T8o: the 12 combos
An offsuit hand pairs any ten with any eight of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Below are the 12 exact two-card holdings in T8o. When a range chart marks T8o, it marks all of them together.
How cards you can see change the count
How many T8o combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | T8o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 9 |
| Nine | 12 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Holding a ten or an eight takes T8o from 12 combos down to 9, a cut of 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Board pairs take away more combos than a single card does. The table lists the T8o count for each possible pair on the board.
| Board pair | T8o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 6 |
| Nines | 12 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Tens or eights paired on the board leave 6 combos of T8o, and no other pair changes the count of 12.
A worked example
Here is the count in a real spot. You hold a ten and a two, which leaves 1,225 hands for your opponent. T8o is 9 of them, a 0.73% chance. A hand with no ten in it would give 12 combos, 0.98%.
How strong is T8o?
Number 91 of 169: that is where T8o sits when hands are ordered by equity against a random hand, in the middle of the ranking. The figure is 49.72%, wins plus half the ties.
Counting from the top, T8o is where the running total reaches 670 combos (50.53% of 1,326). The 658 combos before it are all stronger classes.
T8o against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for T8o: 25.59% against the top 5 percent (60 combos), 30.85% against the top 10 percent (130 combos), 33.38% against the top 20 percent (264 combos), 35.25% against the top 30 percent (386 combos) and 37.64% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T8o equity |
|---|---|---|
| Top 5 percent | 60 | 25.59% |
| Top 10 percent | 130 | 30.85% |
| Top 20 percent | 264 | 33.38% |
| Top 30 percent | 386 | 35.25% |
| Top 50 percent | 658 | 37.64% |
T8o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
How much of the top 10 percent can an opponent still hold? Across the 12 combos of T8o you might hold, 120.00 of its 130 combos remain on average. That is 10.00 combos fewer than the 130 an opponent has before you look.
Hands next to T8o
The hands on either side of T8o in the ranking make a useful pair of comparisons. T8o has 41.87% equity against J5s, the hand ranked number 90: it wins 41.21% of boards, ties 1.33% and loses 57.46%. It is the underdog in that matchup. T8o has 42.12% equity against J7o, the hand ranked number 92: it wins 41.46% of boards, ties 1.33% and loses 57.21%. It is the underdog in that matchup.
The suited form, T8s, ranks number 73 with 52.33% equity against a random hand. T8o has 3 times as many combos as T8s and is 2.61 points weaker against a random hand.
Questions about T8o combos
- How many combos of T8o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt T8o about 1 time in 110.5.
- How many T8o combos are left if I hold a ten?
- 9 combos of T8o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is T8o stronger than T8s?
- No: T8o has 49.72% equity against a random hand and ranks number 91, while T8s has 52.33% and ranks number 73. T8s has 4 combos to T8o's 12.
How this was computed
We counted from the deck itself: 1,326 possible two-card hands, each placed in one of 169 classes. A table row then deletes the combos that need a card known to be elsewhere, and the survivors are tallied.
Equity comes from an exact table of preflop matchups, every one of the 1,712,304 boards counted. A tie is half a win, and each hand in a range is weighted by the combos your cards leave.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.