T3o: the 12 combos
For T3o, there are 4 tens and 4 threes, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
Every T3o you can be dealt is one of these 12 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 T3o, the table lists the combos left after one card of each rank is out of play.
| Known card | T3o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 9 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 9 |
| Two | 12 |
A ten or a three you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The T3o combos that survive are in the table, one row per rank.
| Board pair | T3o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 6 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 6 |
| Twos | 12 |
Pairing tens or threes on the board cuts T3o to 6 combos. Every other paired board leaves the full 12.
A worked example
Take a hand of a ten and a two. Your opponent then holds one of 1,225 possible hands, and 9 of them are T3o. That is 0.73%, or 1 in 136, instead of the 0.98% (1 in 102) you get when your cards do not block it.
How strong is T3o?
Rank 131 of 169 belongs to T3o, below the middle of the ranking, on 42.59% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add T3o to every hand ranked above it and you hold 990 of the 1,326 two-card hands, 74.66% of all deals.
T3o against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For T3o the five ranges give 20.92% against the top 5 percent (60 combos), 25.81% against the top 10 percent (130 combos), 28.96% against the top 20 percent (264 combos), 30.29% against the top 30 percent (386 combos) and 32.23% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T3o equity |
|---|---|---|
| Top 5 percent | 60 | 20.92% |
| Top 10 percent | 130 | 25.81% |
| Top 20 percent | 264 | 28.96% |
| Top 30 percent | 386 | 30.29% |
| Top 50 percent | 658 | 32.23% |
T3o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding T3o removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 123.00 remain. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to T3o
A one-place difference in rank can be a large or small gap in a direct matchup. T3o has 58.50% equity against 95o, the hand ranked number 130: it wins 57.47% of boards, ties 2.06% and loses 40.47%. It is the favorite in that matchup. T3o has 59.99% equity against 92s, the hand ranked number 132: it wins 58.99% of boards, ties 2.00% and loses 39.02%. It is the favorite in that matchup.
Same ranks, other suits: T3s is the suited version, number 114 of 169 at 45.69%. T3o has 3 times as many combos as T3s and is 3.10 points weaker against a random hand.
Questions about T3o combos
- How many combos of T3o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt T3o about 1 time in 110.5.
- How many T3o combos are left if I hold a ten?
- 9 combos of T3o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is T3o stronger than T3s?
- No: T3o has 42.59% equity against a random hand and ranks number 131, while T3s has 45.69% and ranks number 114. T3s has 4 combos to T3o's 12.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the T3o 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.