A4s
56.94%
Wins 56.68%, ties 0.52%
Q9s
43.06%
Wins 42.80%, ties 0.52%
A4s against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 56.677 | 0.522 | 42.801 | 56.938 |
| Q9s | 42.801 | 0.522 | 56.677 | 43.062 |
Each side holds one of the suited hands: A4s and Q9s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A4s is ahead, but Q9s is far from dead: it takes 428 of every 1,000 deals outright. A split pot comes up on 0.52% of boards, so the wins and the equity differ by half of that.
Among the 169 starting hands, A4s is number 35 and Q9s is number 43 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 15,528,000 | 143,000 | 11,726,000 |
| Q9s | 11,726,000 | 143,000 | 15,528,000 |
The board total is exact, 16 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) |
|---|---|---|---|---|
| A4s | 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
A4s prefers paired flops, where it holds 62.10%, and likes monotone flops least, where it holds 54.55%. A4s stays ahead on all five textures.
| Flop | Share of flops | A4s wins | Ties | Q9s wins | A4s 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 | 52.833 | 3.436 | 43.731 | 54.551 |
| Paired | 17.091 | 61.774 | 0.645 | 37.581 | 62.096 |
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
Start from the random-hand figures, 59.03% for A4s and 57.66% for Q9s. This opponent changes them by -2.09 and -14.60 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 56.938 | 59.034 | -2.096 | 0.96450 |
| A4s, rainbow, ten or higher | 56.223 | 59.034 | -2.811 | 0.95238 |
| A4s, rainbow, nine or lower | 56.204 | 59.034 | -2.830 | 0.95206 |
| A4s, two-tone | 55.796 | 59.034 | -3.238 | 0.94515 |
| A4s, monotone | 54.551 | 59.034 | -4.483 | 0.92406 |
| A4s, paired | 62.096 | 59.034 | +3.062 | 1.05187 |
| Q9s, all flops | 43.062 | 57.664 | -14.602 | 0.74677 |
| 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 | 37.904 | 57.664 | -19.760 | 0.65733 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A4s has 58.79% equity, and with none in common it has 56.32%. A4s does better with a shared suit, by 2.47 points.
| Deals | Specific deals | Share of deals | A4s wins | Ties | Q9s wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 58.488 | 0.604 | 40.908 | 58.790 |
| No shared suit | 12 | 75.00 | 56.073 | 0.495 | 43.432 | 56.320 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 16 are A4s in one seat and Q9s in the other (0.0010%); with the seats swapped too, 32 (0.0020%).
A worked example
With $100 from each side, the $200 pot is split on average as $113.88 for A4s and $86.12 for Q9s; the first side gains $13.88 per all-in and the second gives up $13.88.
In 1,000 deals of exactly this matchup, expect about 567 won outright by A4s, about 428 won outright by Q9s and about 5 split.
The same matchup from the other side
Q9s versus A4s is this same page seen from the other hand: 43.06% for Q9s, 56.94% for A4s.
Keep exploring
As4s against Qh9h is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
We counted every case. Each suit pattern of the 16 specific A4s against Q9s 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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