AQo vs A9o: preflop equity

In equity, AQo against A9o stands at 73.68% to 26.32%, a gap of 47.36 points.

AQo

73.68%

Wins 70.76%, ties 5.85%

A9o

26.32%

Wins 23.39%, ties 5.85%

Equity counts a tie as half a win. Exact over every board.

AQo against A9o: the numbers

Exact preflop results for AQo against A9o, in percent
HandWinsTiesLosesEquity
AQo70.7575.84923.39473.682
A9o23.3945.84970.75726.318

Each side holds one of the offsuit hands: AQo and A9o. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.

AQo is well ahead, and A9o needs a specific kind of board to catch up. Split pots make up 5.85% of the boards, and both equity figures count them as half a win each.

In the ranking of all 169 starting hands, AQo is number 14 and A9o is number 25.

Boards behind the percentages: 184,928,832 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AQo130,850,00010,816,00043,262,000
A9o43,262,00010,816,000130,850,000

108 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

AQo against A9o read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AQo2.8001.4134.2750.357
A9o0.3574.2751.4132.800

In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.

Who is ahead on which flops

AQo prefers rainbow flops topped by a ten or better, where it holds 78.87%, and likes low rainbow flops (nine high or lower) least, where it holds 60.35%. AQo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AQo against A9o by flop texture, in percent
FlopShare of flopsAQo winsTiesA9o winsAQo equity
Rainbow, ten or higher24.00377.0783.59019.33278.873
Rainbow, nine or lower7.04258.0474.60437.34960.349
Two-tone46.47772.0953.75524.15073.973
Monotone5.14466.3094.58729.10468.602
Paired17.33464.90115.47419.62572.638

Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.

Compared with a random hand

How much does the opponent matter? Compared with its random-hand 64.43%, AQo changes by +9.25 points, and A9o, from 60.77%, by -34.45.

AQo and A9o here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AQo, all flops73.68264.432+9.2501.14356
AQo, rainbow, ten or higher78.87364.432+14.4411.22413
AQo, rainbow, nine or lower60.34964.432-4.0830.93663
AQo, two-tone73.97364.432+9.5411.14808
AQo, monotone68.60264.432+4.1701.06472
AQo, paired72.63864.432+8.2061.12736
A9o, all flops26.31860.773-34.4550.43305
A9o, rainbow, ten or higher21.12760.773-39.6460.34764
A9o, rainbow, nine or lower39.65160.773-21.1220.65244
A9o, two-tone26.02760.773-34.7460.42827
A9o, monotone31.39860.773-29.3750.51664
A9o, paired27.36260.773-33.4110.45023

Does a shared suit matter?

Split by suits, the deals give AQo 73.79% when the hands overlap in a suit and 73.31% when they do not. AQo does better with a shared suit, by 0.48 points.

AQo against A9o by suit overlap, in percent
DealsSpecific dealsShare of dealsAQo winsTiesA9o winsAQo equity
Share a suit8477.7870.8495.87623.27573.787
No shared suit2422.2270.4365.75423.81073.313

How often this matchup comes up

AQo against A9o is made up of 108 specific-card matchups in one seat order, 0.0066% of the 1,624,350 ordered deals, and 216 counting both seat orders, 0.0133%.

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, AQo's average share is $147.36 (a gain of $47.36) and A9o's is $52.64 (a loss of $47.36).

In 1,000 deals of exactly this matchup, expect about 708 won outright by AQo, about 234 won outright by A9o and about 58 split.

The same matchup from the other side

One page covers both views. From A9o's side the equity is 26.32%, and from AQo's side it is 73.68%.

Try AsQh against Ad9c in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.

How this was computed

All 1,712,304 five-card boards are dealt for every suit pattern among the 108 specific deals of AQo against A9o, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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