K5s: 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.
Below are the 4 exact two-card holdings in K5s. When a range chart marks K5s, it marks all of them together.
How cards you can see change the count
How many K5s combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | K5s combos left |
|---|---|
| Ace | 4 |
| King | 3 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 3 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding a king or a five takes K5s 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
Board pairs take away more combos than a single card does. The table lists the K5s count for each possible pair on the board.
| Board pair | K5s combos left |
|---|---|
| Aces | 4 |
| Kings | 2 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 2 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Kings or fives paired on the board leave 2 combos of K5s, and no other pair changes the count of 4.
A worked example
Here is the count in a real spot. You hold a king and a two, which leaves 1,225 hands for your opponent. K5s is 3 of them, a 0.24% chance. A hand with no king in it would give 4 combos, 0.33%.
How strong is K5s?
Number 54 of 169: that is where K5s sits when hands are ordered by equity against a random hand, inside the top 60 classes. The figure is 55.79%, wins plus half the ties.
Counting from the top, K5s is where the running total reaches 382 combos (28.81% of 1,326). The 378 combos before it are all stronger classes.
K5s against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for K5s: 29.86% against the top 5 percent (60 combos), 33.14% against the top 10 percent (130 combos), 36.42% against the top 20 percent (264 combos), 38.79% against the top 30 percent (386 combos) and 46.34% against the top 50 percent (658 combos).
| Opponent range | Combos in range | K5s equity |
|---|---|---|
| Top 5 percent | 60 | 29.86% |
| Top 10 percent | 130 | 33.14% |
| Top 20 percent | 264 | 36.42% |
| Top 30 percent | 386 | 38.79% |
| Top 50 percent | 658 | 46.34% |
K5s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
How much of the top 10 percent can an opponent still hold? Across the 4 combos of K5s you might hold, 121.00 of its 130 combos remain on average. That is 9.00 combos fewer than the 130 an opponent has before you look.
Hands next to K5s
The hands on either side of K5s in the ranking make a useful pair of comparisons. K5s has 42.51% equity against A3o, the hand ranked number 53: it wins 42.23% of boards, ties 0.55% and loses 57.22%. It is the underdog in that matchup. K5s has 55.69% equity against J9s, the hand ranked number 55: it wins 55.33% of boards, ties 0.72% and loses 43.95%. It is the favorite in that matchup.
The offsuit form, K5o, ranks number 69 with 53.31% equity against a random hand. K5o is 3 times as many combos but 2.48 points weaker against a random hand.
Questions about K5s combos
- How many combos of K5s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt K5s about 1 time in 331.5.
- How many K5s combos are left if I hold a king?
- 3 combos of K5s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is K5s stronger than K5o?
- Yes, by 2.48 points: K5s has 55.79% equity against a random hand and ranks number 54, while K5o has 53.31% and ranks number 69. K5o has 12 combos to K5s's 4.
How this was computed
Counting is done on the deck: 1,326 hands, 169 classes. The rows of each table apply the same rule, delete any combo that uses a card now visible, and report what is left.
For rank and equity, the page reads a table of preflop matchups with all 1,712,304 boards counted per pair of classes. Ties are halves and ranges use live-combo weights.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.