73s: the 4 combos
There is one seven-three pairing per suit, and a suited hand counts each suit once, so 73s is 4 combos.
The list below names all 4 holdings behind 73s. A hand range that says 73s 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 | 73s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 3 |
| Two | 4 |
Only two ranks change the count: a seven or a three 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 73s for a board pair of each rank, ace down to two.
| Board pair | 73s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 2 |
| Twos | 4 |
A board pair of sevens or threes leaves 2 combos of 73s; a pair of any other rank leaves all 4.
A worked example
Try it with a seven and a two in your hand. 1,225 two-card holdings are left, 3 of which are 73s. The chance is 0.24%, about 1 in 408, against 0.33% when none of your cards blocks it.
How strong is 73s?
By equity against a random hand, 73s is number 143 of 169, among the 30 weakest classes. Its 40.04% 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 73s and the list holds 1,078 combos, 81.30% of the 1,326. The hands above it account for 1,074 of those.
73s against ranges of hands
Opponents rarely hold a random hand, so here is 73s against five top-percent ranges, each hand weighted by its live combos: 21.00% against the top 5 percent (60 combos), 29.44% against the top 10 percent (130 combos), 32.47% against the top 20 percent (264 combos), 33.85% against the top 30 percent (386 combos) and 35.35% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 73s equity |
|---|---|---|
| Top 5 percent | 60 | 21.00% |
| Top 10 percent | 130 | 29.44% |
| Top 20 percent | 264 | 32.47% |
| Top 30 percent | 386 | 33.85% |
| Top 50 percent | 658 | 35.35% |
73s 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 73s. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 73s
Hands next to 73s in the ranking are not always close in a head-to-head. 73s has 43.38% equity against 82s, the hand ranked number 142: it wins 41.05% of boards, ties 4.66% and loses 54.30%. It is the underdog in that matchup. 73s has 33.55% equity against 93o, the hand ranked number 144: it wins 28.86% of boards, ties 9.38% and loses 61.76%. It is the underdog in that matchup.
73o holds the same two ranks as 73s but not the same suits, and it ranks number 160 at 36.60% equity. 73o is 3 times as many combos but 3.43 points weaker against a random hand.
Questions about 73s combos
- How many combos of 73s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 73s about 1 time in 331.5.
- How many 73s combos are left if I hold a seven?
- 3 combos of 73s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 73s stronger than 73o?
- Yes, by 3.43 points: 73s has 40.04% equity against a random hand and ranks number 143, while 73o has 36.60% and ranks number 160. 73o has 12 combos to 73s'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.