53o: the 12 combos
An offsuit hand pairs any five with any three of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Below are the 12 exact two-card holdings in 53o. When a range chart marks 53o, it marks all of them together.
How cards you can see change the count
How many 53o combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | 53o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 9 |
| Four | 12 |
| Three | 9 |
| Two | 12 |
Holding a five or a three takes 53o from 12 combos down to 9, a cut of 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Board pairs take away more combos than a single card does. The table lists the 53o count for each possible pair on the board.
| Board pair | 53o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 6 |
| Fours | 12 |
| Threes | 6 |
| Twos | 12 |
Fives or threes paired on the board leave 6 combos of 53o, and no other pair changes the count of 12.
A worked example
Here is the count in a real spot. You hold a five and a two, which leaves 1,225 hands for your opponent. 53o is 9 of them, a 0.73% chance. A hand with no five in it would give 12 combos, 0.98%.
How strong is 53o?
Number 161 of 169: that is where 53o sits when hands are ordered by equity against a random hand, among the 30 weakest classes. The figure is 36.27%, wins plus half the ties.
Counting from the top, 53o is where the running total reaches 1,238 combos (93.36% of 1,326). The 1,226 combos before it are all stronger classes.
53o against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for 53o: 20.06% against the top 5 percent (60 combos), 27.43% against the top 10 percent (130 combos), 30.89% against the top 20 percent (264 combos), 31.82% against the top 30 percent (386 combos) and 33.39% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 53o equity |
|---|---|---|
| Top 5 percent | 60 | 20.06% |
| Top 10 percent | 130 | 27.43% |
| Top 20 percent | 264 | 30.89% |
| Top 30 percent | 386 | 31.82% |
| Top 50 percent | 658 | 33.39% |
53o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
How much of the top 10 percent can an opponent still hold? Across the 12 combos of 53o you might hold, 130.00 of its 130 combos remain on average. That is no loss at all: 53o blocks none of those hands.
Hands next to 53o
The hands on either side of 53o in the ranking make a useful pair of comparisons. 53o has 35.57% equity against 73o, the hand ranked number 160: it wins 26.28% of boards, ties 18.58% and loses 55.13%. It is the underdog in that matchup. 53o has 37.52% equity against 63o, the hand ranked number 162: it wins 24.69% of boards, ties 25.65% and loses 49.66%. It is the underdog in that matchup.
The suited form, 53s, ranks number 146 with 39.69% equity against a random hand. 53o has 3 times as many combos as 53s and is 3.43 points weaker against a random hand.
Questions about 53o combos
- How many combos of 53o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 53o about 1 time in 110.5.
- How many 53o combos are left if I hold a five?
- 9 combos of 53o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 53o stronger than 53s?
- No: 53o has 36.27% equity against a random hand and ranks number 161, while 53s has 39.69% and ranks number 146. 53s has 4 combos to 53o's 12.
How this was computed
The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.
Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.