95s: the 4 combos
There is one nine-five pairing per suit, and a suited hand counts each suit once, so 95s is 4 combos.
All 4 ways to hold 95s are shown here, one tile each. Counting them is how a range gets its size.
How cards you can see change the count
Every card you can see is a card nobody else can hold. The table shows how many of the 4 combos of 95s are still possible when you hold one card of each rank, and the same count applies when that card is on the board.
| Known card | 95s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 3 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 3 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: a nine or a five leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
How does a paired board change the count? For 95s, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | 95s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 2 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 2 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
A board pair of nines or fives leaves 2 combos of 95s; a pair of any other rank leaves all 4.
A worked example
Worked example: your cards are a nine and a two, so 1,225 two-card hands remain for your opponent. Of those, 3 are 95s, a 0.24% chance (about 1 in 408). With two cards that do not touch 95s, it would be 4 combos and 0.33%.
How strong is 95s?
95s holds rank 113 among the 169 classes, below the middle of the ranking. Against a random hand it has 45.72% equity: wins in full, ties as half, every board counted.
842 combos rank above 95s, and with its own 4 the running total is 846, 63.80% of the 1,326 hands.
95s against ranges of hands
Take the strongest hands in rank order and ask how 95s does against them. The answers, with live combos as weights: 24.59% against the top 5 percent (60 combos), 31.07% against the top 10 percent (130 combos), 34.02% against the top 20 percent (264 combos), 35.38% against the top 30 percent (386 combos) and 36.98% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 95s equity |
|---|---|---|
| Top 5 percent | 60 | 24.59% |
| Top 10 percent | 130 | 31.07% |
| Top 20 percent | 264 | 34.02% |
| Top 30 percent | 386 | 35.38% |
| Top 50 percent | 658 | 36.98% |
95s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your cards matter to the opponent's range too: with 95s, 126.00 of the 130 top-10-percent combos survive on average. That is 4.00 combos fewer than the 130 an opponent has before you look.
Hands next to 95s
Two quick matchups show where 95s stands among its neighbours. 95s has 40.14% equity against T6o, the hand ranked number 112: it wins 39.18% of boards, ties 1.93% and loses 58.89%. It is the underdog in that matchup. 95s has 42.11% equity against T3s, the hand ranked number 114: it wins 41.13% of boards, ties 1.94% and loses 56.92%. It is the underdog in that matchup.
Next to 95s sits 95o, its offsuit twin: rank 130, 12 combos, 42.67% equity against a random hand. 95o is 3 times as many combos but 3.05 points weaker against a random hand.
Questions about 95s combos
- How many combos of 95s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 95s about 1 time in 331.5.
- How many 95s combos are left if I hold a nine?
- 3 combos of 95s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 95s stronger than 95o?
- Yes, by 3.05 points: 95s has 45.72% equity against a random hand and ranks number 113, while 95o has 42.67% and ranks number 130. 95o has 12 combos to 95s'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.