AQo
68.40%
Wins 65.53%, ties 5.72%
A4s
31.60%
Wins 28.75%, ties 5.72%
AQo against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 65.533 | 5.723 | 28.744 | 68.395 |
| A4s | 28.744 | 5.723 | 65.533 | 31.605 |
We compare an offsuit hand with a suited hand. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
AQo is the clear favorite, though A4s gets there on roughly one board in 3. Of every 100 boards, about 5.72 are split pots, and the equity figures already include them.
AQo ranks number 14 of 169 starting hands, and A4s ranks number 35, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 40,396,000 | 3,528,000 | 17,719,000 |
| A4s | 17,719,000 | 3,528,000 | 40,396,000 |
36 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| AQo | 2.164 | 1.526 | 3.479 | 0.462 |
| A4s | 0.462 | 3.479 | 1.526 | 2.164 |
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
Split by what the flop looks like, AQo peaks at 75.88% on rainbow flops topped by a ten or better and bottoms out at 53.93% on low rainbow flops (nine high or lower). AQo 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 | AQo wins | Ties | A4s wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 74.088 | 3.590 | 22.322 | 75.883 |
| Rainbow, nine or lower | 7.042 | 51.752 | 4.355 | 43.893 | 53.930 |
| Two-tone | 46.527 | 65.437 | 3.577 | 30.986 | 67.225 |
| Monotone | 5.192 | 61.085 | 4.805 | 34.110 | 63.487 |
| Paired | 17.334 | 60.924 | 15.257 | 23.819 | 68.553 |
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
Compared with a random opponent, this matchup shifts AQo from 64.43% by +3.97 points and A4s from 59.03% by -27.43 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 68.395 | 64.432 | +3.963 | 1.06151 |
| AQo, rainbow, ten or higher | 75.883 | 64.432 | +11.451 | 1.17772 |
| AQo, rainbow, nine or lower | 53.930 | 64.432 | -10.502 | 0.83701 |
| AQo, two-tone | 67.225 | 64.432 | +2.793 | 1.04335 |
| AQo, monotone | 63.487 | 64.432 | -0.945 | 0.98533 |
| AQo, paired | 68.553 | 64.432 | +4.121 | 1.06396 |
| A4s, all flops | 31.605 | 59.034 | -27.429 | 0.53537 |
| A4s, rainbow, ten or higher | 24.117 | 59.034 | -34.917 | 0.40853 |
| A4s, rainbow, nine or lower | 46.070 | 59.034 | -12.964 | 0.78040 |
| A4s, two-tone | 32.775 | 59.034 | -26.259 | 0.55519 |
| A4s, monotone | 36.513 | 59.034 | -22.521 | 0.61851 |
| A4s, paired | 31.447 | 59.034 | -27.587 | 0.53269 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and AQo holds 69.21%. In 24 they do not, and it holds 67.99%. AQo does better with a shared suit, by 1.22 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | A4s wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 66.301 | 5.815 | 27.884 | 69.209 |
| No shared suit | 24 | 66.67 | 65.149 | 5.677 | 29.174 | 67.988 |
How often this matchup comes up
The class pair covers 36 combinations of specific cards in a fixed seat order, 0.0022% of 1,624,350, and 72 (0.0044%) in either order.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AQo takes back $136.80 of it, which is $36.80 more than it put in, and A4s takes back $63.20, $36.80 less than it put in.
Scaled to 1,000 deals, that is roughly 655 wins for AQo, 288 for A4s and 57 chopped pots.
The same matchup from the other side
A4s versus AQo is this same page seen from the other hand: 31.60% for A4s, 68.40% for AQo.
Keep exploring
The calculator link fills in AsQh against Ad4d, 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
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 36 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
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