K4s: the 4 combos
Fix the suit, and the king and four of that suit are the only choice; four suits make 4 combos.
Spelled out, K4s is these 4 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 K4s for each rank of card you can see.
| Known card | K4s combos left |
|---|---|
| Ace | 4 |
| King | 3 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 3 |
| Three | 4 |
| Two | 4 |
With a king or a four in view, 3 of the 4 combos of K4s remain, which removes 25%. Any card of a different rank leaves all 4 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 K4s combos that remain for each paired rank.
| Board pair | K4s combos left |
|---|---|
| Aces | 4 |
| Kings | 2 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 2 |
| Threes | 4 |
| Twos | 4 |
Only a board pair of kings or fours matters here: 2 combos of K4s remain, against 4 for any other pair.
A worked example
Say your hole cards are a king and a two. That leaves 1,225 possible two-card hands for an opponent, and 3 of them are K4s: a 0.24% chance, roughly 1 in 408. Without the king in your hand it would be 4 combos, 0.33%, roughly 1 in 306.
How strong is K4s?
K4s ranks number 60 of the 169 starting-hand classes, inside the top 60 classes. Against one random hand it has 54.88% equity, which counts a win as 1 and a tie as one half over every five-card board.
438 of the 1,326 starting hands are K4s or better by this ranking. That is 33.03% of deals.
K4s against ranges of hands
Tighter ranges are harder to beat. K4s gets 29.54% against the top 5 percent (60 combos), 32.84% against the top 10 percent (130 combos), 36.05% against the top 20 percent (264 combos), 38.11% against the top 30 percent (386 combos) and 45.37% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | K4s equity |
|---|---|---|
| Top 5 percent | 60 | 29.54% |
| Top 10 percent | 130 | 32.84% |
| Top 20 percent | 264 | 36.05% |
| Top 30 percent | 386 | 38.11% |
| Top 50 percent | 658 | 45.37% |
K4s 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 K4s does to the top 10 percent range of 130 combos: averaged over its 4, 121.00 remain for an opponent. That is 9.00 combos fewer than the 130 an opponent has before you look.
Hands next to K4s
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. K4s has 42.52% equity against A2o, the hand ranked number 59: it wins 42.23% of boards, ties 0.59% and loses 57.18%. It is the underdog in that matchup. K4s has 58.95% equity against Q7s, the hand ranked number 61: it wins 58.58% of boards, ties 0.73% and loses 40.69%. It is the favorite in that matchup.
Switch K4s from suited to offsuit and you get K4o: 12 combos, rank 74, 52.33% equity. K4o is 3 times as many combos but 2.56 points weaker against a random hand.
Questions about K4s combos
- How many combos of K4s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt K4s about 1 time in 331.5.
- How many K4s combos are left if I hold a king?
- 3 combos of K4s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is K4s stronger than K4o?
- Yes, by 2.56 points: K4s has 54.88% equity against a random hand and ranks number 60, while K4o has 52.33% and ranks number 74. K4o has 12 combos to K4s's 4.
How this was computed
Every K4s 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.