AQo
46.98%
Wins 46.70%, ties 0.54%
33
53.02%
Wins 52.76%, ties 0.54%
AQo against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 46.703 | 0.544 | 52.753 | 46.975 |
| 33 | 52.753 | 0.544 | 46.703 | 53.025 |
AQo and 33 are an offsuit hand and a pocket pair, in that order. 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.
33 leads by less than 7 points of equity, so the result of any one deal is close to a toss-up. The tie share is 0.54%: on those boards the pot is chopped and neither hand wins outright.
By strength against a random hand, AQo holds place 14 of 169 and 33 holds place 66.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 57,578,000 | 671,000 | 65,037,000 |
| 33 | 65,037,000 | 671,000 | 57,578,000 |
The board total is exact, 72 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AQo | 0.886 | 2.141 | 1.896 | 1.129 |
| 33 | 1.129 | 1.896 | 2.141 | 0.886 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
Split by what the flop looks like, 33 peaks at 79.37% on low rainbow flops (nine high or lower) and bottoms out at 46.79% on rainbow flops topped by a ten or better. AQo is ahead on rainbow flops topped by a ten or better, even though it trails 33 when every flop is counted.
| Flop | Share of flops | AQo wins | Ties | 33 wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 53.116 | 0.195 | 46.689 | 53.213 |
| Rainbow, nine or lower | 6.314 | 19.996 | 1.261 | 78.743 | 20.626 |
| Two-tone | 46.485 | 46.719 | 0.394 | 52.887 | 46.916 |
| Monotone | 5.151 | 48.589 | 2.270 | 49.141 | 49.724 |
| Paired | 17.333 | 46.687 | 0.669 | 52.644 | 47.022 |
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
Against one random hand instead, AQo holds 64.43% and 33 holds 53.69%. Facing each other changes that by -17.45 points for AQo and -0.67 points for 33.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 46.975 | 64.432 | -17.457 | 0.72906 |
| AQo, rainbow, ten or higher | 53.213 | 64.432 | -11.219 | 0.82588 |
| AQo, rainbow, nine or lower | 20.626 | 64.432 | -43.806 | 0.32012 |
| AQo, two-tone | 46.916 | 64.432 | -17.516 | 0.72815 |
| AQo, monotone | 49.724 | 64.432 | -14.708 | 0.77173 |
| AQo, paired | 47.022 | 64.432 | -17.410 | 0.72979 |
| 33, all flops | 53.025 | 53.693 | -0.668 | 0.98756 |
| 33, rainbow, ten or higher | 46.787 | 53.693 | -6.906 | 0.87138 |
| 33, rainbow, nine or lower | 79.374 | 53.693 | +25.681 | 1.47829 |
| 33, two-tone | 53.084 | 53.693 | -0.609 | 0.98866 |
| 33, monotone | 50.276 | 53.693 | -3.417 | 0.93636 |
| 33, paired | 52.978 | 53.693 | -0.715 | 0.98668 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, 33 has 52.94%; looking only at deals where they do not, 53.43%. 33 does better with no shared suit, by 0.49 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | 33 wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 46.778 | 0.555 | 52.667 | 47.056 |
| No shared suit | 12 | 16.67 | 46.330 | 0.489 | 53.181 | 46.574 |
How often this matchup comes up
The class pair covers 72 combinations of specific cards in a fixed seat order, 0.0044% of 1,624,350, and 144 (0.0089%) in either order.
A worked example
Take a $200 pot built from $100 each. 33's equity of 53.02% is worth $106.04, a $6.04 edge, and AQo's 46.98% is worth $93.96, which is $6.04 under its stake.
Out of 1,000 deals you should see around 528 outright wins for 33, 467 for AQo, and 5 split pots.
The same matchup from the other side
One page covers both views. From 33's side the equity is 53.02%, and from AQo's side it is 46.98%.
Keep exploring
Open the calculator with AsQh against 3d3c 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
We counted every case. Each suit pattern of the 72 specific AQo against 33 deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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