AJo
72.74%
Wins 72.01%, ties 1.45%
QJo
27.26%
Wins 26.54%, ties 1.45%
AJo against QJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJo | 72.012 | 1.451 | 26.537 | 72.737 |
| QJo | 26.537 | 1.451 | 72.012 | 27.263 |
AJo and QJo are both offsuit hands. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
That is a clear edge, 72.74% to 27.26%, but QJo still wins often enough that one hand proves nothing. Split pots make up 1.45% of the boards, and both equity figures count them as half a win each.
In the ranking of all 169 starting hands, AJo is number 15 and QJo is number 39.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJo | 133,171,000 | 2,683,000 | 49,075,000 |
| QJo | 49,075,000 | 2,683,000 | 133,171,000 |
Exact total: 108 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AJo | 2.668 | 1.389 | 3.768 | 0.375 |
| QJo | 0.375 | 3.768 | 1.389 | 2.668 |
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
Low rainbow flops (nine high or lower) are the best for AJo (84.40%); monotone flops are the worst (67.36%). AJo 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 | AJo wins | Ties | QJo wins | AJo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.275 | 67.941 | 1.267 | 30.792 | 68.575 |
| Rainbow, nine or lower | 7.771 | 83.716 | 1.371 | 14.913 | 84.401 |
| Two-tone | 46.477 | 71.329 | 1.245 | 27.426 | 71.951 |
| Monotone | 5.144 | 66.239 | 2.243 | 31.518 | 67.361 |
| Paired | 17.333 | 75.774 | 2.051 | 22.175 | 76.800 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
A random hand would give AJo 63.56% and QJo 58.14%. Against each other the change is +9.18 points for AJo and -30.88 for QJo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJo, all flops | 72.737 | 63.563 | +9.174 | 1.14433 |
| AJo, rainbow, ten or higher | 68.575 | 63.563 | +5.012 | 1.07885 |
| AJo, rainbow, nine or lower | 84.401 | 63.563 | +20.838 | 1.32783 |
| AJo, two-tone | 71.951 | 63.563 | +8.388 | 1.13196 |
| AJo, monotone | 67.361 | 63.563 | +3.798 | 1.05975 |
| AJo, paired | 76.800 | 63.563 | +13.237 | 1.20825 |
| QJo, all flops | 27.263 | 58.135 | -30.872 | 0.46896 |
| QJo, rainbow, ten or higher | 31.425 | 58.135 | -26.710 | 0.54055 |
| QJo, rainbow, nine or lower | 15.599 | 58.135 | -42.536 | 0.26832 |
| QJo, two-tone | 28.049 | 58.135 | -30.086 | 0.48248 |
| QJo, monotone | 32.639 | 58.135 | -25.496 | 0.56143 |
| QJo, paired | 23.200 | 58.135 | -34.935 | 0.39907 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common AJo has 72.83% equity, and with none in common it has 72.40%. AJo does better with a shared suit, by 0.43 points.
| Deals | Specific deals | Share of deals | AJo wins | Ties | QJo wins | AJo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 72.096 | 1.474 | 26.430 | 72.833 |
| No shared suit | 24 | 22.22 | 71.716 | 1.369 | 26.915 | 72.400 |
How often this matchup comes up
Counting specific cards, AJo against QJo appears in 108 of the 1,624,350 ordered heads-up deals (0.0066%), and in 216 when the seats are swapped too (0.0133%).
A worked example
Take a $200 pot built from $100 each. AJo's equity of 72.74% is worth $145.48, a $45.48 edge, and QJo's 27.26% is worth $54.52, which is $45.48 under its stake.
Scaled to 1,000 deals, that is roughly 720 wins for AJo, 265 for QJo and 15 chopped pots.
The same matchup from the other side
Swap the hands and you get QJo with 27.26% against AJo with 72.74%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Open the calculator with AsJh against QdJc 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 108 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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