AA
93.78%
Wins 93.09%, ties 1.39%
A9o
6.22%
Wins 5.52%, ties 1.39%
AA against A9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 93.088 | 1.388 | 5.524 | 93.782 |
| A9o | 5.524 | 1.388 | 93.088 | 6.218 |
The matchup pits a pocket pair against an offsuit hand. The non-pair hand shares a rank with the pair, so two of its outs for pairing are blocked by the pair itself.
This is one of the lopsided matchups: A9o wins only 5.52% of the boards outright. The tie share is 1.39%: on those boards the pot is chopped and neither hand wins outright.
Among the 169 starting hands, AA is number 1 and A9o is number 25 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 57,382,000 | 856,000 | 3,405,000 |
| A9o | 3,405,000 | 856,000 | 57,382,000 |
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.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AA | 15.082 | 1.074 | 18.103 | 0.066 |
| A9o | 0.066 | 18.103 | 1.074 | 15.082 |
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
Rainbow flops topped by a ten or better are the best for AA (95.85%); monotone flops are the worst (84.28%). AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | A9o wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.782 | 95.216 | 1.271 | 3.513 | 95.851 |
| Rainbow, nine or lower | 7.042 | 91.852 | 2.747 | 5.401 | 93.225 |
| Two-tone | 46.215 | 93.149 | 1.531 | 5.320 | 93.915 |
| Monotone | 5.130 | 83.261 | 2.036 | 14.703 | 84.279 |
| Paired | 17.831 | 93.405 | 0.452 | 6.143 | 93.631 |
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
The table below sets each hand against its own random-hand baseline: a change of +8.58 points for AA, from 85.20%, and -54.55 for A9o, from 60.77%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 93.782 | 85.204 | +8.578 | 1.10068 |
| AA, rainbow, ten or higher | 95.851 | 85.204 | +10.647 | 1.12496 |
| AA, rainbow, nine or lower | 93.225 | 85.204 | +8.021 | 1.09414 |
| AA, two-tone | 93.915 | 85.204 | +8.711 | 1.10224 |
| AA, monotone | 84.279 | 85.204 | -0.925 | 0.98914 |
| AA, paired | 93.631 | 85.204 | +8.427 | 1.09890 |
| A9o, all flops | 6.218 | 60.773 | -54.555 | 0.10232 |
| A9o, rainbow, ten or higher | 4.149 | 60.773 | -56.624 | 0.06827 |
| A9o, rainbow, nine or lower | 6.775 | 60.773 | -53.998 | 0.11148 |
| A9o, two-tone | 6.085 | 60.773 | -54.688 | 0.10013 |
| A9o, monotone | 15.721 | 60.773 | -45.052 | 0.25868 |
| A9o, paired | 6.369 | 60.773 | -54.404 | 0.10480 |
Does a shared suit matter?
Of the deals of this matchup, 24 share a suit (AA at 94.08%) and 12 do not (93.18%). AA does better with a shared suit, by 0.90 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | A9o wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 93.371 | 1.420 | 5.209 | 94.081 |
| No shared suit | 12 | 33.33 | 92.522 | 1.325 | 6.153 | 93.184 |
How often this matchup comes up
Counting specific cards, AA against A9o appears in 36 of the 1,624,350 ordered heads-up deals (0.0022%), and in 72 when the seats are swapped too (0.0044%).
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AA takes back $187.56 of it, which is $87.56 more than it put in, and A9o takes back $12.44, $87.56 less than it put in.
Think in thousands: about 931 of 1,000 go to AA, about 55 go to A9o, and about 14 are chopped.
The same matchup from the other side
A9o versus AA is this same page seen from the other hand: 6.22% for A9o, 93.78% for AA.
Keep exploring
Try AsAh 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 36 specific deals of AA 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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