42o: the 12 combos
Pair each of the 4 fours with each of the 4 twos to get 16, then remove the 4 suited pairings. 42o is the other 12.
The list below names all 12 holdings behind 42o. A hand range that says 42o means every one of them at once.
How cards you can see change the count
Start from 12 combos and remove every combo that uses a card you can see. The table does that for one known card of each rank.
| Known card | 42o 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 | 12 |
| Two | 9 |
Only two ranks change the count: a four or a two leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of 42o for a board pair of each rank, ace down to two.
| Board pair | 42o 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 | 12 |
| Twos | 6 |
A board pair of fours or twos leaves 6 combos of 42o; a pair of any other rank leaves all 12.
A worked example
Try it with a four and a three in your hand. 1,225 two-card holdings are left, 9 of which are 42o. The chance is 0.73%, about 1 in 136, against 0.98% when none of your cards blocks it.
How strong is 42o?
By equity against a random hand, 42o is number 168 of 169, among the 30 weakest classes. Its 33.20% counts wins in full and ties as half, over all 1,712,304 boards, for every pair of hands that can be dealt.
Stop the ranking at 42o and the list holds 1,314 combos, 99.10% of the 1,326. The hands above it account for 1,302 of those.
42o against ranges of hands
Opponents rarely hold a random hand, so here is 42o against five top-percent ranges, each hand weighted by its live combos: 18.14% against the top 5 percent (60 combos), 25.67% against the top 10 percent (130 combos), 29.08% against the top 20 percent (264 combos), 30.02% against the top 30 percent (386 combos) and 31.12% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 42o equity |
|---|---|---|
| Top 5 percent | 60 | 18.14% |
| Top 10 percent | 130 | 25.67% |
| Top 20 percent | 264 | 29.08% |
| Top 30 percent | 386 | 30.02% |
| Top 50 percent | 658 | 31.12% |
42o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
On average 130.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of 42o. That is no loss at all: 42o blocks none of those hands.
Hands next to 42o
Hands next to 42o in the ranking are not always close in a head-to-head. 42o has 37.28% equity against 62o, the hand ranked number 167: it wins 24.59% of boards, ties 25.39% and loses 50.02%. It is the underdog in that matchup. 42o has 53.18% equity against 32o, the hand ranked number 169: it wins 28.85% of boards, ties 48.67% and loses 22.48%. It is the favorite in that matchup.
42s holds the same two ranks as 42o but not the same suits, and it ranks number 158 at 36.83% equity. 42o has 3 times as many combos as 42s and is 3.63 points weaker against a random hand.
Questions about 42o combos
- How many combos of 42o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 42o about 1 time in 110.5.
- How many 42o combos are left if I hold a four?
- 9 combos of 42o remain out of 12. With a three as your other card, an opponent has it about 1 time in 136.
- Is 42o stronger than 42s?
- No: 42o has 33.20% equity against a random hand and ranks number 168, while 42s has 36.83% and ranks number 158. 42s has 4 combos to 42o'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.