A9s
56.46%
Wins 56.21%, ties 0.50%
QJs
43.54%
Wins 43.29%, ties 0.50%
A9s against QJs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9s | 56.210 | 0.496 | 43.294 | 56.458 |
| QJs | 43.294 | 0.496 | 56.210 | 43.542 |
Both hands are suited hands: A9s and QJs. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Split pots make up 0.50% of the boards, and both equity figures count them as half a win each.
Ranked by equity against a random hand, A9s is number 18 of the 169 starting hands and QJs is number 28.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9s | 15,400,000 | 136,000 | 11,861,000 |
| QJs | 11,861,000 | 136,000 | 15,400,000 |
The total is exact: 16 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) |
|---|---|---|---|---|
| A9s | 1.297 | 1.779 | 2.310 | 0.771 |
| QJs | 0.771 | 2.310 | 1.779 | 1.297 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
If you know the kind of flop that came, the numbers shift: A9s holds 73.24% on low rainbow flops (nine high or lower) and 50.50% on rainbow flops topped by a ten or better. A9s 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 | A9s wins | Ties | QJs wins | A9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 50.444 | 0.113 | 49.443 | 50.501 |
| Rainbow, nine or lower | 7.042 | 72.791 | 0.899 | 26.310 | 73.241 |
| Two-tone | 46.727 | 55.082 | 0.258 | 44.660 | 55.211 |
| Monotone | 5.273 | 52.179 | 3.408 | 44.413 | 53.883 |
| Paired | 17.091 | 61.757 | 0.616 | 37.627 | 62.065 |
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 62.78%, A9s changes by -6.32 points, and QJs, from 60.26%, by -16.72.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9s, all flops | 56.458 | 62.781 | -6.323 | 0.89928 |
| A9s, rainbow, ten or higher | 50.501 | 62.781 | -12.280 | 0.80440 |
| A9s, rainbow, nine or lower | 73.241 | 62.781 | +10.460 | 1.16661 |
| A9s, two-tone | 55.211 | 62.781 | -7.570 | 0.87942 |
| A9s, monotone | 53.883 | 62.781 | -8.898 | 0.85827 |
| A9s, paired | 62.065 | 62.781 | -0.716 | 0.98860 |
| QJs, all flops | 43.542 | 60.259 | -16.717 | 0.72258 |
| QJs, rainbow, ten or higher | 49.499 | 60.259 | -10.760 | 0.82144 |
| QJs, rainbow, nine or lower | 26.759 | 60.259 | -33.500 | 0.44407 |
| QJs, two-tone | 44.789 | 60.259 | -15.470 | 0.74327 |
| QJs, monotone | 46.117 | 60.259 | -14.142 | 0.76531 |
| QJs, paired | 37.935 | 60.259 | -22.324 | 0.62953 |
Does a shared suit matter?
Of the deals of this matchup, 4 share a suit (A9s at 58.33%) and 12 do not (55.83%). A9s does better with a shared suit, by 2.50 points.
| Deals | Specific deals | Share of deals | A9s wins | Ties | QJs wins | A9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.042 | 0.573 | 41.385 | 58.329 |
| No shared suit | 12 | 75.00 | 55.599 | 0.470 | 43.931 | 55.834 |
How often this matchup comes up
How often does it happen? 16 of the 1,624,350 ordered deals (0.0010%) are A9s against QJs, and 32 (0.0020%) if either hand may sit in either seat.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says A9s gets $112.92 of it on average and QJs gets $87.08.
A thousand deals look like this: A9s takes 562, QJs takes 433, 5 are ties.
The same matchup from the other side
The reversed view, QJs against A9s, shows 43.54% for QJs and 56.46% for A9s. It is the same count, so it redirects here.
Keep exploring
The calculator link fills in As9s against QhJh, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of A9s against QJs, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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