T7s: the 4 combos
For T7s, the ten and the seven must share a suit. With 4 suits and one way to pair them in each, the count is 4.
Every T7s you can be dealt is one of these 4 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 T7s, the table lists the combos left after one card of each rank is out of play.
| Known card | T7s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 3 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
A ten or a seven 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
A pair on the board uses up two of the four cards of its rank. The T7s combos that survive are in the table, one row per rank.
| Board pair | T7s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 2 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Pairing tens or sevens on the board cuts T7s to 2 combos. Every other paired board leaves the full 4.
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 T7s. That is 0.24%, or 1 in 408, instead of the 0.33% (1 in 306) you get when your cards do not block it.
How strong is T7s?
Rank 84 of 169 belongs to T7s, in the middle of the ranking, on 50.64% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add T7s to every hand ranked above it and you hold 616 of the 1,326 two-card hands, 46.46% of all deals.
T7s against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For T7s the five ranges give 26.73% against the top 5 percent (60 combos), 32.73% against the top 10 percent (130 combos), 35.52% against the top 20 percent (264 combos), 37.64% against the top 30 percent (386 combos) and 39.56% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T7s equity |
|---|---|---|
| Top 5 percent | 60 | 26.73% |
| Top 10 percent | 130 | 32.73% |
| Top 20 percent | 264 | 35.52% |
| Top 30 percent | 386 | 37.64% |
| Top 50 percent | 658 | 39.56% |
T7s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding T7s removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 120.00 remain. That is 10.00 combos fewer than the 130 an opponent has before you look.
Hands next to T7s
A one-place difference in rank can be a large or small gap in a direct matchup. T7s has 57.03% equity against 98s, the hand ranked number 83: it wins 56.10% of boards, ties 1.86% and loses 42.04%. It is the favorite in that matchup. T7s has 42.68% equity against J6s, the hand ranked number 85: it wins 42.03% of boards, ties 1.30% and loses 56.67%. It is the underdog in that matchup.
Same ranks, other suits: T7o is the offsuit version, number 101 of 169 at 47.91%. T7o is 3 times as many combos but 2.73 points weaker against a random hand.
Questions about T7s combos
- How many combos of T7s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt T7s about 1 time in 331.5.
- How many T7s combos are left if I hold a ten?
- 3 combos of T7s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is T7s stronger than T7o?
- Yes, by 2.73 points: T7s has 50.64% equity against a random hand and ranks number 84, while T7o has 47.91% and ranks number 101. T7o has 12 combos to T7s's 4.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the T7s group was counted. The blocker rows drop each combo containing a visible card; the board-pair rows do it for a visible pair.
Exact matchups, counted over all 1,712,304 boards, supply the rank and equity. A tie counts as half, and ranges are weighted by the combos that remain.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.