32o: the 12 combos
For 32o, there are 4 threes and 4 twos, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
Every 32o you can be dealt is one of these 12 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 32o, the table lists the combos left after one card of each rank is out of play.
| Known card | 32o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 9 |
| Two | 9 |
A three or a two you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The 32o combos that survive are in the table, one row per rank.
| Board pair | 32o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 6 |
| Twos | 6 |
Pairing threes or twos on the board cuts 32o to 6 combos. Every other paired board leaves the full 12.
A worked example
Take a hand of a three and a four. Your opponent then holds one of 1,225 possible hands, and 9 of them are 32o. That is 0.73%, or 1 in 136, instead of the 0.98% (1 in 102) you get when your cards do not block it.
How strong is 32o?
Rank 169 of 169 belongs to 32o, among the 30 weakest classes, on 32.30% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add 32o to every hand ranked above it and you hold 1,326 of the 1,326 two-card hands, 100.00% of all deals.
32o against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For 32o the five ranges give 17.73% against the top 5 percent (60 combos), 25.28% against the top 10 percent (130 combos), 28.65% against the top 20 percent (264 combos), 29.41% against the top 30 percent (386 combos) and 30.43% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 32o equity |
|---|---|---|
| Top 5 percent | 60 | 17.73% |
| Top 10 percent | 130 | 25.28% |
| Top 20 percent | 264 | 28.65% |
| Top 30 percent | 386 | 29.41% |
| Top 50 percent | 658 | 30.43% |
32o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding 32o 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: 32o blocks none of those hands.
Hands next to 32o
Nothing ranks below 32o. 32o has 46.82% equity against 42o, the hand ranked number 168: it wins 22.48% of boards, ties 48.67% and loses 28.85%. It is the underdog in that matchup. The hand directly above it is the closest comparison.
Same ranks, other suits: 32s is the suited version, number 163 of 169 at 35.98%. 32o has 3 times as many combos as 32s and is 3.68 points weaker against a random hand.
Questions about 32o combos
- How many combos of 32o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 32o about 1 time in 110.5.
- How many 32o combos are left if I hold a three?
- 9 combos of 32o remain out of 12. With a four as your other card, an opponent has it about 1 time in 136.
- Is 32o stronger than 32s?
- No: 32o has 32.30% equity against a random hand and ranks number 169, while 32s has 35.98% and ranks number 163. 32s has 4 combos to 32o's 12.
How this was computed
Every 32o combo was listed from the 1,326 two-card holdings. For each blocker or board-pair row, the combos that contain a visible card were dropped and the rest were counted.
The rank and equity figures use our matchup table, which counts all 1,712,304 boards for each pair of classes. Ties are halves, and range matchups are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.