A3s
56.94%
Wins 56.68%, ties 0.52%
Q9s
43.06%
Wins 42.80%, ties 0.52%
A3s against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 56.676 | 0.523 | 42.801 | 56.937 |
| Q9s | 42.801 | 0.523 | 56.676 | 43.063 |
A3s meets Q9s, and both are suited hands. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 13.88 point lead is real, and Q9s still takes about 428 of every 1,000 deals outright. About 0.52% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
The hand ranking puts A3s at 38 and Q9s at 43 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 15,527,000 | 143,000 | 11,726,000 |
| Q9s | 11,726,000 | 143,000 | 15,527,000 |
Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| A3s | 1.322 | 1.764 | 2.336 | 0.756 |
| Q9s | 0.756 | 2.336 | 1.764 | 1.322 |
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, A3s peaks at 62.09% on paired flops and bottoms out at 54.55% on monotone flops. A3s stays ahead on all five textures.
| Flop | Share of flops | A3s wins | Ties | Q9s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.543 | 56.142 | 0.162 | 43.696 | 56.223 |
| Rainbow, nine or lower | 6.366 | 55.747 | 0.914 | 43.339 | 56.204 |
| Two-tone | 46.727 | 55.653 | 0.285 | 44.062 | 55.796 |
| Monotone | 5.273 | 52.832 | 3.437 | 43.731 | 54.551 |
| Paired | 17.091 | 61.770 | 0.649 | 37.581 | 62.094 |
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
The table below sets each hand against its own random-hand baseline: a change of -1.28 points for A3s, from 58.22%, and -14.60 for Q9s, from 57.66%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 56.937 | 58.220 | -1.283 | 0.97796 |
| A3s, rainbow, ten or higher | 56.223 | 58.220 | -1.997 | 0.96570 |
| A3s, rainbow, nine or lower | 56.204 | 58.220 | -2.016 | 0.96537 |
| A3s, two-tone | 55.796 | 58.220 | -2.424 | 0.95836 |
| A3s, monotone | 54.551 | 58.220 | -3.669 | 0.93698 |
| A3s, paired | 62.094 | 58.220 | +3.874 | 1.06654 |
| Q9s, all flops | 43.063 | 57.664 | -14.601 | 0.74679 |
| Q9s, rainbow, ten or higher | 43.777 | 57.664 | -13.887 | 0.75917 |
| Q9s, rainbow, nine or lower | 43.796 | 57.664 | -13.868 | 0.75950 |
| Q9s, two-tone | 44.204 | 57.664 | -13.460 | 0.76658 |
| Q9s, monotone | 45.449 | 57.664 | -12.215 | 0.78817 |
| Q9s, paired | 37.906 | 57.664 | -19.758 | 0.65736 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A3s has 58.79% equity, and with none in common it has 56.32%. A3s does better with a shared suit, by 2.47 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | Q9s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.488 | 0.605 | 40.907 | 58.790 |
| No shared suit | 12 | 75.00 | 56.072 | 0.496 | 43.432 | 56.320 |
How often this matchup comes up
How often does it happen? 16 of the 1,624,350 ordered deals (0.0010%) are A3s against Q9s, and 32 (0.0020%) if either hand may sit in either seat.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. A3s averages $113.88 from the $200, up $13.88; Q9s averages $86.12, down $13.88.
Per 1,000 deals: A3s wins about 567, Q9s wins about 428, and about 5 end in a split pot.
The same matchup from the other side
The reversed view, Q9s against A3s, shows 43.06% for Q9s and 56.94% for A3s. It is the same count, so it redirects here.
Keep exploring
Try As3s 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 16 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.
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