55: the 6 combos
Each pairing of two fives is its own combo: 4 x 3 = 12 ordered picks, halved because order does not matter, gives 6.
These are the 6 specific hands that count as 55. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for 55. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | 55 combos left |
|---|---|
| Ace | 6 |
| King | 6 |
| Queen | 6 |
| Jack | 6 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 3 |
| Four | 6 |
| Three | 6 |
| Two | 6 |
With a five in view, 3 of the 6 combos of 55 remain, which removes 50%. Any card of a different rank leaves all 6 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the 55 combos left for each paired rank.
| Board pair | 55 combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 1 |
| Fours | 6 |
| Threes | 6 |
| Twos | 6 |
Only a board pair of fives matters here: 1 combo of 55 remain, against 6 for any other pair.
A worked example
Suppose you look down at a five and a two. Any opponent hand comes from 1,225 possibilities. 55 makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with 55, it would be 6 of them, 0.49%.
How strong is 55?
Order all 169 classes by equity against a random hand and 55 lands at number 27, inside the top 30 classes, with 60.32%. A tie is worth half a win in that figure.
Down to and including 55, the ranking holds 184 combos, or 13.88% of deals; 178 of them belong to hands above it.
55 against ranges of hands
Five ranges, five equities for 55. Counting only the combos your cards leave possible, it has 25.68% against the top 5 percent (60 combos), 38.96% against the top 10 percent (130 combos), 46.40% against the top 20 percent (264 combos), 50.43% against the top 30 percent (386 combos) and 54.17% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 55 equity |
|---|---|---|
| Top 5 percent | 60 | 25.68% |
| Top 10 percent | 130 | 38.96% |
| Top 20 percent | 264 | 46.40% |
| Top 30 percent | 386 | 50.43% |
| Top 50 percent | 658 | 54.17% |
The line sits between the top 20 and top 30 percent: 55 is behind the narrower range and ahead of the wider one.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, 55 leaves an average of 130.00. That is no loss at all: 55 blocks none of those hands.
Hands next to 55
Look at 55 against the hands that rank next to it. 55 has 52.70% equity against KJo, the hand ranked number 26: it wins 52.43% of boards, ties 0.55% and loses 47.02%. It is the favorite in that matchup. 55 has 49.15% equity against QJs, the hand ranked number 28: it wins 48.81% of boards, ties 0.67% and loses 50.52%. It is the underdog in that matchup.
There is only one way to write 55, 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 55 combos
- How many combos of 55 are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt 55 about 1 time in 221.0.
- How many 55 combos are left if I hold a five?
- 3 combos of 55 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 55?
- KJo ranks number 26, just above 55, and 55 has 52.70% equity against it. QJs ranks number 28, just below, and 55 has 49.15% 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.