AJo
59.26%
Wins 59.03%, ties 0.45%
Q9s
40.74%
Wins 40.52%, ties 0.45%
AJo against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJo | 59.034 | 0.451 | 40.515 | 59.259 |
| Q9s | 40.515 | 0.451 | 59.034 | 40.741 |
We compare an offsuit hand with a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 18.52 point lead is real, and Q9s still takes about 405 of every 1,000 deals outright. Split pots make up 0.45% of the boards, and both equity figures count them as half a win each.
For context, AJo sits at number 15 of 169 starting hands and Q9s at number 43 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJo | 48,520,000 | 371,000 | 33,300,000 |
| Q9s | 33,300,000 | 371,000 | 48,520,000 |
Exact total: 48 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 | 1.455 | 1.694 | 2.468 | 0.688 |
| Q9s | 0.688 | 2.468 | 1.694 | 1.455 |
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
If you know the kind of flop that came, the numbers shift: AJo holds 62.79% on paired flops and 56.13% on low rainbow flops (nine high or lower). AJo stays ahead on all five textures.
| Flop | Share of flops | AJo wins | Ties | Q9s wins | AJo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 61.634 | 0.117 | 38.249 | 61.693 |
| Rainbow, nine or lower | 7.042 | 55.667 | 0.931 | 43.402 | 56.133 |
| Two-tone | 46.667 | 57.350 | 0.276 | 42.374 | 57.488 |
| Monotone | 5.212 | 55.368 | 2.372 | 42.260 | 56.554 |
| Paired | 17.091 | 62.486 | 0.616 | 36.898 | 62.794 |
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
Start from the random-hand figures, 63.56% for AJo and 57.66% for Q9s. This opponent changes them by -4.30 and -16.92 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJo, all flops | 59.259 | 63.563 | -4.304 | 0.93229 |
| AJo, rainbow, ten or higher | 61.693 | 63.563 | -1.870 | 0.97058 |
| AJo, rainbow, nine or lower | 56.133 | 63.563 | -7.430 | 0.88311 |
| AJo, two-tone | 57.488 | 63.563 | -6.075 | 0.90443 |
| AJo, monotone | 56.554 | 63.563 | -7.009 | 0.88973 |
| AJo, paired | 62.794 | 63.563 | -0.769 | 0.98790 |
| Q9s, all flops | 40.741 | 57.664 | -16.923 | 0.70652 |
| Q9s, rainbow, ten or higher | 38.307 | 57.664 | -19.357 | 0.66431 |
| Q9s, rainbow, nine or lower | 43.867 | 57.664 | -13.797 | 0.76073 |
| Q9s, two-tone | 42.512 | 57.664 | -15.152 | 0.73724 |
| Q9s, monotone | 43.446 | 57.664 | -14.218 | 0.75343 |
| Q9s, paired | 37.206 | 57.664 | -20.458 | 0.64522 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, AJo has 59.80%; looking only at deals where they do not, 58.72%. AJo does better with a shared suit, by 1.08 points.
| Deals | Specific deals | Share of deals | AJo wins | Ties | Q9s wins | AJo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 59.555 | 0.492 | 39.953 | 59.801 |
| No shared suit | 24 | 50.00 | 58.513 | 0.410 | 41.077 | 58.718 |
How often this matchup comes up
AJo against Q9s is made up of 48 specific-card matchups in one seat order, 0.0030% of the 1,624,350 ordered deals, and 96 counting both seat orders, 0.0059%.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AJo averages $118.52 from the $200, up $18.52; Q9s averages $81.48, down $18.52.
Run 1,000 deals and the tally comes out near 590 for AJo, 405 for Q9s and 5 ties.
The same matchup from the other side
One page covers both views. From Q9s' side the equity is 40.74%, and from AJo's side it is 59.26%.
Keep exploring
Open the calculator with AsJh against Qd9d 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
This is an exact count with no sampling. For the 48 ways to deal one AJo and one Q9s 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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