A4s combos

A4s: the 4 combos

For A4s, the ace and the four must share a suit. With 4 suits and one way to pair them in each, the count is 4.

The 4 holdings of A4s are listed below, higher card first. Nothing is left out and nothing appears twice.

• A♠4♠
• A♥4♥
• A♦4♦
• A♣4♣

How cards you can see change the count

Combos shrink when cards are visible. The rows below give the A4s count left after one known card of each rank, from the ace down to the two.

An ace or a four 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

Now put two cards of the same rank on the board. This table counts the combos of A4s that are still possible after a board pair of each rank.

Pairing aces or fours on the board cuts A4s to 2 combos. Every other paired board leaves the full 4.

A worked example

Walk through it once. Your hole cards: an ace and a two. Your opponent's possible hands: 1,225. Of those, A4s is 3, so the chance is 3 / 1,225 = 0.24%. With no blocking card it would be 4 / 1,225 = 0.33%.

How strong is A4s?

The ranking puts A4s at number 35 out of 169, inside the top 60 classes. Its equity against a random hand is 59.03%, with a tie counted as half a win.

A range that runs from the top of the ranking down to A4s is 232 combos, 17.50% of all two-card hands, and 228 of them rank above A4s itself.

A4s against ranges of hands

Here is how A4s fares against five ranges that run from the top of the ranking down. It scores 31.69% against the top 5 percent (60 combos), 33.97% against the top 10 percent (130 combos), 42.75% against the top 20 percent (264 combos), 46.69% against the top 30 percent (386 combos) and 53.07% against the top 50 percent (658 combos).

The line sits between the top 30 and top 50 percent: A4s is behind the narrower range and ahead of the wider one.

The top 10 percent is 130 combos before you look at your cards. With A4s in your hand, an average of 110.00 are left. That is 20.00 combos fewer than the 130 an opponent has before you look.

Hands next to A4s

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. A4s has 55.63% equity against QTs, the hand ranked number 34: it wins 55.37% of boards, ties 0.52% and loses 44.11%. It is the favorite in that matchup. A4s has 41.64% equity against A7o, the hand ranked number 36: it wins 28.28% of boards, ties 26.71% and loses 45.01%. It is the underdog in that matchup.

A4o is 3 times as many combos but 2.30 points weaker against a random hand, and A4o is the offsuit twin, number 49 of 169 with 56.73% equity.

Questions about A4s combos

How many combos of A4s are there?

4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt A4s about 1 time in 331.5.

How many A4s combos are left if I hold an ace?

3 combos of A4s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.

Is A4s stronger than A4o?

Yes, by 2.30 points: A4s has 59.03% equity against a random hand and ranks number 35, while A4o has 56.73% and ranks number 49. A4o has 12 combos to A4s's 4.

How this was computed

Every A4s 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.