73o: the 12 combos
Pair each of the 4 sevens with each of the 4 threes to get 16, then remove the 4 suited pairings. 73o is the other 12.
All 12 ways to hold 73o 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 73o 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 | 73o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 9 |
| Two | 12 |
Only two ranks change the count: a seven or a three 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 73o, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | 73o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 6 |
| Twos | 12 |
A board pair of sevens or threes leaves 6 combos of 73o; a pair of any other rank leaves all 12.
A worked example
Worked example: your cards are a seven and a two, so 1,225 two-card hands remain for your opponent. Of those, 9 are 73o, a 0.73% chance (about 1 in 136). With two cards that do not touch 73o, it would be 12 combos and 0.98%.
How strong is 73o?
73o holds rank 160 among the 169 classes, among the 30 weakest classes. Against a random hand it has 36.60% equity: wins in full, ties as half, every board counted.
1,214 combos rank above 73o, and with its own 12 the running total is 1,226, 92.46% of the 1,326 hands.
73o against ranges of hands
Take the strongest hands in rank order and ask how 73o does against them. The answers, with live combos as weights: 17.04% against the top 5 percent (60 combos), 25.65% against the top 10 percent (130 combos), 28.73% against the top 20 percent (264 combos), 30.15% against the top 30 percent (386 combos) and 31.68% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 73o equity |
|---|---|---|
| Top 5 percent | 60 | 17.04% |
| Top 10 percent | 130 | 25.65% |
| Top 20 percent | 264 | 28.73% |
| Top 30 percent | 386 | 30.15% |
| Top 50 percent | 658 | 31.68% |
73o 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 73o, 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 73o
Two quick matchups show where 73o stands among its neighbours. 73o has 42.95% equity against 82o, the hand ranked number 159: it wins 40.36% of boards, ties 5.18% and loses 54.46%. It is the underdog in that matchup. 73o has 64.43% equity against 53o, the hand ranked number 161: it wins 55.13% of boards, ties 18.58% and loses 26.28%. It is the favorite in that matchup.
Next to 73o sits 73s, its suited twin: rank 143, 4 combos, 40.04% equity against a random hand. 73o has 3 times as many combos as 73s and is 3.43 points weaker against a random hand.
Questions about 73o combos
- How many combos of 73o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 73o about 1 time in 110.5.
- How many 73o combos are left if I hold a seven?
- 9 combos of 73o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 73o stronger than 73s?
- No: 73o has 36.60% equity against a random hand and ranks number 160, while 73s has 40.04% and ranks number 143. 73s has 4 combos to 73o'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.