K7s: the 4 combos
There is one king-seven pairing per suit, and a suited hand counts each suit once, so K7s is 4 combos.
The list below names all 4 holdings behind K7s. A hand range that says K7s means every one of them at once.
How cards you can see change the count
Start from 4 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 | K7s combos left |
|---|---|
| Ace | 4 |
| King | 3 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: a king or a seven leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of K7s for a board pair of each rank, ace down to two.
| Board pair | K7s combos left |
|---|---|
| Aces | 4 |
| Kings | 2 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
A board pair of kings or sevens leaves 2 combos of K7s; a pair of any other rank leaves all 4.
A worked example
Try it with a king and a two in your hand. 1,225 two-card holdings are left, 3 of which are K7s. The chance is 0.24%, about 1 in 408, against 0.33% when none of your cards blocks it.
How strong is K7s?
By equity against a random hand, K7s is number 44 of 169, inside the top 60 classes. Its 57.54% 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 K7s and the list holds 308 combos, 23.23% of the 1,326. The hands above it account for 304 of those.
K7s against ranges of hands
Opponents rarely hold a random hand, so here is K7s against five top-percent ranges, each hand weighted by its live combos: 29.63% against the top 5 percent (60 combos), 33.83% against the top 10 percent (130 combos), 36.72% against the top 20 percent (264 combos), 40.03% against the top 30 percent (386 combos) and 48.59% against the top 50 percent (658 combos).
| Opponent range | Combos in range | K7s equity |
|---|---|---|
| Top 5 percent | 60 | 29.63% |
| Top 10 percent | 130 | 33.83% |
| Top 20 percent | 264 | 36.72% |
| Top 30 percent | 386 | 40.03% |
| Top 50 percent | 658 | 48.59% |
K7s 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 118.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of K7s. That is 12.00 combos fewer than the 130 an opponent has before you look.
Hands next to K7s
Hands next to K7s in the ranking are not always close in a head-to-head. K7s has 57.04% equity against Q9s, the hand ranked number 43: it wins 56.70% of boards, ties 0.69% and loses 42.61%. It is the favorite in that matchup. K7s has 54.69% equity against JTs, the hand ranked number 45: it wins 54.35% of boards, ties 0.69% and loses 44.97%. It is the favorite in that matchup.
K7o holds the same two ranks as K7s but not the same suits, and it ranks number 58 at 55.19% equity. K7o is 3 times as many combos but 2.35 points weaker against a random hand.
Questions about K7s combos
- How many combos of K7s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt K7s about 1 time in 331.5.
- How many K7s combos are left if I hold a king?
- 3 combos of K7s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is K7s stronger than K7o?
- Yes, by 2.35 points: K7s has 57.54% equity against a random hand and ranks number 44, while K7o has 55.19% and ranks number 58. K7o has 12 combos to K7s'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.