AQs
49.53%
Wins 49.24%, ties 0.57%
33
50.47%
Wins 50.19%, ties 0.57%
AQs against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 49.241 | 0.572 | 50.187 | 49.527 |
| 33 | 50.187 | 0.572 | 49.241 | 50.473 |
We compare a suited hand with a pocket pair. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.
With only 0.94 points between them, the board decides this matchup far more than the cards in hand. Of every 100 boards, about 0.57 are split pots, and the equity figures already include them.
Ranked by equity against a random hand, AQs is number 10 of the 169 starting hands and 33 is number 66.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 20,236,000 | 235,000 | 20,624,000 |
| 33 | 20,624,000 | 235,000 | 20,236,000 |
The total is exact: 24 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 | 0.981 | 2.031 | 1.993 | 1.019 |
| 33 | 1.019 | 1.993 | 2.031 | 0.981 |
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
Break the boards down by their first three cards and 33 is strongest on low rainbow flops (nine high or lower) (76.70%) and weakest on rainbow flops topped by a ten or better (45.34%). AQs is ahead on rainbow flops topped by a ten or better and two-tone flops, even though it trails 33 when every flop is counted.
| Flop | Share of flops | AQs wins | Ties | 33 wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 54.570 | 0.188 | 45.242 | 54.664 |
| Rainbow, nine or lower | 6.314 | 22.701 | 1.204 | 76.095 | 23.303 |
| Two-tone | 46.545 | 50.296 | 0.361 | 49.343 | 50.477 |
| Monotone | 5.212 | 48.018 | 3.191 | 48.791 | 49.613 |
| Paired | 17.334 | 48.880 | 0.669 | 50.451 | 49.214 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
How much does the opponent matter? Compared with its random-hand 66.21%, AQs changes by -16.68 points, and 33, from 53.69%, by -3.22.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 49.527 | 66.209 | -16.682 | 0.74804 |
| AQs, rainbow, ten or higher | 54.664 | 66.209 | -11.545 | 0.82563 |
| AQs, rainbow, nine or lower | 23.303 | 66.209 | -42.906 | 0.35196 |
| AQs, two-tone | 50.477 | 66.209 | -15.732 | 0.76239 |
| AQs, monotone | 49.613 | 66.209 | -16.596 | 0.74934 |
| AQs, paired | 49.214 | 66.209 | -16.995 | 0.74331 |
| 33, all flops | 50.473 | 53.693 | -3.220 | 0.94003 |
| 33, rainbow, ten or higher | 45.336 | 53.693 | -8.357 | 0.84436 |
| 33, rainbow, nine or lower | 76.697 | 53.693 | +23.004 | 1.42844 |
| 33, two-tone | 49.523 | 53.693 | -4.170 | 0.92234 |
| 33, monotone | 50.387 | 53.693 | -3.306 | 0.93843 |
| 33, paired | 50.786 | 53.693 | -2.907 | 0.94586 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and 33 holds 50.66%. In 12 they do not, and it holds 50.29%. 33 does better with a shared suit, by 0.37 points.
| Deals | Specific deals | Share of deals | AQs wins | Ties | 33 wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 49.042 | 0.603 | 50.355 | 49.343 |
| No shared suit | 12 | 50.00 | 49.440 | 0.542 | 50.018 | 49.711 |
How often this matchup comes up
Exactly 24 specific deals fit this matchup in one seat order, which is 0.0015% of 1,624,350; both orders together give 48, or 0.0030%.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says 33 gets $100.94 of it on average and AQs gets $99.06.
Out of 1,000 deals you should see around 502 outright wins for 33, 492 for AQs, and 6 split pots.
The same matchup from the other side
33 against AQs adds nothing new: it is 50.47% for 33 and 49.53% for AQs, the same figures reversed.
Keep exploring
Try AsQs against 3h3d 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 24 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.
Bring your own hands to a session
Review the spots you actually play against these numbers in a Game Assessment, and leave with a one-page written plan.
Book a session