K2s combos

K2s: the 4 combos

For K2s, the king and the two must share a suit. With 4 suits and one way to pair them in each, the count is 4.

The 4 holdings of K2s are listed below, higher card first. Nothing is left out and nothing appears twice.

• K♠2♠
• K♥2♥
• K♦2♦
• K♣2♣

How cards you can see change the count

Combos shrink when cards are visible. The rows below give the K2s count left after one known card of each rank, from the ace down to the two.

A king or a two you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.

When the board is paired

Now put two cards of the same rank on the board. This table counts the combos of K2s that are still possible after a board pair of each rank.

Pairing kings or twos on the board cuts K2s to 2 combos. Every other paired board leaves the full 4.

A worked example

Walk through it once. Your hole cards: a king and a three. Your opponent's possible hands: 1,225. Of those, K2s is 3, so the chance is 3 / 1,225 = 0.24%. With no blocking card it would be 4 / 1,225 = 0.33%.

How strong is K2s?

The ranking puts K2s at number 71 out of 169, in the middle of the ranking. Its equity against a random hand is 53.21%, with a tie counted as half a win.

A range that runs from the top of the ranking down to K2s is 516 combos, 38.91% of all two-card hands, and 512 of them rank above K2s itself.

K2s against ranges of hands

Here is how K2s fares against five ranges that run from the top of the ranking down. It scores 28.85% against the top 5 percent (60 combos), 32.13% against the top 10 percent (130 combos), 35.49% against the top 20 percent (264 combos), 37.62% against the top 30 percent (386 combos) and 44.15% against the top 50 percent (658 combos).

K2s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.

The top 10 percent is 130 combos before you look at your cards. With K2s in your hand, an average of 121.00 are left. That is 9.00 combos fewer than the 130 an opponent has before you look.

Hands next to K2s

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. K2s has 57.91% equity against J9o, the hand ranked number 70: it wins 57.55% of boards, ties 0.71% and loses 41.74%. It is the favorite in that matchup. K2s has 58.56% equity against Q5s, the hand ranked number 72: it wins 58.17% of boards, ties 0.78% and loses 41.05%. It is the favorite in that matchup.

K2o is 3 times as many combos but 2.70 points weaker against a random hand, and K2o is the offsuit twin, number 86 of 169 with 50.51% equity.

Questions about K2s combos

How many combos of K2s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt K2s about 1 time in 331.5.

How many K2s combos are left if I hold a king?

3 combos of K2s remain out of 4. With a three as your other card, an opponent has it about 1 time in 408.

Is K2s stronger than K2o?

Yes, by 2.70 points: K2s has 53.21% equity against a random hand and ranks number 71, while K2o has 50.51% and ranks number 86. K2o has 12 combos to K2s's 4.

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.