74o: the 12 combos
Count every seven and four pairing (16) and take away the suited ones (4): 12 combos are offsuit.
Spelled out, 74o is these 12 holdings. The suits are what separate them from each other, and the ranks are the same in all.
How cards you can see change the count
A card in your hand or on the board takes combos away from your opponent's possible hands. This table counts what is left of 74o for each rank of card you can see.
| Known card | 74o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 9 |
| Three | 12 |
| Two | 12 |
With a seven or a four in view, 9 of the 12 combos of 74o remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Two board cards of one rank are out of reach for your opponent. The table gives the 74o combos that remain for each paired rank.
| Board pair | 74o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 6 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of sevens or fours matters here: 6 combos of 74o remain, against 12 for any other pair.
A worked example
Say your hole cards are a seven and a two. That leaves 1,225 possible two-card hands for an opponent, and 9 of them are 74o: a 0.73% chance, roughly 1 in 136. Without the seven in your hand it would be 12 combos, 0.98%, roughly 1 in 102.
How strong is 74o?
74o ranks number 151 of the 169 starting-hand classes, among the 30 weakest classes. Against one random hand it has 38.55% equity, which counts a win as 1 and a tie as one half over every five-card board.
1,150 of the 1,326 starting hands are 74o or better by this ranking. That is 86.73% of deals.
74o against ranges of hands
Tighter ranges are harder to beat. 74o gets 18.61% against the top 5 percent (60 combos), 27.09% against the top 10 percent (130 combos), 30.20% against the top 20 percent (264 combos), 31.73% against the top 30 percent (386 combos) and 33.43% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | 74o equity |
|---|---|---|
| Top 5 percent | 60 | 18.61% |
| Top 10 percent | 130 | 27.09% |
| Top 20 percent | 264 | 30.20% |
| Top 30 percent | 386 | 31.73% |
| Top 50 percent | 658 | 33.43% |
74o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Check what 74o does to the top 10 percent range of 130 combos: averaged over its 12, 127.00 remain for an opponent. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 74o
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. 74o has 62.00% equity against 43s, the hand ranked number 150: it wins 52.78% of boards, ties 18.44% and loses 28.78%. It is the favorite in that matchup. 74o has 52.01% equity against 72s, the hand ranked number 152: it wins 29.54% of boards, ties 44.94% and loses 25.52%. It is the favorite in that matchup.
Switch 74o from offsuit to suited and you get 74s: 4 combos, rank 134, 41.85% equity. 74o has 3 times as many combos as 74s and is 3.30 points weaker against a random hand.
Questions about 74o combos
- How many combos of 74o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 74o about 1 time in 110.5.
- How many 74o combos are left if I hold a seven?
- 9 combos of 74o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 74o stronger than 74s?
- No: 74o has 38.55% equity against a random hand and ranks number 151, while 74s has 41.85% and ranks number 134. 74s has 4 combos to 74o's 12.
How this was computed
Every 74o 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.