QTs combos

QTs: the 4 combos

For QTs, the queen and the ten must share a suit. With 4 suits and one way to pair them in each, the count is 4.

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

• Q♠10♠
• Q♥10♥
• Q♦10♦
• Q♣10♣

How cards you can see change the count

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

A queen or a ten 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 QTs that are still possible after a board pair of each rank.

Pairing queens or tens on the board cuts QTs to 2 combos. Every other paired board leaves the full 4.

A worked example

Walk through it once. Your hole cards: a queen and a two. Your opponent's possible hands: 1,225. Of those, QTs 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 QTs?

The ranking puts QTs at number 34 out of 169, inside the top 60 classes. Its equity against a random hand is 59.47%, with a tie counted as half a win.

A range that runs from the top of the ranking down to QTs is 228 combos, 17.19% of all two-card hands, and 224 of them rank above QTs itself.

QTs against ranges of hands

Here is how QTs fares against five ranges that run from the top of the ranking down. It scores 35.13% against the top 5 percent (60 combos), 36.62% against the top 10 percent (130 combos), 39.09% against the top 20 percent (264 combos), 42.45% against the top 30 percent (386 combos) and 49.67% against the top 50 percent (658 combos).

QTs 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 QTs in your hand, an average of 115.00 are left. That is 15.00 combos fewer than the 130 an opponent has before you look.

Hands next to QTs

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. QTs has 30.37% equity against KTo, the hand ranked number 33: it wins 28.96% of boards, ties 2.83% and loses 68.22%. It is the underdog in that matchup. QTs has 44.37% equity against A4s, the hand ranked number 35: it wins 44.11% of boards, ties 0.52% and loses 55.37%. It is the underdog in that matchup.

QTo is 3 times as many combos but 2.18 points weaker against a random hand, and QTo is the offsuit twin, number 47 of 169 with 57.29% equity.

Questions about QTs combos

How many combos of QTs are there?

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

How many QTs combos are left if I hold a queen?

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

Is QTs stronger than QTo?

Yes, by 2.18 points: QTs has 59.47% equity against a random hand and ranks number 34, while QTo has 57.29% and ranks number 47. QTo has 12 combos to QTs'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.