T6s: the 4 combos
There is one ten-six pairing per suit, and a suited hand counts each suit once, so T6s is 4 combos.
The list below names all 4 holdings behind T6s. A hand range that says T6s means every one of them at once.
How cards you can see change the count
Start from 4 combos and remove every combo that uses a card you can see. The table does that for one known card of each rank.
| Known card | T6s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 3 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 3 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: a ten or a six leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of T6s for a board pair of each rank, ace down to two.
| Board pair | T6s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 2 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 2 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
A board pair of tens or sixes leaves 2 combos of T6s; a pair of any other rank leaves all 4.
A worked example
Try it with a ten and a two in your hand. 1,225 two-card holdings are left, 3 of which are T6s. The chance is 0.24%, about 1 in 408, against 0.33% when none of your cards blocks it.
How strong is T6s?
By equity against a random hand, T6s is number 96 of 169, in the middle of the ranking. Its 48.94% counts wins in full and ties as half, over all 1,712,304 boards, for every pair of hands that can be dealt.
Stop the ranking at T6s and the list holds 706 combos, 53.24% of the 1,326. The hands above it account for 702 of those.
T6s against ranges of hands
Opponents rarely hold a random hand, so here is T6s against five top-percent ranges, each hand weighted by its live combos: 26.11% against the top 5 percent (60 combos), 31.11% against the top 10 percent (130 combos), 34.67% against the top 20 percent (264 combos), 36.33% against the top 30 percent (386 combos) and 38.13% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T6s equity |
|---|---|---|
| Top 5 percent | 60 | 26.11% |
| Top 10 percent | 130 | 31.11% |
| Top 20 percent | 264 | 34.67% |
| Top 30 percent | 386 | 36.33% |
| Top 50 percent | 658 | 38.13% |
T6s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
On average 120.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of T6s. That is 10.00 combos fewer than the 130 an opponent has before you look.
Hands next to T6s
Hands next to T6s in the ranking are not always close in a head-to-head. T6s has 41.89% equity against J4s, the hand ranked number 95: it wins 41.23% of boards, ties 1.33% and loses 57.44%. It is the underdog in that matchup. T6s has 42.24% equity against J3s, the hand ranked number 97: it wins 41.57% of boards, ties 1.34% and loses 57.09%. It is the underdog in that matchup.
T6o holds the same two ranks as T6s but not the same suits, and it ranks number 112 at 46.09% equity. T6o is 3 times as many combos but 2.85 points weaker against a random hand.
Questions about T6s combos
- How many combos of T6s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt T6s about 1 time in 331.5.
- How many T6s combos are left if I hold a ten?
- 3 combos of T6s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is T6s stronger than T6o?
- Yes, by 2.85 points: T6s has 48.94% equity against a random hand and ranks number 96, while T6o has 46.09% and ranks number 112. T6o has 12 combos to T6s's 4.
How this was computed
The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.
Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.