AQs
71.54%
Wins 70.79%, ties 1.50%
Q9s
28.46%
Wins 27.71%, ties 1.50%
AQs against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 70.788 | 1.495 | 27.717 | 71.536 |
| Q9s | 27.717 | 1.495 | 70.788 | 28.464 |
Both hands are suited hands: AQs and Q9s. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
A lead of 43.08 points is large but not decisive: Q9s still takes about 277 of every 1,000 deals. About 1.50% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
The hand ranking puts AQs at 10 and Q9s at 43 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 14,545,000 | 307,000 | 5,695,000 |
| Q9s | 5,695,000 | 307,000 | 14,545,000 |
The total is exact: 12 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) |
|---|---|---|---|---|
| AQs | 2.513 | 1.413 | 3.608 | 0.398 |
| Q9s | 0.398 | 3.608 | 1.413 | 2.513 |
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. AQs does best on rainbow flops topped by a ten or better, at 76.53%, and worst on low rainbow flops (nine high or lower), at 60.98%. AQs 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 | AQs wins | Ties | Q9s wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 75.857 | 1.347 | 22.796 | 76.530 |
| Rainbow, nine or lower | 7.042 | 60.429 | 1.105 | 38.466 | 60.982 |
| Two-tone | 46.543 | 69.545 | 1.133 | 29.322 | 70.112 |
| Monotone | 5.215 | 62.484 | 3.737 | 33.779 | 64.353 |
| Paired | 17.333 | 73.854 | 2.156 | 23.990 | 74.932 |
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 66.21%, AQs changes by +5.33 points, and Q9s, from 57.66%, by -29.20.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 71.536 | 66.209 | +5.327 | 1.08046 |
| AQs, rainbow, ten or higher | 76.530 | 66.209 | +10.321 | 1.15589 |
| AQs, rainbow, nine or lower | 60.982 | 66.209 | -5.227 | 0.92105 |
| AQs, two-tone | 70.112 | 66.209 | +3.903 | 1.05895 |
| AQs, monotone | 64.353 | 66.209 | -1.856 | 0.97197 |
| AQs, paired | 74.932 | 66.209 | +8.723 | 1.13175 |
| Q9s, all flops | 28.464 | 57.664 | -29.200 | 0.49362 |
| Q9s, rainbow, ten or higher | 23.470 | 57.664 | -34.194 | 0.40701 |
| Q9s, rainbow, nine or lower | 39.018 | 57.664 | -18.646 | 0.67664 |
| Q9s, two-tone | 29.888 | 57.664 | -27.776 | 0.51831 |
| Q9s, monotone | 35.647 | 57.664 | -22.017 | 0.61818 |
| Q9s, paired | 25.068 | 57.664 | -32.596 | 0.43473 |
Does a shared suit matter?
The hands cannot hold a suit in common here, which leaves a single case and a single number: 71.54% for AQs.
| Deals | Specific deals | Share of deals | AQs wins | Ties | Q9s wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 70.788 | 1.495 | 27.717 | 71.536 |
How often this matchup comes up
AQs against Q9s is made up of 12 specific-card matchups in one seat order, 0.0007% of the 1,624,350 ordered deals, and 24 counting both seat orders, 0.0015%.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AQs takes back $143.08 of it, which is $43.08 more than it put in, and Q9s takes back $56.92, $43.08 less than it put in.
Over a long run, 1,000 deals split into about 708 for AQs, 277 for Q9s and 15 tied.
The same matchup from the other side
Q9s versus AQs is this same page seen from the other hand: 28.46% for Q9s, 71.54% for AQs.
Keep exploring
Try AsQs against Qh9h 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 12 specific deals of AQs against Q9s, 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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