68.03%
Wins 67.82%, ties 0.42%
AJs
31.97%
Wins 31.76%, ties 0.42%
QQ against AJs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 67.818 | 0.415 | 31.767 | 68.025 | |
| AJs | 31.767 | 0.415 | 67.818 | 31.975 |
QQ, a pocket pair, plays AJs, a suited hand. The pair is ahead of one card and behind the other, so the board decides how that plays out.
QQ is the clear favorite, though AJs gets there on roughly one board in 3. About 0.42% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
The hand ranking puts QQ at 3 and AJs at 11 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 27,870,000 | 171,000 | 13,055,000 | |
| AJs | 13,055,000 | 171,000 | 27,870,000 |
The board total is exact, 24 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) |
|---|---|---|---|---|
| 2.127 | 1.475 | 3.148 | 0.470 | |
| AJs | 0.470 | 3.148 | 1.475 | 2.127 |
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
The flop changes the picture. QQ does best on low rainbow flops (nine high or lower), at 81.56%, and worst on monotone flops, at 63.28%. QQ stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | QQ wins | Ties | AJs wins | QQ equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.138 | 65.310 | 0.103 | 34.587 | 65.362 |
| Rainbow, nine or lower | 7.771 | 80.968 | 1.187 | 17.845 | 81.561 |
| Two-tone | 46.545 | 65.979 | 0.341 | 33.680 | 66.150 |
| Monotone | 5.212 | 62.074 | 2.414 | 35.512 | 63.281 |
| Paired | 17.334 | 71.933 | 0.083 | 27.984 | 71.975 |
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
How much does the opponent matter? Compared with its random-hand 79.93%, QQ changes by -11.90 points, and AJs, from 65.39%, by -33.42.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QQ, all flops | 68.025 | 79.925 | -11.900 | 0.85111 |
| QQ, rainbow, ten or higher | 65.362 | 79.925 | -14.563 | 0.81779 |
| QQ, rainbow, nine or lower | 81.561 | 79.925 | +1.636 | 1.02047 |
| QQ, two-tone | 66.150 | 79.925 | -13.775 | 0.82765 |
| QQ, monotone | 63.281 | 79.925 | -16.644 | 0.79175 |
| QQ, paired | 71.975 | 79.925 | -7.950 | 0.90053 |
| AJs, all flops | 31.975 | 65.393 | -33.418 | 0.48897 |
| AJs, rainbow, ten or higher | 34.638 | 65.393 | -30.755 | 0.52969 |
| AJs, rainbow, nine or lower | 18.439 | 65.393 | -46.954 | 0.28197 |
| AJs, two-tone | 33.850 | 65.393 | -31.543 | 0.51764 |
| AJs, monotone | 36.719 | 65.393 | -28.674 | 0.56151 |
| AJs, paired | 28.025 | 65.393 | -37.368 | 0.42856 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and QQ holds 68.29%. In 12 they do not, and it holds 67.76%. QQ does better with a shared suit, by 0.53 points.
| Deals | Specific deals | Share of deals | QQ wins | Ties | AJs wins | QQ equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 68.063 | 0.455 | 31.482 | 68.290 |
| No shared suit | 12 | 50.00 | 67.573 | 0.374 | 32.053 | 67.760 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 24 are QQ in one seat and AJs in the other (0.0015%); with the seats swapped too, 48 (0.0030%).
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average QQ takes back $136.06 of it, which is $36.06 more than it put in, and AJs takes back $63.94, $36.06 less than it put in.
Over a long run, 1,000 deals split into about 678 for QQ, 318 for AJs and 4 tied.
The same matchup from the other side
The mirror image, AJs against QQ, is 31.97% to 68.03%, and its address redirects to this page.
Keep exploring
Open the calculator with QsQh against AdJd already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
Each figure is a complete count over boards. Take the 24 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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