95o: the 12 combos
Pair each of the 4 nines with each of the 4 fives to get 16, then remove the 4 suited pairings. 95o is the other 12.
The list below names all 12 holdings behind 95o. A hand range that says 95o means every one of them at once.
How cards you can see change the count
Start from 12 combos and remove every combo that uses a card you can see. The table does that for one known card of each rank.
| Known card | 95o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 9 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 9 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: a nine or a five leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of 95o for a board pair of each rank, ace down to two.
| Board pair | 95o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 6 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 6 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
A board pair of nines or fives leaves 6 combos of 95o; a pair of any other rank leaves all 12.
A worked example
Try it with a nine and a two in your hand. 1,225 two-card holdings are left, 9 of which are 95o. The chance is 0.73%, about 1 in 136, against 0.98% when none of your cards blocks it.
How strong is 95o?
By equity against a random hand, 95o is number 130 of 169, below the middle of the ranking. Its 42.67% counts wins in full and ties as half, over all 1,712,304 boards, for every pair of hands that can be dealt.
Stop the ranking at 95o and the list holds 978 combos, 73.76% of the 1,326. The hands above it account for 966 of those.
95o against ranges of hands
Opponents rarely hold a random hand, so here is 95o against five top-percent ranges, each hand weighted by its live combos: 20.79% against the top 5 percent (60 combos), 27.33% against the top 10 percent (130 combos), 30.36% against the top 20 percent (264 combos), 31.75% against the top 30 percent (386 combos) and 33.40% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 95o equity |
|---|---|---|
| Top 5 percent | 60 | 20.79% |
| Top 10 percent | 130 | 27.33% |
| Top 20 percent | 264 | 30.36% |
| Top 30 percent | 386 | 31.75% |
| Top 50 percent | 658 | 33.40% |
95o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
On average 126.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of 95o. That is 4.00 combos fewer than the 130 an opponent has before you look.
Hands next to 95o
Hands next to 95o in the ranking are not always close in a head-to-head. 95o has 59.74% equity against 84s, the hand ranked number 129: it wins 58.21% of boards, ties 3.06% and loses 38.73%. It is the favorite in that matchup. 95o has 41.50% equity against T3o, the hand ranked number 131: it wins 40.47% of boards, ties 2.06% and loses 57.47%. It is the underdog in that matchup.
95s holds the same two ranks as 95o but not the same suits, and it ranks number 113 at 45.72% equity. 95o has 3 times as many combos as 95s and is 3.05 points weaker against a random hand.
Questions about 95o combos
- How many combos of 95o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 95o about 1 time in 110.5.
- How many 95o combos are left if I hold a nine?
- 9 combos of 95o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 95o stronger than 95s?
- No: 95o has 42.67% equity against a random hand and ranks number 130, while 95s has 45.72% and ranks number 113. 95s has 4 combos to 95o's 12.
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.