QJs
51.36%
Wins 50.95%, ties 0.81%
44
48.64%
Wins 48.24%, ties 0.81%
QJs against 44: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QJs | 50.954 | 0.812 | 48.234 | 51.360 |
| 44 | 48.234 | 0.812 | 50.954 | 48.640 |
QJs and 44 are a suited hand and a pocket pair, in that order. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.
QJs leads by less than 3 points of equity, so the result of any one deal is close to a toss-up. Split pots make up 0.81% of the boards, and both equity figures count them as half a win each.
In the ranking of all 169 starting hands, QJs is number 28 and 44 is number 48.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QJs | 20,940,000 | 334,000 | 19,822,000 |
| 44 | 19,822,000 | 334,000 | 20,940,000 |
Exact total: 24 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 | 1.056 | 1.963 | 2.073 | 0.947 |
| 44 | 0.947 | 2.073 | 1.963 | 1.056 |
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
If you know the kind of flop that came, the numbers shift: QJs holds 57.51% on rainbow flops topped by a ten or better and 24.91% on low rainbow flops (nine high or lower). Watch for low rainbow flops (nine high or lower) and paired flops: on those flops 44 holds the better equity.
| Flop | Share of flops | QJs wins | Ties | 44 wins | QJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 57.325 | 0.372 | 42.303 | 57.511 |
| Rainbow, nine or lower | 6.314 | 24.450 | 0.914 | 74.636 | 24.907 |
| Two-tone | 46.545 | 52.573 | 0.455 | 46.972 | 52.801 |
| Monotone | 5.212 | 49.529 | 2.932 | 47.539 | 50.995 |
| Paired | 17.334 | 47.648 | 1.719 | 50.633 | 48.508 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
How much does the opponent matter? Compared with its random-hand 60.26%, QJs changes by -8.90 points, and 44, from 57.02%, by -8.38.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QJs, all flops | 51.360 | 60.259 | -8.899 | 0.85232 |
| QJs, rainbow, ten or higher | 57.511 | 60.259 | -2.748 | 0.95440 |
| QJs, rainbow, nine or lower | 24.907 | 60.259 | -35.352 | 0.41333 |
| QJs, two-tone | 52.801 | 60.259 | -7.458 | 0.87623 |
| QJs, monotone | 50.995 | 60.259 | -9.264 | 0.84626 |
| QJs, paired | 48.508 | 60.259 | -11.751 | 0.80499 |
| 44, all flops | 48.640 | 57.023 | -8.383 | 0.85299 |
| 44, rainbow, ten or higher | 42.489 | 57.023 | -14.534 | 0.74512 |
| 44, rainbow, nine or lower | 75.093 | 57.023 | +18.070 | 1.31689 |
| 44, two-tone | 47.199 | 57.023 | -9.824 | 0.82772 |
| 44, monotone | 49.005 | 57.023 | -8.018 | 0.85939 |
| 44, paired | 51.492 | 57.023 | -5.531 | 0.90300 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and QJs holds 51.20%. In 12 they do not, and it holds 51.52%. QJs does better with no shared suit, by 0.32 points.
| Deals | Specific deals | Share of deals | QJs wins | Ties | 44 wins | QJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 50.779 | 0.850 | 48.371 | 51.204 |
| No shared suit | 12 | 50.00 | 51.129 | 0.773 | 48.098 | 51.516 |
How often this matchup comes up
Counting specific cards, QJs against 44 appears in 24 of the 1,624,350 ordered heads-up deals (0.0015%), and in 48 when the seats are swapped too (0.0030%).
A worked example
Put $100 each into a $200 pot and deal every board once: QJs averages $102.72 back, ahead of its $100 by $2.72, while 44 averages $97.28, short of its $100 by $2.72.
Scaled to 1,000 deals, that is roughly 510 wins for QJs, 482 for 44 and 8 chopped pots.
The same matchup from the other side
44 against QJs adds nothing new: it is 48.64% for 44 and 51.36% for QJs, the same figures reversed.
Keep exploring
QsJs against 4h4d 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 24 specific QJs against 44 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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