T5o: the 12 combos
Count every ten and five pairing (16) and take away the suited ones (4): 12 combos are offsuit.
These are the 12 specific hands that count as T5o. 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 T5o. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | T5o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 9 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 9 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With a ten or a five in view, 9 of the 12 combos of T5o remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the T5o combos left for each paired rank.
| Board pair | T5o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 6 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 6 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of tens or fives matters here: 6 combos of T5o remain, against 12 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. T5o makes up 9 of them, which is 0.73% (1 in 136); if you held neither card's rank in common with T5o, it would be 12 of them, 0.98%.
How strong is T5o?
Order all 169 classes by equity against a random hand and T5o lands at number 122, below the middle of the ranking, with 44.25%. A tie is worth half a win in that figure.
Down to and including T5o, the ranking holds 922 combos, or 69.53% of deals; 910 of them belong to hands above it.
T5o against ranges of hands
Five ranges, five equities for T5o. Counting only the combos your cards leave possible, it has 21.35% against the top 5 percent (60 combos), 26.24% against the top 10 percent (130 combos), 29.43% against the top 20 percent (264 combos), 31.06% against the top 30 percent (386 combos) and 32.99% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T5o equity |
|---|---|---|
| Top 5 percent | 60 | 21.35% |
| Top 10 percent | 130 | 26.24% |
| Top 20 percent | 264 | 29.43% |
| Top 30 percent | 386 | 31.06% |
| Top 50 percent | 658 | 32.99% |
T5o 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, T5o leaves an average of 123.00. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to T5o
Look at T5o against the hands that rank next to it. T5o has 40.72% equity against J2o, the hand ranked number 121: it wins 40.00% of boards, ties 1.44% and loses 58.56%. It is the underdog in that matchup. T5o has 60.20% equity against 94s, the hand ranked number 123: it wins 59.21% of boards, ties 1.97% and loses 38.82%. It is the favorite in that matchup.
T5s is what the same two ranks look like when they are suited: 4 combos at number 106, 47.22% equity. T5o has 3 times as many combos as T5s and is 2.97 points weaker against a random hand.
Questions about T5o combos
- How many combos of T5o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt T5o about 1 time in 110.5.
- How many T5o combos are left if I hold a ten?
- 9 combos of T5o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is T5o stronger than T5s?
- No: T5o has 44.25% equity against a random hand and ranks number 122, while T5s has 47.22% and ranks number 106. T5s has 4 combos to T5o'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.