A3s
58.57%
Wins 58.32%, ties 0.50%
QJo
41.43%
Wins 41.18%, ties 0.50%
A3s against QJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 58.317 | 0.495 | 41.188 | 58.565 |
| QJo | 41.188 | 0.495 | 58.317 | 41.435 |
The first hand is a suited hand; the second is an offsuit hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
The lead is steady rather than large, and the flop still has plenty of say in who wins. The tie share is 0.50%: on those boards the pot is chopped and neither hand wins outright.
By strength against a random hand, A3s holds place 38 of 169 and QJo holds place 39.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 47,931,000 | 407,000 | 33,853,000 |
| QJo | 33,853,000 | 407,000 | 47,931,000 |
The board total is exact, 48 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) |
|---|---|---|---|---|
| A3s | 1.413 | 1.715 | 2.428 | 0.708 |
| QJo | 0.708 | 2.428 | 1.715 | 1.413 |
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
Across the five flop textures A3s' equity moves by 25.00 points, from 50.79% on rainbow flops topped by a ten or better to 75.79% on low rainbow flops (nine high or lower). A3s 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 | A3s wins | Ties | QJo wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 50.732 | 0.119 | 49.149 | 50.792 |
| Rainbow, nine or lower | 7.042 | 75.220 | 1.144 | 23.636 | 75.792 |
| Two-tone | 46.667 | 58.025 | 0.323 | 41.652 | 58.186 |
| Monotone | 5.212 | 54.337 | 2.408 | 43.255 | 55.541 |
| Paired | 17.091 | 64.010 | 0.641 | 35.349 | 64.330 |
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
The table below sets each hand against its own random-hand baseline: a change of +0.35 points for A3s, from 58.22%, and -16.71 for QJo, from 58.14%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 58.565 | 58.220 | +0.345 | 1.00593 |
| A3s, rainbow, ten or higher | 50.792 | 58.220 | -7.428 | 0.87241 |
| A3s, rainbow, nine or lower | 75.792 | 58.220 | +17.572 | 1.30182 |
| A3s, two-tone | 58.186 | 58.220 | -0.034 | 0.99942 |
| A3s, monotone | 55.541 | 58.220 | -2.679 | 0.95398 |
| A3s, paired | 64.330 | 58.220 | +6.110 | 1.10495 |
| QJo, all flops | 41.435 | 58.135 | -16.700 | 0.71274 |
| QJo, rainbow, ten or higher | 49.208 | 58.135 | -8.927 | 0.84644 |
| QJo, rainbow, nine or lower | 24.208 | 58.135 | -33.927 | 0.41641 |
| QJo, two-tone | 41.814 | 58.135 | -16.321 | 0.71926 |
| QJo, monotone | 44.459 | 58.135 | -13.676 | 0.76475 |
| QJo, paired | 35.670 | 58.135 | -22.465 | 0.61357 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A3s has 58.22% equity, and with none in common it has 58.91%. A3s does better with no shared suit, by 0.69 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | QJo wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 57.947 | 0.537 | 41.516 | 58.216 |
| No shared suit | 24 | 50.00 | 58.687 | 0.453 | 40.860 | 58.913 |
How often this matchup comes up
The class pair covers 48 combinations of specific cards in a fixed seat order, 0.0030% of 1,624,350, and 96 (0.0059%) in either order.
A worked example
With $100 from each side, the $200 pot is split on average as $117.14 for A3s and $82.86 for QJo; the first side gains $17.14 per all-in and the second gives up $17.14.
Over a long run, 1,000 deals split into about 583 for A3s, 412 for QJo and 5 tied.
The same matchup from the other side
QJo against A3s adds nothing new: it is 41.43% for QJo and 58.57% for A3s, the same figures reversed.
Keep exploring
Open the calculator with As3s against QhJd 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
This is an exact count with no sampling. For the 48 ways to deal one A3s and one QJo without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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