98o: the 12 combos
For 98o, there are 4 nines and 4 eights, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
The 12 holdings of 98o are listed below, higher card first. Nothing is left out and nothing appears twice.
How cards you can see change the count
Combos shrink when cards are visible. The rows below give the 98o count left after one known card of each rank, from the ace down to the two.
| Known card | 98o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 9 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
A nine or an eight you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Now put two cards of the same rank on the board. This table counts the combos of 98o that are still possible after a board pair of each rank.
| Board pair | 98o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Pairing nines or eights on the board cuts 98o to 6 combos. Every other paired board leaves the full 12.
A worked example
Walk through it once. Your hole cards: a nine and a two. Your opponent's possible hands: 1,225. Of those, 98o is 9, so the chance is 9 / 1,225 = 0.73%. With no blocking card it would be 12 / 1,225 = 0.98%.
How strong is 98o?
The ranking puts 98o at number 99 out of 169, in the middle of the ranking. Its equity against a random hand is 48.10%, with a tie counted as half a win.
A range that runs from the top of the ranking down to 98o is 734 combos, 55.35% of all two-card hands, and 722 of them rank above 98o itself.
98o against ranges of hands
Here is how 98o fares against five ranges that run from the top of the ranking down. It scores 24.85% against the top 5 percent (60 combos), 31.66% against the top 10 percent (130 combos), 34.15% against the top 20 percent (264 combos), 35.77% against the top 30 percent (386 combos) and 37.71% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 98o equity |
|---|---|---|
| Top 5 percent | 60 | 24.85% |
| Top 10 percent | 130 | 31.66% |
| Top 20 percent | 264 | 34.15% |
| Top 30 percent | 386 | 35.77% |
| Top 50 percent | 658 | 37.71% |
98o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
The top 10 percent is 130 combos before you look at your cards. With 98o in your hand, an average of 123.00 are left. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to 98o
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 98o has 45.70% equity against Q3o, the hand ranked number 98: it wins 45.22% of boards, ties 0.96% and loses 53.82%. It is the underdog in that matchup. 98o has 67.14% equity against 87s, the hand ranked number 100: it wins 62.42% of boards, ties 9.43% and loses 28.15%. It is the favorite in that matchup.
98o has 3 times as many combos as 98s and is 2.70 points weaker against a random hand, and 98s is the suited twin, number 83 of 169 with 50.80% equity.
Questions about 98o combos
- How many combos of 98o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 98o about 1 time in 110.5.
- How many 98o combos are left if I hold a nine?
- 9 combos of 98o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 98o stronger than 98s?
- No: 98o has 48.10% equity against a random hand and ranks number 99, while 98s has 50.80% and ranks number 83. 98s has 4 combos to 98o's 12.
How this was computed
Every 98o combo was listed from the 1,326 two-card holdings. For each blocker or board-pair row, the combos that contain a visible card were dropped and the rest were counted.
The rank and equity figures use our matchup table, which counts all 1,712,304 boards for each pair of classes. Ties are halves, and range matchups are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.