QJs
44.15%
Wins 43.88%, ties 0.54%
A3s
55.85%
Wins 55.58%, ties 0.54%
QJs against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QJs | 43.884 | 0.536 | 55.580 | 44.152 |
| A3s | 55.580 | 0.536 | 43.884 | 55.848 |
Two suited hands meet here: QJs against A3s. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
A 11.70 point lead is real, and QJs still takes about 439 of every 1,000 deals outright. Of every 100 boards, about 0.54 are split pots, and the equity figures already include them.
QJs ranks number 28 of 169 starting hands, and A3s ranks number 38, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QJs | 12,023,000 | 147,000 | 15,227,000 |
| A3s | 15,227,000 | 147,000 | 12,023,000 |
The total is exact: 16 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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) |
|---|---|---|---|---|
| QJs | 0.791 | 2.279 | 1.799 | 1.265 |
| A3s | 1.265 | 1.799 | 2.279 | 0.791 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
The flop changes the picture. A3s does best on low rainbow flops (nine high or lower), at 73.36%, and worst on rainbow flops topped by a ten or better, at 49.53%. QJs is ahead on rainbow flops topped by a ten or better, even though it trails A3s when every flop is counted.
| Flop | Share of flops | QJs wins | Ties | A3s wins | QJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 50.419 | 0.113 | 49.468 | 50.475 |
| Rainbow, nine or lower | 7.042 | 26.086 | 1.099 | 72.815 | 26.636 |
| Two-tone | 46.727 | 45.217 | 0.300 | 54.483 | 45.367 |
| Monotone | 5.273 | 44.696 | 3.443 | 51.861 | 46.418 |
| Paired | 17.091 | 38.195 | 0.641 | 61.164 | 38.516 |
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
Relative to a random opponent, QJs changes by -16.11 points (baseline 60.26%) and A3s by -2.37 points (baseline 58.22%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QJs, all flops | 44.152 | 60.259 | -16.107 | 0.73270 |
| QJs, rainbow, ten or higher | 50.475 | 60.259 | -9.784 | 0.83763 |
| QJs, rainbow, nine or lower | 26.636 | 60.259 | -33.623 | 0.44203 |
| QJs, two-tone | 45.367 | 60.259 | -14.892 | 0.75287 |
| QJs, monotone | 46.418 | 60.259 | -13.841 | 0.77031 |
| QJs, paired | 38.516 | 60.259 | -21.743 | 0.63917 |
| A3s, all flops | 55.848 | 58.220 | -2.372 | 0.95926 |
| A3s, rainbow, ten or higher | 49.525 | 58.220 | -8.695 | 0.85065 |
| A3s, rainbow, nine or lower | 73.364 | 58.220 | +15.144 | 1.26012 |
| A3s, two-tone | 54.633 | 58.220 | -3.587 | 0.93839 |
| A3s, monotone | 53.582 | 58.220 | -4.638 | 0.92034 |
| A3s, paired | 61.484 | 58.220 | +3.264 | 1.05606 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, A3s has 57.60%; looking only at deals where they do not, 55.27%. A3s does better with a shared suit, by 2.33 points.
| Deals | Specific deals | Share of deals | QJs wins | Ties | A3s wins | QJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 42.091 | 0.618 | 57.291 | 42.400 |
| No shared suit | 12 | 75.00 | 44.481 | 0.508 | 55.011 | 44.735 |
How often this matchup comes up
QJs against A3s is made up of 16 specific-card matchups in one seat order, 0.0010% of the 1,624,350 ordered deals, and 32 counting both seat orders, 0.0020%.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, A3s' average share is $111.70 (a gain of $11.70) and QJs' is $88.30 (a loss of $11.70).
Per 1,000 deals: A3s wins about 556, QJs wins about 439, and about 5 end in a split pot.
The same matchup from the other side
Read it from the other side: A3s against QJs is the same matchup with the numbers swapped, so A3s holds 55.85% and QJs holds 44.15%. That address sends you back to this page.
Keep exploring
QsJs against Ah3h 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
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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