98s: the 4 combos
For 98s, the nine and the eight must share a suit. With 4 suits and one way to pair them in each, the count is 4.
Every 98s you can be dealt is one of these 4 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For 98s, the table lists the combos left after one card of each rank is out of play.
| Known card | 98s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 3 |
| Eight | 3 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
A nine or an eight you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The 98s combos that survive are in the table, one row per rank.
| Board pair | 98s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 2 |
| Eights | 2 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Pairing nines or eights on the board cuts 98s to 2 combos. Every other paired board leaves the full 4.
A worked example
Take a hand of a nine and a two. Your opponent then holds one of 1,225 possible hands, and 3 of them are 98s. That is 0.24%, or 1 in 408, instead of the 0.33% (1 in 306) you get when your cards do not block it.
How strong is 98s?
Rank 83 of 169 belongs to 98s, in the middle of the ranking, on 50.80% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add 98s to every hand ranked above it and you hold 612 of the 1,326 two-card hands, 46.15% of all deals.
98s against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For 98s the five ranges give 28.43% against the top 5 percent (60 combos), 35.16% against the top 10 percent (130 combos), 37.59% against the top 20 percent (264 combos), 39.16% against the top 30 percent (386 combos) and 41.04% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 98s equity |
|---|---|---|
| Top 5 percent | 60 | 28.43% |
| Top 10 percent | 130 | 35.16% |
| Top 20 percent | 264 | 37.59% |
| Top 30 percent | 386 | 39.16% |
| Top 50 percent | 658 | 41.04% |
98s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding 98s removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 123.00 remain. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to 98s
A one-place difference in rank can be a large or small gap in a direct matchup. 98s has 45.87% equity against Q3s, the hand ranked number 82: it wins 45.39% of boards, ties 0.97% and loses 53.64%. It is the underdog in that matchup. 98s has 42.97% equity against T7s, the hand ranked number 84: it wins 42.04% of boards, ties 1.86% and loses 56.10%. It is the underdog in that matchup.
Same ranks, other suits: 98o is the offsuit version, number 99 of 169 at 48.10%. 98o is 3 times as many combos but 2.70 points weaker against a random hand.
Questions about 98s combos
- How many combos of 98s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 98s about 1 time in 331.5.
- How many 98s combos are left if I hold a nine?
- 3 combos of 98s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 98s stronger than 98o?
- Yes, by 2.70 points: 98s has 50.80% equity against a random hand and ranks number 83, while 98o has 48.10% and ranks number 99. 98o has 12 combos to 98s'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.