64o: the 12 combos
Pair each of the 4 sixes with each of the 4 fours to get 16, then remove the 4 suited pairings. 64o is the other 12.
All 12 ways to hold 64o 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 12 combos of 64o 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 | 64o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 9 |
| Five | 12 |
| Four | 9 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: a six or a four leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
How does a paired board change the count? For 64o, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | 64o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 6 |
| Fives | 12 |
| Fours | 6 |
| Threes | 12 |
| Twos | 12 |
A board pair of sixes or fours leaves 6 combos of 64o; a pair of any other rank leaves all 12.
A worked example
Worked example: your cards are a six and a two, so 1,225 two-card hands remain for your opponent. Of those, 9 are 64o, a 0.73% chance (about 1 in 136). With two cards that do not touch 64o, it would be 12 combos and 0.98%.
How strong is 64o?
64o holds rank 154 among the 169 classes, among the 30 weakest classes. Against a random hand it has 38.01% equity: wins in full, ties as half, every board counted.
1,166 combos rank above 64o, and with its own 12 the running total is 1,178, 88.84% of the 1,326 hands.
64o against ranges of hands
Take the strongest hands in rank order and ask how 64o does against them. The answers, with live combos as weights: 19.90% against the top 5 percent (60 combos), 27.71% against the top 10 percent (130 combos), 31.41% against the top 20 percent (264 combos), 32.54% against the top 30 percent (386 combos) and 34.20% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 64o equity |
|---|---|---|
| Top 5 percent | 60 | 19.90% |
| Top 10 percent | 130 | 27.71% |
| Top 20 percent | 264 | 31.41% |
| Top 30 percent | 386 | 32.54% |
| Top 50 percent | 658 | 34.20% |
64o 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 64o, 127.00 of the 130 top-10-percent combos survive on average. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 64o
Two quick matchups show where 64o stands among its neighbours. 64o has 62.36% equity against 54o, the hand ranked number 153: it wins 49.43% of boards, ties 25.88% and loses 24.70%. It is the favorite in that matchup. 64o has 56.14% equity against 52s, the hand ranked number 155: it wins 49.88% of boards, ties 12.52% and loses 37.60%. It is the favorite in that matchup.
Next to 64o sits 64s, its suited twin: rank 138, 4 combos, 41.33% equity against a random hand. 64o has 3 times as many combos as 64s and is 3.32 points weaker against a random hand.
Questions about 64o combos
- How many combos of 64o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 64o about 1 time in 110.5.
- How many 64o combos are left if I hold a six?
- 9 combos of 64o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 64o stronger than 64s?
- No: 64o has 38.01% equity against a random hand and ranks number 154, while 64s has 41.33% and ranks number 138. 64s has 4 combos to 64o's 12.
How this was computed
The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.
Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.