T9o: the 12 combos
Count every ten and nine pairing (16) and take away the suited ones (4): 12 combos are offsuit.
Spelled out, T9o is these 12 holdings. The suits are what separate them from each other, and the ranks are the same in all.
How cards you can see change the count
A card in your hand or on the board takes combos away from your opponent's possible hands. This table counts what is left of T9o for each rank of card you can see.
| Known card | T9o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 9 |
| Nine | 9 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With a ten or a nine in view, 9 of the 12 combos of T9o remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Two board cards of one rank are out of reach for your opponent. The table gives the T9o combos that remain for each paired rank.
| Board pair | T9o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 6 |
| Nines | 6 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of tens or nines matters here: 6 combos of T9o remain, against 12 for any other pair.
A worked example
Say your hole cards are a ten and a two. That leaves 1,225 possible two-card hands for an opponent, and 9 of them are T9o: a 0.73% chance, roughly 1 in 136. Without the ten in your hand it would be 12 combos, 0.98%, roughly 1 in 102.
How strong is T9o?
T9o ranks number 78 of the 169 starting-hand classes, in the middle of the ranking. Against one random hand it has 51.53% equity, which counts a win as 1 and a tie as one half over every five-card board.
568 of the 1,326 starting hands are T9o or better by this ranking. That is 42.84% of deals.
T9o against ranges of hands
Tighter ranges are harder to beat. T9o gets 28.12% against the top 5 percent (60 combos), 32.11% against the top 10 percent (130 combos), 34.95% against the top 20 percent (264 combos), 36.76% against the top 30 percent (386 combos) and 39.64% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | T9o equity |
|---|---|---|
| Top 5 percent | 60 | 28.12% |
| Top 10 percent | 130 | 32.11% |
| Top 20 percent | 264 | 34.95% |
| Top 30 percent | 386 | 36.76% |
| Top 50 percent | 658 | 39.64% |
T9o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Check what T9o does to the top 10 percent range of 130 combos: averaged over its 12, 119.00 remain for an opponent. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to T9o
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. T9o has 44.36% equity against Q7o, the hand ranked number 77: it wins 43.91% of boards, ties 0.90% and loses 55.19%. It is the underdog in that matchup. T9o has 42.19% equity against J8o, the hand ranked number 79: it wins 41.52% of boards, ties 1.33% and loses 57.15%. It is the underdog in that matchup.
Switch T9o from offsuit to suited and you get T9s: 4 combos, rank 64, 54.03% equity. T9o has 3 times as many combos as T9s and is 2.50 points weaker against a random hand.
Questions about T9o combos
- How many combos of T9o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt T9o about 1 time in 110.5.
- How many T9o combos are left if I hold a ten?
- 9 combos of T9o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is T9o stronger than T9s?
- No: T9o has 51.53% equity against a random hand and ranks number 78, while T9s has 54.03% and ranks number 64. T9s has 4 combos to T9o's 12.
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.