63s: the 4 combos
Fix the suit, and the six and three of that suit are the only choice; four suits make 4 combos.
These are the 4 specific hands that count as 63s. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for 63s. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | 63s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 3 |
| Five | 4 |
| Four | 4 |
| Three | 3 |
| Two | 4 |
With a six or a three in view, 3 of the 4 combos of 63s remain, which removes 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the 63s combos left for each paired rank.
| Board pair | 63s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 2 |
| Fives | 4 |
| Fours | 4 |
| Threes | 2 |
| Twos | 4 |
Only a board pair of sixes or threes matters here: 2 combos of 63s remain, against 4 for any other pair.
A worked example
Suppose you look down at a six and a two. Any opponent hand comes from 1,225 possibilities. 63s makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with 63s, it would be 4 of them, 0.33%.
How strong is 63s?
Order all 169 classes by equity against a random hand and 63s lands at number 147, among the 30 weakest classes, with 39.53%. A tie is worth half a win in that figure.
Down to and including 63s, the ranking holds 1,110 combos, or 83.71% of deals; 1,106 of them belong to hands above it.
63s against ranges of hands
Five ranges, five equities for 63s. Counting only the combos your cards leave possible, it has 22.29% against the top 5 percent (60 combos), 30.03% against the top 10 percent (130 combos), 33.61% against the top 20 percent (264 combos), 34.59% against the top 30 percent (386 combos) and 36.08% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 63s equity |
|---|---|---|
| Top 5 percent | 60 | 22.29% |
| Top 10 percent | 130 | 30.03% |
| Top 20 percent | 264 | 33.61% |
| Top 30 percent | 386 | 34.59% |
| Top 50 percent | 658 | 36.08% |
63s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, 63s leaves an average of 127.00. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 63s
Look at 63s against the hands that rank next to it. 63s has 60.72% equity against 53s, the hand ranked number 146: it wins 49.26% of boards, ties 22.92% and loses 27.82%. It is the favorite in that matchup. 63s has 42.13% equity against 84o, the hand ranked number 148: it wins 39.72% of boards, ties 4.82% and loses 55.45%. It is the underdog in that matchup.
63o is what the same two ranks look like when they are offsuit: 12 combos at number 162, 36.08% equity. 63o is 3 times as many combos but 3.46 points weaker against a random hand.
Questions about 63s combos
- How many combos of 63s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 63s about 1 time in 331.5.
- How many 63s combos are left if I hold a six?
- 3 combos of 63s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 63s stronger than 63o?
- Yes, by 3.46 points: 63s has 39.53% equity against a random hand and ranks number 147, while 63o has 36.08% and ranks number 162. 63o has 12 combos to 63s's 4.
How this was computed
Every 63s combo was listed from the 1,326 two-card holdings. For each blocker or board-pair row, the combos that contain a visible card were dropped and the rest were counted.
The rank and equity figures use our matchup table, which counts all 1,712,304 boards for each pair of classes. Ties are halves, and range matchups are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.