74s: the 4 combos
Fix the suit, and the seven and four of that suit are the only choice; four suits make 4 combos.
These are the 4 specific hands that count as 74s. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for 74s. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | 74s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 3 |
| Three | 4 |
| Two | 4 |
With a seven or a four in view, 3 of the 4 combos of 74s remain, which removes 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the 74s combos left for each paired rank.
| Board pair | 74s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 2 |
| Threes | 4 |
| Twos | 4 |
Only a board pair of sevens or fours matters here: 2 combos of 74s remain, against 4 for any other pair.
A worked example
Suppose you look down at a seven and a two. Any opponent hand comes from 1,225 possibilities. 74s makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with 74s, it would be 4 of them, 0.33%.
How strong is 74s?
Order all 169 classes by equity against a random hand and 74s lands at number 134, below the middle of the ranking, with 41.85%. A tie is worth half a win in that figure.
Down to and including 74s, the ranking holds 1,010 combos, or 76.17% of deals; 1,006 of them belong to hands above it.
74s against ranges of hands
Five ranges, five equities for 74s. Counting only the combos your cards leave possible, it has 22.47% against the top 5 percent (60 combos), 30.79% against the top 10 percent (130 combos), 33.84% against the top 20 percent (264 combos), 35.33% against the top 30 percent (386 combos) and 36.99% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 74s equity |
|---|---|---|
| Top 5 percent | 60 | 22.47% |
| Top 10 percent | 130 | 30.79% |
| Top 20 percent | 264 | 33.84% |
| Top 30 percent | 386 | 35.33% |
| Top 50 percent | 658 | 36.99% |
74s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, 74s leaves an average of 127.00. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 74s
Look at 74s against the hands that rank next to it. 74s has 42.85% equity against 76o, the hand ranked number 133: it wins 26.20% of boards, ties 33.31% and loses 40.49%. It is the underdog in that matchup. 74s has 46.52% equity against T2o, the hand ranked number 135: it wins 45.52% of boards, ties 2.00% and loses 52.48%. It is the underdog in that matchup.
74o is what the same two ranks look like when they are offsuit: 12 combos at number 151, 38.55% equity. 74o is 3 times as many combos but 3.30 points weaker against a random hand.
Questions about 74s combos
- How many combos of 74s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 74s about 1 time in 331.5.
- How many 74s combos are left if I hold a seven?
- 3 combos of 74s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 74s stronger than 74o?
- Yes, by 3.30 points: 74s has 41.85% equity against a random hand and ranks number 134, while 74o has 38.55% and ranks number 151. 74o has 12 combos to 74s's 4.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the 74s group was counted. The blocker rows drop each combo containing a visible card; the board-pair rows do it for a visible pair.
Exact matchups, counted over all 1,712,304 boards, supply the rank and equity. A tie counts as half, and ranges are weighted by the combos that remain.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.