QJs
52.55%
Wins 51.96%, ties 1.17%
22
47.45%
Wins 46.87%, ties 1.17%
QJs against 22: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QJs | 51.963 | 1.171 | 46.866 | 52.548 |
| 22 | 46.866 | 1.171 | 51.963 | 47.452 |
One side is a suited hand, the other is a pocket pair. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.
That is a slim edge: neither hand is far ahead. 1.17% of boards are ties, so the equity of each hand is its win rate plus half of that.
QJs ranks number 28 of 169 starting hands, and 22 ranks number 87, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QJs | 21,354,000 | 481,000 | 19,260,000 |
| 22 | 19,260,000 | 481,000 | 21,354,000 |
The total is exact: 24 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 | 1.107 | 1.924 | 2.134 | 0.903 |
| 22 | 0.903 | 2.134 | 1.924 | 1.107 |
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
If you know the kind of flop that came, the numbers shift: QJs holds 58.00% on rainbow flops topped by a ten or better and 26.57% on low rainbow flops (nine high or lower). Low rainbow flops (nine high or lower) favor 22, the hand that is behind overall.
| Flop | Share of flops | QJs wins | Ties | 22 wins | QJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 57.739 | 0.522 | 41.739 | 58.000 |
| Rainbow, nine or lower | 6.314 | 25.944 | 1.253 | 72.803 | 26.571 |
| Two-tone | 46.545 | 53.178 | 0.629 | 46.193 | 53.492 |
| Monotone | 5.212 | 50.015 | 3.950 | 46.035 | 51.990 |
| Paired | 17.334 | 50.565 | 2.683 | 46.752 | 51.907 |
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
The table below sets each hand against its own random-hand baseline: a change of -7.71 points for QJs, from 60.26%, and -2.88 for 22, from 50.33%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QJs, all flops | 52.548 | 60.259 | -7.711 | 0.87204 |
| QJs, rainbow, ten or higher | 58.000 | 60.259 | -2.259 | 0.96251 |
| QJs, rainbow, nine or lower | 26.571 | 60.259 | -33.688 | 0.44095 |
| QJs, two-tone | 53.492 | 60.259 | -6.767 | 0.88770 |
| QJs, monotone | 51.990 | 60.259 | -8.269 | 0.86278 |
| QJs, paired | 51.907 | 60.259 | -8.352 | 0.86140 |
| 22, all flops | 47.452 | 50.334 | -2.882 | 0.94274 |
| 22, rainbow, ten or higher | 42.000 | 50.334 | -8.334 | 0.83443 |
| 22, rainbow, nine or lower | 73.429 | 50.334 | +23.095 | 1.45883 |
| 22, two-tone | 46.508 | 50.334 | -3.826 | 0.92399 |
| 22, monotone | 48.010 | 50.334 | -2.324 | 0.95383 |
| 22, paired | 48.093 | 50.334 | -2.241 | 0.95548 |
Does a shared suit matter?
When the hands share a suit, QJs holds 52.39%; when they do not, it holds 52.71%. QJs does better with no shared suit, by 0.32 points.
| Deals | Specific deals | Share of deals | QJs wins | Ties | 22 wins | QJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 51.792 | 1.192 | 47.016 | 52.388 |
| No shared suit | 12 | 50.00 | 52.133 | 1.151 | 46.716 | 52.709 |
How often this matchup comes up
Counting specific cards, QJs against 22 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
Try it with money: two players each put in $100 and the whole board runs out every possible way. QJs averages $105.10 from the $200, up $5.10; 22 averages $94.90, down $5.10.
Think in thousands: about 519 of 1,000 go to QJs, about 469 go to 22, and about 12 are chopped.
The same matchup from the other side
22 versus QJs is this same page seen from the other hand: 47.45% for 22, 52.55% for QJs.
Keep exploring
QsJs against 2h2d 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
This is an exact count with no sampling. For the 24 ways to deal one QJs and one 22 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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