KK: the 6 combos
Each pairing of two kings is its own combo: 4 x 3 = 12 ordered picks, halved because order does not matter, gives 6.
Spelled out, KK is these 6 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 KK for each rank of card you can see.
| Known card | KK combos left |
|---|---|
| Ace | 6 |
| King | 3 |
| Queen | 6 |
| Jack | 6 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 6 |
| Four | 6 |
| Three | 6 |
| Two | 6 |
With a king in view, 3 of the 6 combos of KK remain, which removes 50%. Any card of a different rank leaves all 6 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 KK combos that remain for each paired rank.
| Board pair | KK combos left |
|---|---|
| Aces | 6 |
| Kings | 1 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 6 |
| Threes | 6 |
| Twos | 6 |
Only a board pair of kings matters here: 1 combo of KK remain, against 6 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 KK: a 0.24% chance, roughly 1 in 408. Without the king in your hand it would be 6 combos, 0.49%, roughly 1 in 204.
How strong is KK?
KK ranks number 2 of the 169 starting-hand classes, inside the top 10 of the 169 classes. Against one random hand it has 82.40% equity, which counts a win as 1 and a tie as one half over every five-card board.
12 of the 1,326 starting hands are KK or better by this ranking. That is 0.90% of deals.
KK against ranges of hands
Tighter ranges are harder to beat. KK gets 70.84% against the top 5 percent (60 combos), 71.79% against the top 10 percent (130 combos), 74.63% against the top 20 percent (264 combos), 75.77% against the top 30 percent (386 combos) and 79.69% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | KK equity |
|---|---|---|
| Top 5 percent | 60 | 70.84% |
| Top 10 percent | 130 | 71.79% |
| Top 20 percent | 264 | 74.63% |
| Top 30 percent | 386 | 75.77% |
| Top 50 percent | 658 | 79.69% |
KK is ahead of all five of these ranges, even the top 5 percent.
Check what KK does to the top 10 percent range of 130 combos: averaged over its 6, 113.00 remain for an opponent. That is 17.00 combos fewer than the 130 an opponent has before you look.
Hands next to KK
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. KK has 18.05% equity against AA, the hand ranked number 1: it wins 17.82% of boards, ties 0.46% and loses 81.72%. It is the underdog in that matchup. KK has 81.93% equity against QQ, the hand ranked number 3: it wins 81.70% of boards, ties 0.46% and loses 17.83%. It is the favorite in that matchup.
There is only one way to write KK, since a pair cannot be suited or offsuit. Every pair is 6 combos, and the 13 of them make 5.88% of deals.
Questions about KK combos
- How many combos of KK are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt KK about 1 time in 221.0.
- How many KK combos are left if I hold a king?
- 3 combos of KK remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.
- Which hands rank next to KK?
- AA ranks number 1, just above KK, and KK has 18.05% equity against it. QQ ranks number 3, just below, and KK has 81.93% equity against it.
How this was computed
Combos are counted by listing all 1,326 two-card hands in a 52-card deck and sorting each into its class. The known-card rows remove every combo that uses a card of that rank; the board-pair rows remove those that use either of two such cards.
Rank and equity read our table of all 169 by 169 preflop matchups, each counted over every one of the 1,712,304 boards. Ties count as half a win, and a range is weighted by its live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.