QJs
44.07%
Wins 43.81%, ties 0.52%
A4s
55.93%
Wins 55.67%, ties 0.52%
QJs against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QJs | 43.807 | 0.524 | 55.669 | 44.069 |
| A4s | 55.669 | 0.524 | 43.807 | 55.931 |
Both hands are suited hands: QJs and A4s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A4s is ahead, but QJs is far from dead: it takes 438 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.
QJs ranks number 28 of 169 starting hands, and A4s ranks number 35, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QJs | 12,002,000 | 144,000 | 15,252,000 |
| A4s | 15,252,000 | 144,000 | 12,002,000 |
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) |
|---|---|---|---|---|
| QJs | 0.788 | 2.283 | 1.796 | 1.269 |
| A4s | 1.269 | 1.796 | 2.283 | 0.788 |
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
The flop changes the picture. A4s does best on low rainbow flops (nine high or lower), at 73.58%, and worst on rainbow flops topped by a ten or better, at 49.60%. Rainbow flops topped by a ten or better favor QJs, the hand that is behind overall.
| Flop | Share of flops | QJs wins | Ties | A4s wins | QJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 50.341 | 0.113 | 49.546 | 50.397 |
| Rainbow, nine or lower | 7.042 | 25.904 | 1.030 | 73.066 | 26.419 |
| Two-tone | 46.727 | 45.128 | 0.288 | 54.584 | 45.272 |
| Monotone | 5.273 | 44.629 | 3.438 | 51.933 | 46.348 |
| Paired | 17.091 | 38.195 | 0.637 | 61.168 | 38.514 |
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
How much does the opponent matter? Compared with its random-hand 60.26%, QJs changes by -16.19 points, and A4s, from 59.03%, by -3.10.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QJs, all flops | 44.069 | 60.259 | -16.190 | 0.73133 |
| QJs, rainbow, ten or higher | 50.397 | 60.259 | -9.862 | 0.83634 |
| QJs, rainbow, nine or lower | 26.419 | 60.259 | -33.840 | 0.43842 |
| QJs, two-tone | 45.272 | 60.259 | -14.987 | 0.75129 |
| QJs, monotone | 46.348 | 60.259 | -13.911 | 0.76915 |
| QJs, paired | 38.514 | 60.259 | -21.745 | 0.63914 |
| A4s, all flops | 55.931 | 59.034 | -3.103 | 0.94744 |
| A4s, rainbow, ten or higher | 49.603 | 59.034 | -9.431 | 0.84024 |
| A4s, rainbow, nine or lower | 73.581 | 59.034 | +14.547 | 1.24642 |
| A4s, two-tone | 54.728 | 59.034 | -4.306 | 0.92706 |
| A4s, monotone | 53.652 | 59.034 | -5.382 | 0.90883 |
| A4s, paired | 61.486 | 59.034 | +2.452 | 1.04154 |
Does a shared suit matter?
Of the deals of this matchup, 4 share a suit (A4s at 57.69%) and 12 do not (55.34%). A4s does better with a shared suit, by 2.35 points.
| Deals | Specific deals | Share of deals | QJs wins | Ties | A4s wins | QJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 42.006 | 0.606 | 57.388 | 42.309 |
| No shared suit | 12 | 75.00 | 44.407 | 0.497 | 55.096 | 44.656 |
How often this matchup comes up
Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, A4s' average share is $111.86 (a gain of $11.86) and QJs' is $88.14 (a loss of $11.86).
Run 1,000 deals and the tally comes out near 557 for A4s, 438 for QJs and 5 ties.
The same matchup from the other side
If you came looking for A4s against QJs, the numbers are the same with the hands swapped: 55.93% and 44.07%.
Keep exploring
Open the calculator with QsJs against Ah4h 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 16 ways to deal one QJs and one A4s 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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