ATs combos

ATs: the 4 combos

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

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

• A♠10♠
• A♥10♥
• A♦10♦
• A♣10♣

How cards you can see change the count

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

An ace or a ten 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 ATs that are still possible after a board pair of each rank.

Pairing aces or tens on the board cuts ATs 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, ATs 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 ATs?

The ranking puts ATs at number 13 out of 169, inside the top 30 classes. Its equity against a random hand is 64.60%, with a tie counted as half a win.

A range that runs from the top of the ranking down to ATs is 76 combos, 5.73% of all two-card hands, and 72 of them rank above ATs itself.

ATs against ranges of hands

Here is how ATs fares against five ranges that run from the top of the ranking down. It scores 36.22% against the top 5 percent (60 combos), 39.55% against the top 10 percent (130 combos), 53.50% against the top 20 percent (264 combos), 58.00% against the top 30 percent (386 combos) and 61.41% against the top 50 percent (658 combos).

The line sits between the top 10 and top 20 percent: ATs 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 ATs in your hand, an average of 104.00 are left. That is 26.00 combos fewer than the 130 an opponent has before you look.

Hands next to ATs

Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. ATs has 30.46% equity against AKo, the hand ranked number 12: it wins 28.25% of boards, ties 4.43% and loses 67.32%. It is the underdog in that matchup. ATs has 30.63% equity against AQo, the hand ranked number 14: it wins 27.87% of boards, ties 5.52% and loses 66.61%. It is the underdog in that matchup.

ATo is 3 times as many combos but 1.88 points weaker against a random hand, and ATo is the offsuit twin, number 19 of 169 with 62.72% equity.

Questions about ATs combos

How many combos of ATs are there?

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

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

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

Is ATs stronger than ATo?

Yes, by 1.88 points: ATs has 64.60% equity against a random hand and ranks number 13, while ATo has 62.72% and ranks number 19. ATo has 12 combos to ATs's 4.

How this was computed

All 1,326 two-card holdings were grouped into classes, and the ATs 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.