A6s combos

A6s: the 4 combos

Fix the suit, and the ace and six of that suit are the only choice; four suits make 4 combos.

These are the 4 specific hands that count as A6s. Each tile is one two-card holding, and no two tiles are the same hand.

• A♠6♠
• A♥6♥
• A♦6♦
• A♣6♣

How cards you can see change the count

This is the blocker table for A6s. One visible card of a given rank removes the combos that need it, and the rest stay possible.

With an ace or a six in view, 3 of the 4 combos of A6s 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 A6s combos left for each paired rank.

Only a board pair of aces or sixes matters here: 2 combos of A6s remain, against 4 for any other pair.

A worked example

Suppose you look down at an ace and a two. Any opponent hand comes from 1,225 possibilities. A6s makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with A6s, it would be 4 of them, 0.33%.

How strong is A6s?

Order all 169 classes by equity against a random hand and A6s lands at number 31, inside the top 60 classes, with 59.91%. A tie is worth half a win in that figure.

Down to and including A6s, the ranking holds 200 combos, or 15.08% of deals; 196 of them belong to hands above it.

A6s against ranges of hands

Five ranges, five equities for A6s. Counting only the combos your cards leave possible, it has 30.55% against the top 5 percent (60 combos), 32.99% against the top 10 percent (130 combos), 42.86% against the top 20 percent (264 combos), 47.93% against the top 30 percent (386 combos) and 54.18% against the top 50 percent (658 combos).

The line sits between the top 30 and top 50 percent: A6s is behind the narrower range and ahead of the wider one.

Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, A6s leaves an average of 107.00. That is 23.00 combos fewer than the 130 an opponent has before you look.

Hands next to A6s

Look at A6s against the hands that rank next to it. A6s has 56.74% equity against A5s, the hand ranked number 30: it wins 40.80% of boards, ties 31.88% and loses 27.32%. It is the favorite in that matchup. A6s has 37.22% equity against A8o, the hand ranked number 32: it wins 27.43% of boards, ties 19.60% and loses 52.98%. It is the underdog in that matchup.

A6o is what the same two ranks look like when they are offsuit: 12 combos at number 42, 57.68% equity. A6o is 3 times as many combos but 2.22 points weaker against a random hand.

Questions about A6s combos

How many combos of A6s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt A6s about 1 time in 331.5.

How many A6s combos are left if I hold an ace?

3 combos of A6s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.

Is A6s stronger than A6o?

Yes, by 2.22 points: A6s has 59.91% equity against a random hand and ranks number 31, while A6o has 57.68% and ranks number 42. A6o has 12 combos to A6s's 4.

How this was computed

Combos are counted by listing all 1,326 two-card hands in a 52-card deck and sorting each into its class. The known-card rows remove every combo that uses a card of that rank; the board-pair rows remove those that use either of two such cards.

Rank and equity read our table of all 169 by 169 preflop matchups, each counted over every one of the 1,712,304 boards. Ties count as half a win, and a range is weighted by its live combos.

Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.