T5s: the 4 combos
Fix the suit, and the ten and five of that suit are the only choice; four suits make 4 combos.
Spelled out, T5s is these 4 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 T5s for each rank of card you can see.
| Known card | T5s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 3 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 3 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
With a ten or a five in view, 3 of the 4 combos of T5s remain, which removes 25%. Any card of a different rank leaves all 4 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 T5s combos that remain for each paired rank.
| Board pair | T5s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 2 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 2 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Only a board pair of tens or fives matters here: 2 combos of T5s remain, against 4 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 3 of them are T5s: a 0.24% chance, roughly 1 in 408. Without the ten in your hand it would be 4 combos, 0.33%, roughly 1 in 306.
How strong is T5s?
T5s ranks number 106 of the 169 starting-hand classes, below the middle of the ranking. Against one random hand it has 47.22% equity, which counts a win as 1 and a tie as one half over every five-card board.
786 of the 1,326 starting hands are T5s or better by this ranking. That is 59.28% of deals.
T5s against ranges of hands
Tighter ranges are harder to beat. T5s gets 25.14% against the top 5 percent (60 combos), 30.03% against the top 10 percent (130 combos), 33.16% against the top 20 percent (264 combos), 34.74% against the top 30 percent (386 combos) and 36.60% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | T5s equity |
|---|---|---|
| Top 5 percent | 60 | 25.14% |
| Top 10 percent | 130 | 30.03% |
| Top 20 percent | 264 | 33.16% |
| Top 30 percent | 386 | 34.74% |
| Top 50 percent | 658 | 36.60% |
T5s 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 T5s does to the top 10 percent range of 130 combos: averaged over its 4, 123.00 remain for an opponent. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to T5s
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. T5s has 44.26% equity against Q2o, the hand ranked number 105: it wins 43.75% of boards, ties 1.02% and loses 55.23%. It is the underdog in that matchup. T5s has 30.35% equity against J5o, the hand ranked number 107: it wins 27.40% of boards, ties 5.90% and loses 66.70%. It is the underdog in that matchup.
Switch T5s from suited to offsuit and you get T5o: 12 combos, rank 122, 44.25% equity. T5o is 3 times as many combos but 2.97 points weaker against a random hand.
Questions about T5s combos
- How many combos of T5s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt T5s about 1 time in 331.5.
- How many T5s combos are left if I hold a ten?
- 3 combos of T5s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is T5s stronger than T5o?
- Yes, by 2.97 points: T5s has 47.22% equity against a random hand and ranks number 106, while T5o has 44.25% and ranks number 122. T5o has 12 combos to T5s's 4.
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.