AA
92.30%
Wins 91.66%, ties 1.29%
AJo
7.70%
Wins 7.05%, ties 1.29%
AA against AJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 91.657 | 1.287 | 7.056 | 92.301 |
| AJo | 7.056 | 1.287 | 91.657 | 7.699 |
The matchup pits a pocket pair against an offsuit hand. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.
AA is a big favorite here before anyone sees a flop. Split pots make up 1.29% of the boards, and both equity figures count them as half a win each.
Place 1 of 169 belongs to AA and place 15 belongs to AJo in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 56,500,000 | 793,000 | 4,350,000 |
| AJo | 4,350,000 | 793,000 | 56,500,000 |
The board total is exact, 36 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AA | 11.989 | 1.091 | 14.172 | 0.083 |
| AJo | 0.083 | 14.172 | 1.091 | 11.989 |
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
Split by what the flop looks like, AA peaks at 97.43% on low rainbow flops (nine high or lower) and bottoms out at 83.16% on monotone flops. AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | AJo wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.053 | 91.755 | 1.044 | 7.201 | 92.277 |
| Rainbow, nine or lower | 7.771 | 96.028 | 2.807 | 1.165 | 97.431 |
| Two-tone | 46.215 | 91.602 | 1.418 | 6.980 | 92.311 |
| Monotone | 5.130 | 82.180 | 1.965 | 15.855 | 83.162 |
| Paired | 17.831 | 92.494 | 0.407 | 7.099 | 92.698 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
The table below sets each hand against its own random-hand baseline: a change of +7.10 points for AA, from 85.20%, and -55.86 for AJo, from 63.56%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 92.301 | 85.204 | +7.097 | 1.08329 |
| AA, rainbow, ten or higher | 92.277 | 85.204 | +7.073 | 1.08301 |
| AA, rainbow, nine or lower | 97.431 | 85.204 | +12.227 | 1.14350 |
| AA, two-tone | 92.311 | 85.204 | +7.107 | 1.08341 |
| AA, monotone | 83.162 | 85.204 | -2.042 | 0.97603 |
| AA, paired | 92.698 | 85.204 | +7.494 | 1.08795 |
| AJo, all flops | 7.699 | 63.563 | -55.864 | 0.12112 |
| AJo, rainbow, ten or higher | 7.723 | 63.563 | -55.840 | 0.12150 |
| AJo, rainbow, nine or lower | 2.569 | 63.563 | -60.994 | 0.04042 |
| AJo, two-tone | 7.689 | 63.563 | -55.874 | 0.12097 |
| AJo, monotone | 16.838 | 63.563 | -46.725 | 0.26490 |
| AJo, paired | 7.302 | 63.563 | -56.261 | 0.11488 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common AA has 92.59% equity, and with none in common it has 91.72%. AA does better with a shared suit, by 0.87 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | AJo wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 91.933 | 1.319 | 6.748 | 92.593 |
| No shared suit | 12 | 33.33 | 91.103 | 1.225 | 7.672 | 91.716 |
How often this matchup comes up
You will meet this exact matchup 0.0044% of the time in a random heads-up deal: 72 of 1,624,350, counting either seat order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AA is worth $184.60 on average (+$84.60); AJo is worth $15.40 (-$84.60).
Over a long run, 1,000 deals split into about 917 for AA, 70 for AJo and 13 tied.
The same matchup from the other side
One page covers both views. From AJo's side the equity is 7.70%, and from AA's side it is 92.30%.
Keep exploring
The calculator link fills in AsAh against AdJc, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
Method: exact enumeration. The 36 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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