K8o: the 12 combos
Count every king and eight pairing (16) and take away the suited ones (4): 12 combos are offsuit.
Spelled out, K8o is these 12 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 K8o for each rank of card you can see.
| Known card | K8o combos left |
|---|---|
| Ace | 12 |
| King | 9 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With a king or an eight in view, 9 of the 12 combos of K8o remain, which removes 25%. Any card of a different rank leaves all 12 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 K8o combos that remain for each paired rank.
| Board pair | K8o combos left |
|---|---|
| Aces | 12 |
| Kings | 6 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of kings or eights matters here: 6 combos of K8o remain, against 12 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 9 of them are K8o: a 0.73% chance, roughly 1 in 136. Without the king in your hand it would be 12 combos, 0.98%, roughly 1 in 102.
How strong is K8o?
K8o ranks number 51 of the 169 starting-hand classes, inside the top 60 classes. Against one random hand it has 56.02% equity, which counts a win as 1 and a tie as one half over every five-card board.
362 of the 1,326 starting hands are K8o or better by this ranking. That is 27.30% of deals.
K8o against ranges of hands
Tighter ranges are harder to beat. K8o gets 27.19% against the top 5 percent (60 combos), 30.48% against the top 10 percent (130 combos), 33.62% against the top 20 percent (264 combos), 37.56% against the top 30 percent (386 combos) and 47.15% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | K8o equity |
|---|---|---|
| Top 5 percent | 60 | 27.19% |
| Top 10 percent | 130 | 30.48% |
| Top 20 percent | 264 | 33.62% |
| Top 30 percent | 386 | 37.56% |
| Top 50 percent | 658 | 47.15% |
K8o 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 K8o does to the top 10 percent range of 130 combos: averaged over its 12, 118.00 remain for an opponent. That is 12.00 combos fewer than the 130 an opponent has before you look.
Hands next to K8o
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. K8o has 62.57% equity against K6s, the hand ranked number 50: it wins 52.56% of boards, ties 20.01% and loses 27.43%. It is the favorite in that matchup. K8o has 69.46% equity against Q8s, the hand ranked number 52: it wins 67.91% of boards, ties 3.10% and loses 28.99%. It is the favorite in that matchup.
Switch K8o from offsuit to suited and you get K8s: 4 combos, rank 37, 58.31% equity. K8o has 3 times as many combos as K8s and is 2.29 points weaker against a random hand.
Questions about K8o combos
- How many combos of K8o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt K8o about 1 time in 110.5.
- How many K8o combos are left if I hold a king?
- 9 combos of K8o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is K8o stronger than K8s?
- No: K8o has 56.02% equity against a random hand and ranks number 51, while K8s has 58.31% and ranks number 37. K8s has 4 combos to K8o's 12.
How this was computed
Every K8o 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.