ATo vs A3s: preflop equity

ATo against A3s: the numbers

ATo is an offsuit hand and A3s is a suited hand. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.

ATo is the clear favorite, though A3s gets there on roughly one board in 3. Split pots make up 10.38% of the boards, and both equity figures count them as half a win each.

The hand ranking puts ATo at 19 and A3s at 38 out of 169 starting hands.

The total is exact: 36 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.

The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.

Who is ahead on which flops

Across the five flop textures ATo's equity moves by 18.00 points, from 55.68% on low rainbow flops (nine high or lower) to 73.68% on rainbow flops topped by a ten or better. ATo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.

Compared with a random hand

Each hand has a baseline against a random hand: 62.72% for ATo, 58.22% for A3s. Here the change is +3.92 and -24.86 points.

Does a shared suit matter?

Two kinds of deal exist here. In 12 of them the hands share a suit and ATo holds 67.45%. In 24 they do not, and it holds 66.24%. ATo does better with a shared suit, by 1.21 points.

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 36 are ATo in one seat and A3s in the other (0.0022%); with the seats swapped too, 72 (0.0044%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, ATo's average share is $133.28 (a gain of $33.28) and A3s' is $66.72 (a loss of $33.28).

In 1,000 deals of exactly this matchup, expect about 614 won outright by ATo, about 282 won outright by A3s and about 104 split.

The same matchup from the other side

A3s versus ATo is this same page seen from the other hand: 33.36% for A3s, 66.64% for ATo.

Keep exploring

AsTh against Ad3d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.

• Open AsTh against Ad3d in the equity calculator
• ATo combos
• A3s combos
• ATo vs QJo
• ATo vs K9o
• KJs vs A3s
• All hand matchups