64s: the 4 combos
There is one six-four pairing per suit, and a suited hand counts each suit once, so 64s is 4 combos.
The list below names all 4 holdings behind 64s. A hand range that says 64s means every one of them at once.
How cards you can see change the count
Start from 4 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 | 64s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 3 |
| Five | 4 |
| Four | 3 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: a six or a four leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of 64s for a board pair of each rank, ace down to two.
| Board pair | 64s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 2 |
| Fives | 4 |
| Fours | 2 |
| Threes | 4 |
| Twos | 4 |
A board pair of sixes or fours leaves 2 combos of 64s; a pair of any other rank leaves all 4.
A worked example
Try it with a six and a two in your hand. 1,225 two-card holdings are left, 3 of which are 64s. The chance is 0.24%, about 1 in 408, against 0.33% when none of your cards blocks it.
How strong is 64s?
By equity against a random hand, 64s is number 138 of 169, below the middle of the ranking. Its 41.33% 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 64s and the list holds 1,042 combos, 78.58% of the 1,326. The hands above it account for 1,038 of those.
64s against ranges of hands
Opponents rarely hold a random hand, so here is 64s against five top-percent ranges, each hand weighted by its live combos: 23.65% against the top 5 percent (60 combos), 31.36% against the top 10 percent (130 combos), 34.97% against the top 20 percent (264 combos), 36.08% against the top 30 percent (386 combos) and 37.71% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 64s equity |
|---|---|---|
| Top 5 percent | 60 | 23.65% |
| Top 10 percent | 130 | 31.36% |
| Top 20 percent | 264 | 34.97% |
| Top 30 percent | 386 | 36.08% |
| Top 50 percent | 658 | 37.71% |
64s 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 127.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of 64s. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 64s
Hands next to 64s in the ranking are not always close in a head-to-head. 64s has 42.15% equity against 85o, the hand ranked number 137: it wins 39.75% of boards, ties 4.80% and loses 55.45%. It is the underdog in that matchup. 64s has 45.00% equity against 83s, the hand ranked number 139: it wins 42.69% of boards, ties 4.63% and loses 52.68%. It is the underdog in that matchup.
64o holds the same two ranks as 64s but not the same suits, and it ranks number 154 at 38.01% equity. 64o is 3 times as many combos but 3.32 points weaker against a random hand.
Questions about 64s combos
- How many combos of 64s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 64s about 1 time in 331.5.
- How many 64s combos are left if I hold a six?
- 3 combos of 64s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 64s stronger than 64o?
- Yes, by 3.32 points: 64s has 41.33% equity against a random hand and ranks number 138, while 64o has 38.01% and ranks number 154. 64o has 12 combos to 64s's 4.
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.