KQs: the 4 combos
A suited hand needs both cards in one suit, so each of the 4 suits gives exactly 1 combo: 4 in all.
Here is every one of the 4 combos, written as the two cards you would see. Clubs, diamonds, hearts and spades each appear in the way the count above requires.
How cards you can see change the count
Seeing a card changes which hands are possible. Here is the count of KQs combos that remain after you hold, or the board shows, one card of each rank.
| Known card | KQs combos left |
|---|---|
| Ace | 4 |
| King | 3 |
| Queen | 3 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding a king or a queen takes KQs from 4 combos down to 3, a cut of 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A paired board shows two cards of one rank, and those two cards cannot be in an opponent's hand either. The table shows the KQs combos left when the board holds a pair of each rank.
| Board pair | KQs combos left |
|---|---|
| Aces | 4 |
| Kings | 2 |
| Queens | 2 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Kings or queens paired on the board leave 2 combos of KQs, and no other pair changes the count of 4.
A worked example
You hold a king and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 3 of them are KQs, which is 0.24%, or about 1 in 408. If your two cards had nothing to do with KQs, the same hand would have 4 combos and a 0.33% chance, about 1 in 306.
How strong is KQs?
Measured against a random hand, KQs has 63.40% equity and the number 16 spot of 169, inside the top 30 classes. Wins count once and ties count half.
Together with all stronger classes, KQs covers 104 combos, which is 7.84% of the 1,326 starting hands.
KQs against ranges of hands
Against a range, equity is averaged over every hand in it, weighted by how many combos of each hand are still possible. KQs makes 38.68% against the top 5 percent (60 combos), 40.20% against the top 10 percent (130 combos), 48.01% against the top 20 percent (264 combos), 51.19% against the top 30 percent (386 combos) and 58.46% against the top 50 percent (658 combos).
| Opponent range | Combos in range | KQs equity |
|---|---|---|
| Top 5 percent | 60 | 38.68% |
| Top 10 percent | 130 | 40.20% |
| Top 20 percent | 264 | 48.01% |
| Top 30 percent | 386 | 51.19% |
| Top 50 percent | 658 | 58.46% |
The line sits between the top 20 and top 30 percent: KQs is behind the narrower range and ahead of the wider one.
Your own cards block part of an opponent's strong range. The top 10 percent holds 130 combos, and when you hold a combo of KQs an average of 114.00 of them stay possible. That is 16.00 combos fewer than the 130 an opponent has before you look.
Hands next to KQs
Compare KQs with the hand ranked just above it and the hand just below it. KQs has 43.68% equity against AJo, the hand ranked number 15: it wins 43.44% of boards, ties 0.48% and loses 56.08%. It is the underdog in that matchup. KQs has 49.09% equity against 66, the hand ranked number 17: it wins 48.85% of boards, ties 0.47% and loses 50.68%. It is the underdog in that matchup.
The offsuit twin of KQs is KQo, ranked number 23 with 61.46% equity against a random hand. KQo is 3 times as many combos but 1.94 points weaker against a random hand.
Questions about KQs combos
- How many combos of KQs are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt KQs about 1 time in 331.5.
- How many KQs combos are left if I hold a king?
- 3 combos of KQs remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is KQs stronger than KQo?
- Yes, by 1.94 points: KQs has 63.40% equity against a random hand and ranks number 16, while KQo has 61.46% and ranks number 23. KQo has 12 combos to KQs's 4.
How this was computed
We counted from the deck itself: 1,326 possible two-card hands, each placed in one of 169 classes. A table row then deletes the combos that need a card known to be elsewhere, and the survivors are tallied.
Equity comes from an exact table of preflop matchups, every one of the 1,712,304 boards counted. A tie is half a win, and each hand in a range is weighted by the combos your cards leave.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.