JJ
66.74%
Wins 65.96%, ties 1.55%
QJo
33.26%
Wins 32.49%, ties 1.55%
JJ against QJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| JJ | 65.962 | 1.546 | 32.492 | 66.735 |
| QJo | 32.492 | 1.546 | 65.962 | 33.265 |
Here a pocket pair (JJ) meets an offsuit hand (QJo). One hand holds a card of the same rank as the pair, which removes a card the pair needs and makes the pair a bigger favorite.
A lead of 33.48 points is large but not decisive: QJo still takes about 325 of every 1,000 deals. 1.55% of boards are ties, so the equity of each hand is its win rate plus half of that.
JJ ranks number 4 of 169 starting hands, and QJo ranks number 39, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| JJ | 40,661,000 | 953,000 | 20,029,000 |
| QJo | 20,029,000 | 953,000 | 40,661,000 |
The board total is exact, 36 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) |
|---|---|---|---|---|
| JJ | 2.006 | 1.516 | 3.078 | 0.498 |
| QJo | 0.498 | 3.078 | 1.516 | 2.006 |
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. JJ does best on low rainbow flops (nine high or lower), at 83.69%, and worst on rainbow flops topped by a ten or better, at 59.89%. JJ stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | JJ wins | Ties | QJo wins | JJ equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.053 | 58.942 | 1.899 | 39.159 | 59.892 |
| Rainbow, nine or lower | 7.771 | 82.994 | 1.400 | 15.606 | 83.694 |
| Two-tone | 46.215 | 64.367 | 1.691 | 33.942 | 65.212 |
| Monotone | 5.130 | 59.113 | 2.159 | 38.728 | 60.193 |
| Paired | 17.831 | 73.720 | 0.600 | 25.680 | 74.020 |
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 77.47%, JJ changes by -10.73 points, and QJo, from 58.14%, by -24.88.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| JJ, all flops | 66.735 | 77.469 | -10.734 | 0.86144 |
| JJ, rainbow, ten or higher | 59.892 | 77.469 | -17.577 | 0.77311 |
| JJ, rainbow, nine or lower | 83.694 | 77.469 | +6.225 | 1.08035 |
| JJ, two-tone | 65.212 | 77.469 | -12.257 | 0.84178 |
| JJ, monotone | 60.193 | 77.469 | -17.276 | 0.77699 |
| JJ, paired | 74.020 | 77.469 | -3.449 | 0.95548 |
| QJo, all flops | 33.265 | 58.135 | -24.870 | 0.57220 |
| QJo, rainbow, ten or higher | 40.108 | 58.135 | -18.027 | 0.68991 |
| QJo, rainbow, nine or lower | 16.306 | 58.135 | -41.829 | 0.28049 |
| QJo, two-tone | 34.788 | 58.135 | -23.347 | 0.59840 |
| QJo, monotone | 39.807 | 58.135 | -18.328 | 0.68473 |
| QJo, paired | 25.980 | 58.135 | -32.155 | 0.44689 |
Does a shared suit matter?
Does suit overlap move the numbers? JJ has 66.66% when the hands share a suit and 66.89% when they do not. The two rows differ by only 0.23 points, so suits barely change this matchup.
| Deals | Specific deals | Share of deals | JJ wins | Ties | QJo wins | JJ equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 65.867 | 1.579 | 32.554 | 66.657 |
| No shared suit | 12 | 33.33 | 66.151 | 1.479 | 32.370 | 66.891 |
How often this matchup comes up
How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are JJ against QJo, and 72 (0.0044%) if either hand may sit in either seat.
A worked example
With $100 from each side, the $200 pot is split on average as $133.48 for JJ and $66.52 for QJo; the first side gains $33.48 per all-in and the second gives up $33.48.
Scaled to 1,000 deals, that is roughly 660 wins for JJ, 325 for QJo and 15 chopped pots.
The same matchup from the other side
QJo versus JJ is this same page seen from the other hand: 33.26% for QJo, 66.74% for JJ.
Keep exploring
The calculator link fills in JsJh against QdJc, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
We counted every case. Each suit pattern of the 36 specific JJ against QJo 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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