T9s: the 4 combos
Fix the suit, and the ten and nine of that suit are the only choice; four suits make 4 combos.
These are the 4 specific hands that count as T9s. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for T9s. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | T9s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 3 |
| Nine | 3 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
With a ten or a nine in view, 3 of the 4 combos of T9s remain, which removes 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the T9s combos left for each paired rank.
| Board pair | T9s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 2 |
| Nines | 2 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Only a board pair of tens or nines matters here: 2 combos of T9s remain, against 4 for any other pair.
A worked example
Suppose you look down at a ten and a two. Any opponent hand comes from 1,225 possibilities. T9s makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with T9s, it would be 4 of them, 0.33%.
How strong is T9s?
Order all 169 classes by equity against a random hand and T9s lands at number 64, in the middle of the ranking, with 54.03%. A tie is worth half a win in that figure.
Down to and including T9s, the ranking holds 462 combos, or 34.84% of deals; 458 of them belong to hands above it.
T9s against ranges of hands
Five ranges, five equities for T9s. Counting only the combos your cards leave possible, it has 31.54% against the top 5 percent (60 combos), 35.58% against the top 10 percent (130 combos), 38.35% against the top 20 percent (264 combos), 40.09% against the top 30 percent (386 combos) and 42.83% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T9s equity |
|---|---|---|
| Top 5 percent | 60 | 31.54% |
| Top 10 percent | 130 | 35.58% |
| Top 20 percent | 264 | 38.35% |
| Top 30 percent | 386 | 40.09% |
| Top 50 percent | 658 | 42.83% |
T9s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, T9s leaves an average of 119.00. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to T9s
Look at T9s against the hands that rank next to it. T9s has 45.84% equity against K3s, the hand ranked number 63: it wins 45.48% of boards, ties 0.72% and loses 53.80%. It is the underdog in that matchup. T9s has 42.80% equity against J8s, the hand ranked number 65: it wins 42.15% of boards, ties 1.30% and loses 56.55%. It is the underdog in that matchup.
T9o is what the same two ranks look like when they are offsuit: 12 combos at number 78, 51.53% equity. T9o is 3 times as many combos but 2.50 points weaker against a random hand.
Questions about T9s combos
- How many combos of T9s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt T9s about 1 time in 331.5.
- How many T9s combos are left if I hold a ten?
- 3 combos of T9s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is T9s stronger than T9o?
- Yes, by 2.50 points: T9s has 54.03% equity against a random hand and ranks number 64, while T9o has 51.53% and ranks number 78. T9o has 12 combos to T9s's 4.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the T9s 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.