T4o: the 12 combos
An offsuit hand pairs any ten with any four of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Here is every one of the 12 combos, written as the two cards you would see. Clubs, diamonds, hearts and spades each appear in the way the count above requires.
How cards you can see change the count
Seeing a card changes which hands are possible. Here is the count of T4o combos that remain after you hold, or the board shows, one card of each rank.
| Known card | T4o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 9 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 9 |
| Three | 12 |
| Two | 12 |
Holding a ten or a four takes T4o 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
A paired board shows two cards of one rank, and those two cards cannot be in an opponent's hand either. The table shows the T4o combos left when the board holds a pair of each rank.
| Board pair | T4o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 6 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 6 |
| Threes | 12 |
| Twos | 12 |
Tens or fours paired on the board leave 6 combos of T4o, and no other pair changes the count of 12.
A worked example
You hold a ten and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 9 of them are T4o, which is 0.73%, or about 1 in 136. If your two cards had nothing to do with T4o, the same hand would have 12 combos and a 0.98% chance, about 1 in 102.
How strong is T4o?
Measured against a random hand, T4o has 43.50% equity and the number 125 spot of 169, below the middle of the ranking. Wins count once and ties count half.
Together with all stronger classes, T4o covers 942 combos, which is 71.04% of the 1,326 starting hands.
T4o against ranges of hands
Against a range, equity is averaged over every hand in it, weighted by how many combos of each hand are still possible. T4o makes 21.29% against the top 5 percent (60 combos), 26.19% against the top 10 percent (130 combos), 29.36% against the top 20 percent (264 combos), 30.76% against the top 30 percent (386 combos) and 32.86% against the top 50 percent (658 combos).
| Opponent range | Combos in range | T4o equity |
|---|---|---|
| Top 5 percent | 60 | 21.29% |
| Top 10 percent | 130 | 26.19% |
| Top 20 percent | 264 | 29.36% |
| Top 30 percent | 386 | 30.76% |
| Top 50 percent | 658 | 32.86% |
T4o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your own cards block part of an opponent's strong range. The top 10 percent holds 130 combos, and when you hold a combo of T4o an average of 123.00 of them stay possible. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to T4o
Compare T4o with the hand ranked just above it and the hand just below it. T4o has 53.78% equity against 75s, the hand ranked number 124: it wins 52.80% of boards, ties 1.96% and loses 45.24%. It is the favorite in that matchup. T4o has 59.87% equity against 93s, the hand ranked number 126: it wins 58.88% of boards, ties 1.98% and loses 39.14%. It is the favorite in that matchup.
The suited twin of T4o is T4s, ranked number 108 with 46.53% equity against a random hand. T4o has 3 times as many combos as T4s and is 3.03 points weaker against a random hand.
Questions about T4o combos
- How many combos of T4o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt T4o about 1 time in 110.5.
- How many T4o combos are left if I hold a ten?
- 9 combos of T4o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is T4o stronger than T4s?
- No: T4o has 43.50% equity against a random hand and ranks number 125, while T4s has 46.53% and ranks number 108. T4s has 4 combos to T4o'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.