TT: the 6 combos
To count TT, pick 2 of the 4 tens: 4 x 3 / 2 = 6 pairings.
Every TT you can be dealt is one of these 6 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For TT, the table lists the combos left after one card of each rank is out of play.
| Known card | TT combos left |
|---|---|
| Ace | 6 |
| King | 6 |
| Queen | 6 |
| Jack | 6 |
| Ten | 3 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 6 |
| Four | 6 |
| Three | 6 |
| Two | 6 |
A ten you can see leaves 3 of 6, so 50% of the combos are gone. Any card of a different rank leaves all 6 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The TT combos that survive are in the table, one row per rank.
| Board pair | TT combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 1 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 6 |
| Threes | 6 |
| Twos | 6 |
Pairing tens on the board cuts TT to 1 combo. Every other paired board leaves the full 6.
A worked example
Take a hand of a ten and a two. Your opponent then holds one of 1,225 possible hands, and 3 of them are TT. That is 0.24%, or 1 in 408, instead of the 0.49% (1 in 204) you get when your cards do not block it.
How strong is TT?
Rank 5 of 169 belongs to TT, inside the top 10 of the 169 classes, on 75.01% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add TT to every hand ranked above it and you hold 30 of the 1,326 two-card hands, 2.26% of all deals.
TT against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For TT the five ranges give 47.57% against the top 5 percent (60 combos), 54.71% against the top 10 percent (130 combos), 60.35% against the top 20 percent (264 combos), 63.65% against the top 30 percent (386 combos) and 67.29% against the top 50 percent (658 combos).
| Opponent range | Combos in range | TT equity |
|---|---|---|
| Top 5 percent | 60 | 47.57% |
| Top 10 percent | 130 | 54.71% |
| Top 20 percent | 264 | 60.35% |
| Top 30 percent | 386 | 63.65% |
| Top 50 percent | 658 | 67.29% |
The line sits between the top 5 and top 10 percent: TT is behind the narrower range and ahead of the wider one.
Holding TT removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 117.00 remain. That is 13.00 combos fewer than the 130 an opponent has before you look.
Hands next to TT
A one-place difference in rank can be a large or small gap in a direct matchup. TT has 18.01% equity against JJ, the hand ranked number 4: it wins 17.79% of boards, ties 0.44% and loses 81.77%. It is the underdog in that matchup. TT has 82.00% equity against 99, the hand ranked number 6: it wins 81.75% of boards, ties 0.50% and loses 17.75%. It is the favorite in that matchup.
Because both cards of TT have the same rank, there is no suited version of it. The 13 pairs are 78 combos in all, 5.88% of the 1,326 hands.
Questions about TT combos
- How many combos of TT are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt TT about 1 time in 221.0.
- How many TT combos are left if I hold a ten?
- 3 combos of TT remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.
- Which hands rank next to TT?
- JJ ranks number 4, just above TT, and TT has 18.01% equity against it. 99 ranks number 6, just below, and TT has 82.00% equity against it.
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.