QJo
50.23%
Wins 49.64%, ties 1.17%
22
49.77%
Wins 49.19%, ties 1.17%
QJo against 22: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QJo | 49.644 | 1.168 | 49.188 | 50.228 |
| 22 | 49.188 | 1.168 | 49.644 | 49.772 |
QJo and 22 are an offsuit 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.
That is a slim edge: neither hand is far ahead. The tie share is 1.17%: on those boards the pot is chopped and neither hand wins outright.
By strength against a random hand, QJo holds place 39 of 169 and 22 holds place 87.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QJo | 61,204,000 | 1,440,000 | 60,642,000 |
| 22 | 60,642,000 | 1,440,000 | 61,204,000 |
The board total is exact, 72 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) |
|---|---|---|---|---|
| QJo | 1.009 | 2.014 | 2.033 | 0.991 |
| 22 | 0.991 | 2.033 | 2.014 | 1.009 |
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
Break the boards down by their first three cards and QJo is strongest on rainbow flops topped by a ten or better (56.68%) and weakest on low rainbow flops (nine high or lower) (24.01%). Low rainbow flops (nine high or lower) and paired flops favor 22, the hand that is behind overall.
| Flop | Share of flops | QJo wins | Ties | 22 wins | QJo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 56.407 | 0.538 | 43.055 | 56.676 |
| Rainbow, nine or lower | 6.314 | 23.350 | 1.314 | 75.336 | 24.007 |
| Two-tone | 46.485 | 49.904 | 0.678 | 49.418 | 50.243 |
| Monotone | 5.151 | 50.925 | 2.917 | 46.158 | 52.384 |
| Paired | 17.333 | 48.500 | 2.809 | 48.691 | 49.904 |
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
Each hand has a baseline against a random hand: 58.14% for QJo, 50.33% for 22. Here the change is -7.91 and -0.56 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QJo, all flops | 50.228 | 58.135 | -7.907 | 0.86399 |
| QJo, rainbow, ten or higher | 56.676 | 58.135 | -1.459 | 0.97490 |
| QJo, rainbow, nine or lower | 24.007 | 58.135 | -34.128 | 0.41295 |
| QJo, two-tone | 50.243 | 58.135 | -7.892 | 0.86425 |
| QJo, monotone | 52.384 | 58.135 | -5.751 | 0.90108 |
| QJo, paired | 49.904 | 58.135 | -8.231 | 0.85842 |
| 22, all flops | 49.772 | 50.334 | -0.562 | 0.98883 |
| 22, rainbow, ten or higher | 43.324 | 50.334 | -7.010 | 0.86073 |
| 22, rainbow, nine or lower | 75.993 | 50.334 | +25.659 | 1.50977 |
| 22, two-tone | 49.757 | 50.334 | -0.577 | 0.98854 |
| 22, monotone | 47.616 | 50.334 | -2.718 | 0.94600 |
| 22, paired | 50.096 | 50.334 | -0.238 | 0.99527 |
Does a shared suit matter?
The suit split reads 50.32% for QJo with a shared suit and 49.79% without one. QJo does better with a shared suit, by 0.53 points.
| Deals | Specific deals | Share of deals | QJo wins | Ties | 22 wins | QJo equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 49.728 | 1.175 | 49.097 | 50.315 |
| No shared suit | 12 | 16.67 | 49.228 | 1.132 | 49.640 | 49.794 |
How often this matchup comes up
QJo against 22 is made up of 72 specific-card matchups in one seat order, 0.0044% of the 1,624,350 ordered deals, and 144 counting both seat orders, 0.0089%.
A worked example
Put $100 each into a $200 pot and deal every board once: QJo averages $100.46 back, ahead of its $100 by $0.46, while 22 averages $99.54, short of its $100 by $0.46.
Per 1,000 deals: QJo wins about 496, 22 wins about 492, and about 12 end in a split pot.
The same matchup from the other side
Swap the hands and you get 22 with 49.77% against QJo with 50.23%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
QsJh against 2d2c 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 72 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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