44: the 6 combos
To count 44, pick 2 of the 4 fours: 4 x 3 / 2 = 6 pairings.
Every 44 you can be dealt is one of these 6 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For 44, the table lists the combos left after one card of each rank is out of play.
| Known card | 44 combos left |
|---|---|
| Ace | 6 |
| King | 6 |
| Queen | 6 |
| Jack | 6 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 6 |
| Four | 3 |
| Three | 6 |
| Two | 6 |
A four you can see leaves 3 of 6, so 50% of the combos are gone. Any card of a different rank leaves all 6 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The 44 combos that survive are in the table, one row per rank.
| Board pair | 44 combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 1 |
| Threes | 6 |
| Twos | 6 |
Pairing fours on the board cuts 44 to 1 combo. Every other paired board leaves the full 6.
A worked example
Take a hand of a four and a two. Your opponent then holds one of 1,225 possible hands, and 3 of them are 44. That is 0.24%, or 1 in 408, instead of the 0.49% (1 in 204) you get when your cards do not block it.
How strong is 44?
Rank 48 of 169 belongs to 44, inside the top 60 classes, on 57.02% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add 44 to every hand ranked above it and you hold 334 of the 1,326 two-card hands, 25.19% of all deals.
44 against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For 44 the five ranges give 25.33% against the top 5 percent (60 combos), 38.51% against the top 10 percent (130 combos), 44.96% against the top 20 percent (264 combos), 48.12% against the top 30 percent (386 combos) and 51.95% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 44 equity |
|---|---|---|
| Top 5 percent | 60 | 25.33% |
| Top 10 percent | 130 | 38.51% |
| Top 20 percent | 264 | 44.96% |
| Top 30 percent | 386 | 48.12% |
| Top 50 percent | 658 | 51.95% |
The line sits between the top 30 and top 50 percent: 44 is behind the narrower range and ahead of the wider one.
Holding 44 removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 130.00 remain. That is no loss at all: 44 blocks none of those hands.
Hands next to 44
A one-place difference in rank can be a large or small gap in a direct matchup. 44 has 50.68% equity against QTo, the hand ranked number 47: it wins 50.28% of boards, ties 0.79% and loses 48.93%. It is the favorite in that matchup. 44 has 66.92% equity against A4o, the hand ranked number 49: it wins 65.73% of boards, ties 2.39% and loses 31.88%. It is the favorite in that matchup.
Because both cards of 44 have the same rank, there is no suited version of it. The 13 pairs are 78 combos in all, 5.88% of the 1,326 hands.
Questions about 44 combos
- How many combos of 44 are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt 44 about 1 time in 221.0.
- How many 44 combos are left if I hold a four?
- 3 combos of 44 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 44?
- QTo ranks number 47, just above 44, and 44 has 50.68% equity against it. A4o ranks number 49, just below, and 44 has 66.92% 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.