83s: the 4 combos
For 83s, the eight and the three must share a suit. With 4 suits and one way to pair them in each, the count is 4.
Every 83s you can be dealt is one of these 4 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For 83s, the table lists the combos left after one card of each rank is out of play.
| Known card | 83s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 3 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 3 |
| Two | 4 |
An eight or a three you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The 83s combos that survive are in the table, one row per rank.
| Board pair | 83s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 2 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 2 |
| Twos | 4 |
Pairing eights or threes on the board cuts 83s to 2 combos. Every other paired board leaves the full 4.
A worked example
Take a hand of an eight and a two. Your opponent then holds one of 1,225 possible hands, and 3 of them are 83s. That is 0.24%, or 1 in 408, instead of the 0.33% (1 in 306) you get when your cards do not block it.
How strong is 83s?
Rank 139 of 169 belongs to 83s, below the middle of the ranking, on 40.87% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add 83s to every hand ranked above it and you hold 1,046 of the 1,326 two-card hands, 78.88% of all deals.
83s against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For 83s the five ranges give 21.34% against the top 5 percent (60 combos), 29.04% against the top 10 percent (130 combos), 31.87% against the top 20 percent (264 combos), 32.94% against the top 30 percent (386 combos) and 34.58% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 83s equity |
|---|---|---|
| Top 5 percent | 60 | 21.34% |
| Top 10 percent | 130 | 29.04% |
| Top 20 percent | 264 | 31.87% |
| Top 30 percent | 386 | 32.94% |
| Top 50 percent | 658 | 34.58% |
83s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding 83s removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 127.00 remain. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 83s
A one-place difference in rank can be a large or small gap in a direct matchup. 83s has 55.00% equity against 64s, the hand ranked number 138: it wins 52.68% of boards, ties 4.63% and loses 42.69%. It is the favorite in that matchup. 83s has 40.30% equity against 94o, the hand ranked number 140: it wins 38.76% of boards, ties 3.08% and loses 58.16%. It is the underdog in that matchup.
Same ranks, other suits: 83o is the offsuit version, number 157 of 169 at 37.48%. 83o is 3 times as many combos but 3.39 points weaker against a random hand.
Questions about 83s combos
- How many combos of 83s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 83s about 1 time in 331.5.
- How many 83s combos are left if I hold an eight?
- 3 combos of 83s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 83s stronger than 83o?
- Yes, by 3.39 points: 83s has 40.87% equity against a random hand and ranks number 139, while 83o has 37.48% and ranks number 157. 83o has 12 combos to 83s's 4.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the 83s group was counted. The blocker rows drop each combo containing a visible card; the board-pair rows do it for a visible pair.
Exact matchups, counted over all 1,712,304 boards, supply the rank and equity. A tie counts as half, and ranges are weighted by the combos that remain.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.