75s: the 4 combos
A suited hand needs both cards in one suit, so each of the 4 suits gives exactly 1 combo: 4 in all.
Here is every one of the 4 combos, written as the two cards you would see. Clubs, diamonds, hearts and spades each appear in the way the count above requires.
How cards you can see change the count
Seeing a card changes which hands are possible. Here is the count of 75s combos that remain after you hold, or the board shows, one card of each rank.
| Known card | 75s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 3 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding a seven or a five takes 75s from 4 combos down to 3, a cut of 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A paired board shows two cards of one rank, and those two cards cannot be in an opponent's hand either. The table shows the 75s combos left when the board holds a pair of each rank.
| Board pair | 75s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 2 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Sevens or fives paired on the board leave 2 combos of 75s, and no other pair changes the count of 4.
A worked example
You hold a seven and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 3 of them are 75s, which is 0.24%, or about 1 in 408. If your two cards had nothing to do with 75s, the same hand would have 4 combos and a 0.33% chance, about 1 in 306.
How strong is 75s?
Measured against a random hand, 75s has 43.68% equity and the number 124 spot of 169, below the middle of the ranking. Wins count once and ties count half.
Together with all stronger classes, 75s covers 930 combos, which is 70.14% of the 1,326 starting hands.
75s against ranges of hands
Against a range, equity is averaged over every hand in it, weighted by how many combos of each hand are still possible. 75s makes 23.82% against the top 5 percent (60 combos), 32.07% against the top 10 percent (130 combos), 35.24% against the top 20 percent (264 combos), 36.90% against the top 30 percent (386 combos) and 38.40% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 75s equity |
|---|---|---|
| Top 5 percent | 60 | 23.82% |
| Top 10 percent | 130 | 32.07% |
| Top 20 percent | 264 | 35.24% |
| Top 30 percent | 386 | 36.90% |
| Top 50 percent | 658 | 38.40% |
75s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your own cards block part of an opponent's strong range. The top 10 percent holds 130 combos, and when you hold a combo of 75s an average of 127.00 of them stay possible. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 75s
Compare 75s with the hand ranked just above it and the hand just below it. 75s has 44.21% equity against 94s, the hand ranked number 123: it wins 42.73% of boards, ties 2.96% and loses 54.31%. It is the underdog in that matchup. 75s has 46.22% equity against T4o, the hand ranked number 125: it wins 45.24% of boards, ties 1.96% and loses 52.80%. It is the underdog in that matchup.
The offsuit twin of 75s is 75o, ranked number 141 with 40.51% equity against a random hand. 75o is 3 times as many combos but 3.16 points weaker against a random hand.
Questions about 75s combos
- How many combos of 75s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 75s about 1 time in 331.5.
- How many 75s combos are left if I hold a seven?
- 3 combos of 75s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 75s stronger than 75o?
- Yes, by 3.16 points: 75s has 43.68% equity against a random hand and ranks number 124, while 75o has 40.51% and ranks number 141. 75o has 12 combos to 75s's 4.
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.