T3s: the 4 combos
For T3s, the ten and the three must share a suit. With 4 suits and one way to pair them in each, the count is 4.
The 4 holdings of T3s are listed below, higher card first. Nothing is left out and nothing appears twice.
How cards you can see change the count
Combos shrink when cards are visible. The rows below give the T3s count left after one known card of each rank, from the ace down to the two.
| Known card | T3s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 3 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 3 |
| Two | 4 |
A ten or a three 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 T3s that are still possible after a board pair of each rank.
| Board pair | T3s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 2 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 2 |
| Twos | 4 |
Pairing tens or threes on the board cuts T3s to 2 combos. Every other paired board leaves the full 4.
A worked example
Walk through it once. Your hole cards: a ten and a two. Your opponent's possible hands: 1,225. Of those, T3s 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 T3s?
The ranking puts T3s at number 114 out of 169, below the middle of the ranking. Its equity against a random hand is 45.69%, with a tie counted as half a win.
A range that runs from the top of the ranking down to T3s is 850 combos, 64.10% of all two-card hands, and 846 of them rank above T3s itself.
T3s against ranges of hands
Here is how T3s fares against five ranges that run from the top of the ranking down. It scores 24.74% against the top 5 percent (60 combos), 29.63% against the top 10 percent (130 combos), 32.72% against the top 20 percent (264 combos), 34.01% against the top 30 percent (386 combos) and 35.90% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T3s equity |
|---|---|---|
| Top 5 percent | 60 | 24.74% |
| Top 10 percent | 130 | 29.63% |
| Top 20 percent | 264 | 32.72% |
| Top 30 percent | 386 | 34.01% |
| Top 50 percent | 658 | 35.90% |
T3s 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 T3s in your hand, an average of 123.00 are left. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to T3s
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. T3s has 57.89% equity against 95s, the hand ranked number 113: it wins 56.92% of boards, ties 1.94% and loses 41.13%. It is the favorite in that matchup. T3s has 54.60% equity against 76s, the hand ranked number 115: it wins 53.65% of boards, ties 1.90% and loses 44.45%. It is the favorite in that matchup.
T3o is 3 times as many combos but 3.10 points weaker against a random hand, and T3o is the offsuit twin, number 131 of 169 with 42.59% equity.
Questions about T3s combos
- How many combos of T3s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt T3s about 1 time in 331.5.
- How many T3s combos are left if I hold a ten?
- 3 combos of T3s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is T3s stronger than T3o?
- Yes, by 3.10 points: T3s has 45.69% equity against a random hand and ranks number 114, while T3o has 42.59% and ranks number 131. T3o has 12 combos to T3s'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.