K4o: the 12 combos
Count every king and four pairing (16) and take away the suited ones (4): 12 combos are offsuit.
These are the 12 specific hands that count as K4o. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for K4o. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | K4o combos left |
|---|---|
| Ace | 12 |
| King | 9 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 9 |
| Three | 12 |
| Two | 12 |
With a king or a four in view, 9 of the 12 combos of K4o remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the K4o combos left for each paired rank.
| Board pair | K4o combos left |
|---|---|
| Aces | 12 |
| Kings | 6 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 6 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of kings or fours matters here: 6 combos of K4o remain, against 12 for any other pair.
A worked example
Suppose you look down at a king and a two. Any opponent hand comes from 1,225 possibilities. K4o makes up 9 of them, which is 0.73% (1 in 136); if you held neither card's rank in common with K4o, it would be 12 of them, 0.98%.
How strong is K4o?
Order all 169 classes by equity against a random hand and K4o lands at number 74, in the middle of the ranking, with 52.33%. A tie is worth half a win in that figure.
Down to and including K4o, the ranking holds 536 combos, or 40.42% of deals; 524 of them belong to hands above it.
K4o against ranges of hands
Five ranges, five equities for K4o. Counting only the combos your cards leave possible, it has 25.83% against the top 5 percent (60 combos), 29.08% against the top 10 percent (130 combos), 32.40% against the top 20 percent (264 combos), 34.52% against the top 30 percent (386 combos) and 42.21% against the top 50 percent (658 combos).
| Opponent range | Combos in range | K4o equity |
|---|---|---|
| Top 5 percent | 60 | 25.83% |
| Top 10 percent | 130 | 29.08% |
| Top 20 percent | 264 | 32.40% |
| Top 30 percent | 386 | 34.52% |
| Top 50 percent | 658 | 42.21% |
K4o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, K4o leaves an average of 121.00. That is 9.00 combos fewer than the 130 an opponent has before you look.
Hands next to K4o
Look at K4o against the hands that rank next to it. K4o has 52.66% equity against T8s, the hand ranked number 73: it wins 52.31% of boards, ties 0.69% and loses 46.99%. It is the favorite in that matchup. K4o has 55.05% equity against J7s, the hand ranked number 75: it wins 54.70% of boards, ties 0.70% and loses 44.60%. It is the favorite in that matchup.
K4s is what the same two ranks look like when they are suited: 4 combos at number 60, 54.88% equity. K4o has 3 times as many combos as K4s and is 2.56 points weaker against a random hand.
Questions about K4o combos
- How many combos of K4o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt K4o about 1 time in 110.5.
- How many K4o combos are left if I hold a king?
- 9 combos of K4o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is K4o stronger than K4s?
- No: K4o has 52.33% equity against a random hand and ranks number 74, while K4s has 54.88% and ranks number 60. K4s has 4 combos to K4o's 12.
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.