71.90%
Wins 71.71%, ties 0.38%
A9o
28.10%
Wins 27.91%, ties 0.38%
QQ against A9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 71.709 | 0.376 | 27.915 | 71.897 | |
| A9o | 27.915 | 0.376 | 71.709 | 28.103 |
We compare a pocket pair with an offsuit hand. The pair is ahead of one card and behind the other, so the board decides how that plays out.
That is a clear edge, 71.90% to 28.10%, but A9o still wins often enough that one hand proves nothing. Ties are 0.38% of the outcomes here; each tied board gives both hands half the pot.
In the ranking of all 169 starting hands, QQ is number 3 and A9o is number 25.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 88,407,000 | 464,000 | 34,415,000 | |
| A9o | 34,415,000 | 464,000 | 88,407,000 |
The board total is exact, 72 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) |
|---|---|---|---|---|
| 2.558 | 1.395 | 3.582 | 0.391 | |
| A9o | 0.391 | 3.582 | 1.395 | 2.558 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Break the boards down by their first three cards and QQ is strongest on low rainbow flops (nine high or lower) (80.45%) and weakest on monotone flops (67.20%). QQ stays ahead on all five textures.
| Flop | Share of flops | QQ wins | Ties | A9o wins | QQ equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 69.214 | 0.154 | 30.632 | 69.291 |
| Rainbow, nine or lower | 7.042 | 79.917 | 1.067 | 19.016 | 80.451 |
| Two-tone | 46.485 | 71.136 | 0.347 | 28.517 | 71.309 |
| Monotone | 5.151 | 66.334 | 1.724 | 31.942 | 67.196 |
| Paired | 17.334 | 74.960 | 0.083 | 24.957 | 75.002 |
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 79.93%, QQ changes by -8.03 points, and A9o, from 60.77%, by -32.67.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QQ, all flops | 71.897 | 79.925 | -8.028 | 0.89956 |
| QQ, rainbow, ten or higher | 69.291 | 79.925 | -10.634 | 0.86695 |
| QQ, rainbow, nine or lower | 80.451 | 79.925 | +0.526 | 1.00658 |
| QQ, two-tone | 71.309 | 79.925 | -8.616 | 0.89220 |
| QQ, monotone | 67.196 | 79.925 | -12.729 | 0.84074 |
| QQ, paired | 75.002 | 79.925 | -4.923 | 0.93840 |
| A9o, all flops | 28.103 | 60.773 | -32.670 | 0.46243 |
| A9o, rainbow, ten or higher | 30.709 | 60.773 | -30.064 | 0.50531 |
| A9o, rainbow, nine or lower | 19.549 | 60.773 | -41.224 | 0.32167 |
| A9o, two-tone | 28.691 | 60.773 | -32.082 | 0.47210 |
| A9o, monotone | 32.804 | 60.773 | -27.969 | 0.53978 |
| A9o, paired | 24.998 | 60.773 | -35.775 | 0.41133 |
Does a shared suit matter?
Two kinds of deal exist here. In 60 of them the hands share a suit and QQ holds 71.93%. In 12 they do not, and it holds 71.71%. The two rows differ by only 0.22 points, so suits barely change this matchup.
| Deals | Specific deals | Share of deals | QQ wins | Ties | A9o wins | QQ equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 71.738 | 0.392 | 27.870 | 71.934 |
| No shared suit | 12 | 16.67 | 71.562 | 0.296 | 28.142 | 71.710 |
How often this matchup comes up
Exactly 72 specific deals fit this matchup in one seat order, which is 0.0044% of 1,624,350; both orders together give 144, or 0.0089%.
A worked example
With $100 from each side, the $200 pot is split on average as $143.80 for QQ and $56.20 for A9o; the first side gains $43.80 per all-in and the second gives up $43.80.
Think in thousands: about 717 of 1,000 go to QQ, about 279 go to A9o, and about 4 are chopped.
The same matchup from the other side
A9o against QQ adds nothing new: it is 28.10% for A9o and 71.90% for QQ, the same figures reversed.
Keep exploring
QsQh against Ad9c 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.
How this was computed
This is an exact count with no sampling. For the 72 ways to deal one QQ and one A9o without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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