

Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. 33 has 48.62% equity against J8s, the hand ranked number 65: it wins 48.00% of boards, ties 1.23% and loses 50.77%. It is the underdog in that matchup. 33 has 50.91% equity against Q6s, the hand ranked number 67: it wins 50.41% of boards, ties 1.01% and loses 48.58%. It is the favorite in that matchup.

There is only one way to write 33, since a pair cannot be suited or offsuit. Every pair is 6 combos, and the 13 of them make 5.88% of deals.

Questions about 33 combos

How many combos of 33 are there?: 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt 33 about 1 time in 221.0.
How many 33 combos are left if I hold a three?: 3 combos of 33 remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.
Which hands rank next to 33?: J8s ranks number 65, just above 33, and 33 has 48.62% equity against it. Q6s ranks number 67, just below, and 33 has 50.91% equity against it.

How this was computed

Combos are counted by listing all 1,326 two-card hands in a 52-card deck and sorting each into its class. The known-card rows remove every combo that uses a card of that rank; the board-pair rows remove those that use either of two such cards.

Rank and equity read our table of all 169 by 169 preflop matchups, each counted over every one of the 1,712,304 boards. Ties count as half a win, and a range is weighted by its live combos.

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