J3s: the 4 combos
Fix the suit, and the jack and three of that suit are the only choice; four suits make 4 combos.
Spelled out, J3s 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 J3s for each rank of card you can see.
| Known card | J3s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 3 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 3 |
| Two | 4 |
With a jack or a three in view, 3 of the 4 combos of J3s 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 J3s combos that remain for each paired rank.
| Board pair | J3s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 2 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 2 |
| Twos | 4 |
Only a board pair of jacks or threes matters here: 2 combos of J3s remain, against 4 for any other pair.
A worked example
Say your hole cards are a jack and a two. That leaves 1,225 possible two-card hands for an opponent, and 3 of them are J3s: a 0.24% chance, roughly 1 in 408. Without the jack in your hand it would be 4 combos, 0.33%, roughly 1 in 306.
How strong is J3s?
J3s ranks number 97 of the 169 starting-hand classes, in the middle of the ranking. Against one random hand it has 48.23% equity, which counts a win as 1 and a tie as one half over every five-card board.
710 of the 1,326 starting hands are J3s or better by this ranking. That is 53.54% of deals.
J3s against ranges of hands
Tighter ranges are harder to beat. J3s gets 25.68% against the top 5 percent (60 combos), 30.45% against the top 10 percent (130 combos), 33.13% against the top 20 percent (264 combos), 34.47% against the top 30 percent (386 combos) and 36.96% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | J3s equity |
|---|---|---|
| Top 5 percent | 60 | 25.68% |
| Top 10 percent | 130 | 30.45% |
| Top 20 percent | 264 | 33.13% |
| Top 30 percent | 386 | 34.47% |
| Top 50 percent | 658 | 36.96% |
J3s 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 J3s does to the top 10 percent range of 130 combos: averaged over its 4, 122.00 remain for an opponent. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to J3s
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. J3s has 57.76% equity against T6s, the hand ranked number 96: it wins 57.09% of boards, ties 1.34% and loses 41.57%. It is the favorite in that matchup. J3s has 29.57% equity against Q3o, the hand ranked number 98: it wins 27.47% of boards, ties 4.20% and loses 68.34%. It is the underdog in that matchup.
Switch J3s from suited to offsuit and you get J3o: 12 combos, rank 116, 45.28% equity. J3o is 3 times as many combos but 2.96 points weaker against a random hand.
Questions about J3s combos
- How many combos of J3s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt J3s about 1 time in 331.5.
- How many J3s combos are left if I hold a jack?
- 3 combos of J3s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is J3s stronger than J3o?
- Yes, by 2.96 points: J3s has 48.23% equity against a random hand and ranks number 97, while J3o has 45.28% and ranks number 116. J3o has 12 combos to J3s'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.