AJs
73.92%
Wins 73.21%, ties 1.43%
QJo
26.08%
Wins 25.36%, ties 1.43%
AJs against QJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJs | 73.209 | 1.426 | 25.365 | 73.922 |
| QJo | 25.365 | 1.426 | 73.209 | 26.078 |
We compare a suited hand with an offsuit hand. 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.
AJs is well ahead, and QJo needs a specific kind of board to catch up. About 1.43% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
Ranked by equity against a random hand, AJs is number 11 of the 169 starting hands and QJo is number 39.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJs | 45,128,000 | 879,000 | 15,636,000 |
| QJo | 15,636,000 | 879,000 | 45,128,000 |
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) |
|---|---|---|---|---|
| AJs | 2.835 | 1.366 | 3.942 | 0.353 |
| QJo | 0.353 | 3.942 | 1.366 | 2.835 |
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
The flop changes the picture. AJs does best on low rainbow flops (nine high or lower), at 85.00%, and worst on monotone flops, at 66.34%. AJs 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 | AJs wins | Ties | QJo wins | AJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.177 | 68.918 | 1.233 | 29.849 | 69.535 |
| Rainbow, nine or lower | 7.771 | 84.347 | 1.311 | 14.342 | 85.002 |
| Two-tone | 46.527 | 73.110 | 1.158 | 25.732 | 73.689 |
| Monotone | 5.192 | 64.937 | 2.802 | 32.261 | 66.338 |
| Paired | 17.333 | 76.697 | 2.042 | 21.261 | 77.718 |
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
How much does the opponent matter? Compared with its random-hand 65.39%, AJs changes by +8.53 points, and QJo, from 58.14%, by -32.06.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJs, all flops | 73.922 | 65.393 | +8.529 | 1.13043 |
| AJs, rainbow, ten or higher | 69.535 | 65.393 | +4.142 | 1.06334 |
| AJs, rainbow, nine or lower | 85.002 | 65.393 | +19.609 | 1.29986 |
| AJs, two-tone | 73.689 | 65.393 | +8.296 | 1.12686 |
| AJs, monotone | 66.338 | 65.393 | +0.945 | 1.01445 |
| AJs, paired | 77.718 | 65.393 | +12.325 | 1.18848 |
| QJo, all flops | 26.078 | 58.135 | -32.057 | 0.44858 |
| QJo, rainbow, ten or higher | 30.465 | 58.135 | -27.670 | 0.52404 |
| QJo, rainbow, nine or lower | 14.998 | 58.135 | -43.137 | 0.25799 |
| QJo, two-tone | 26.311 | 58.135 | -31.824 | 0.45258 |
| QJo, monotone | 33.662 | 58.135 | -24.473 | 0.57903 |
| QJo, paired | 22.282 | 58.135 | -35.853 | 0.38328 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and AJs holds 73.67%. In 24 they do not, and it holds 74.05%. AJs does better with no shared suit, by 0.38 points.
| Deals | Specific deals | Share of deals | AJs wins | Ties | QJo wins | AJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 72.921 | 1.507 | 25.572 | 73.674 |
| No shared suit | 24 | 66.67 | 73.354 | 1.385 | 25.261 | 74.046 |
How often this matchup comes up
AJs against QJo is made up of 36 specific-card matchups in one seat order, 0.0022% of the 1,624,350 ordered deals, and 72 counting both seat orders, 0.0044%.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AJs gets $147.84 of it on average and QJo gets $52.16.
Run 1,000 deals and the tally comes out near 732 for AJs, 254 for QJo and 14 ties.
The same matchup from the other side
QJo versus AJs is this same page seen from the other hand: 26.08% for QJo, 73.92% for AJs.
Keep exploring
Try AsJs against QhJd 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
We counted every case. Each suit pattern of the 36 specific AJs against QJo deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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