J6s: the 4 combos
A suited hand needs both cards in one suit, so each of the 4 suits gives exactly 1 combo: 4 in all.
Here is every one of the 4 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 J6s combos that remain after you hold, or the board shows, one card of each rank.
| Known card | J6s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 3 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 3 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding a jack or a six takes J6s from 4 combos down to 3, a cut of 25%. Any card of a different rank leaves all 4 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 J6s combos left when the board holds a pair of each rank.
| Board pair | J6s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 2 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 2 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Jacks or sixes paired on the board leave 2 combos of J6s, and no other pair changes the count of 4.
A worked example
You hold a jack and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 3 of them are J6s, which is 0.24%, or about 1 in 408. If your two cards had nothing to do with J6s, the same hand would have 4 combos and a 0.33% chance, about 1 in 306.
How strong is J6s?
Measured against a random hand, J6s has 50.61% equity and the number 85 spot of 169, in the middle of the ranking. Wins count once and ties count half.
Together with all stronger classes, J6s covers 620 combos, which is 46.76% of the 1,326 starting hands.
J6s 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. J6s makes 26.10% against the top 5 percent (60 combos), 30.93% against the top 10 percent (130 combos), 34.07% against the top 20 percent (264 combos), 35.76% against the top 30 percent (386 combos) and 38.35% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J6s equity |
|---|---|---|
| Top 5 percent | 60 | 26.10% |
| Top 10 percent | 130 | 30.93% |
| Top 20 percent | 264 | 34.07% |
| Top 30 percent | 386 | 35.76% |
| Top 50 percent | 658 | 38.35% |
J6s 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 J6s an average of 119.00 of them stay possible. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to J6s
Compare J6s with the hand ranked just above it and the hand just below it. J6s has 57.32% equity against T7s, the hand ranked number 84: it wins 56.67% of boards, ties 1.30% and loses 42.03%. It is the favorite in that matchup. J6s has 44.52% equity against K2o, the hand ranked number 86: it wins 44.15% of boards, ties 0.74% and loses 55.11%. It is the underdog in that matchup.
The offsuit twin of J6s is J6o, ranked number 102 with 47.84% equity against a random hand. J6o is 3 times as many combos but 2.76 points weaker against a random hand.
Questions about J6s combos
- How many combos of J6s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt J6s about 1 time in 331.5.
- How many J6s combos are left if I hold a jack?
- 3 combos of J6s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is J6s stronger than J6o?
- Yes, by 2.76 points: J6s has 50.61% equity against a random hand and ranks number 85, while J6o has 47.84% and ranks number 102. J6o has 12 combos to J6s's 4.
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.