43o: the 12 combos
For 43o, there are 4 fours and 4 threes, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
Every 43o 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 43o, the table lists the combos left after one card of each rank is out of play.
| Known card | 43o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 9 |
| Three | 9 |
| Two | 12 |
A four or a three 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 43o combos that survive are in the table, one row per rank.
| Board pair | 43o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 6 |
| Threes | 6 |
| Twos | 12 |
Pairing fours or threes on the board cuts 43o to 6 combos. Every other paired board leaves the full 12.
A worked example
Take a hand of a four and a two. Your opponent then holds one of 1,225 possible hands, and 9 of them are 43o. 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 43o?
Rank 164 of 169 belongs to 43o, among the 30 weakest classes, on 35.15% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add 43o to every hand ranked above it and you hold 1,266 of the 1,326 two-card hands, 95.48% of all deals.
43o against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For 43o the five ranges give 19.67% against the top 5 percent (60 combos), 27.09% against the top 10 percent (130 combos), 30.31% against the top 20 percent (264 combos), 31.13% against the top 30 percent (386 combos) and 32.86% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 43o equity |
|---|---|---|
| Top 5 percent | 60 | 19.67% |
| Top 10 percent | 130 | 27.09% |
| Top 20 percent | 264 | 30.31% |
| Top 30 percent | 386 | 31.13% |
| Top 50 percent | 658 | 32.86% |
43o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding 43o 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: 43o blocks none of those hands.
Hands next to 43o
A one-place difference in rank can be a large or small gap in a direct matchup. 43o has 51.82% equity against 32s, the hand ranked number 163: it wins 29.33% of boards, ties 44.99% and loses 25.68%. It is the favorite in that matchup. 43o has 46.33% equity against 72o, the hand ranked number 165: it wins 42.14% of boards, ties 8.38% and loses 49.48%. It is the underdog in that matchup.
Same ranks, other suits: 43s is the suited version, number 150 of 169 at 38.64%. 43o has 3 times as many combos as 43s and is 3.50 points weaker against a random hand.
Questions about 43o combos
- How many combos of 43o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 43o about 1 time in 110.5.
- How many 43o combos are left if I hold a four?
- 9 combos of 43o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 43o stronger than 43s?
- No: 43o has 35.15% equity against a random hand and ranks number 164, while 43s has 38.64% and ranks number 150. 43s has 4 combos to 43o's 12.
How this was computed
Every 43o 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.