89.18%
Wins 88.36%, ties 1.64%
QJo
10.82%
Wins 10.00%, ties 1.64%
QQ against QJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 88.362 | 1.635 | 10.003 | 89.180 | |
| QJo | 10.003 | 1.635 | 88.362 | 10.820 |
QQ is a pocket pair and QJo is an offsuit hand. 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.
That is a heavy lead: QJo needs the board to help it on most runouts and still falls behind far more often than not. Ties are part of the picture: 1.64% of boards end in a split pot, and each side counts that as half a win.
The hand ranking puts QQ at 3 and QJo at 39 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 54,469,000 | 1,008,000 | 6,166,000 | |
| QJo | 6,166,000 | 1,008,000 | 54,469,000 |
Exact total: 36 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) |
|---|---|---|---|---|
| 8.242 | 1.132 | 9.997 | 0.121 | |
| QJo | 0.121 | 9.997 | 1.132 | 8.242 |
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
Split by what the flop looks like, QQ peaks at 95.99% on low rainbow flops (nine high or lower) and bottoms out at 80.83% on monotone flops. QQ 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 | QQ wins | Ties | QJo wins | QQ equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.053 | 87.136 | 1.944 | 10.920 | 88.108 |
| Rainbow, nine or lower | 7.771 | 95.288 | 1.400 | 3.312 | 95.988 |
| Two-tone | 46.215 | 88.112 | 1.724 | 10.164 | 88.974 |
| Monotone | 5.130 | 79.736 | 2.194 | 18.070 | 80.833 |
| Paired | 17.831 | 90.059 | 0.946 | 8.995 | 90.532 |
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
A random hand would give QQ 79.93% and QJo 58.14%. Against each other the change is +9.25 points for QQ and -47.32 for QJo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QQ, all flops | 89.180 | 79.925 | +9.255 | 1.11580 |
| QQ, rainbow, ten or higher | 88.108 | 79.925 | +8.183 | 1.10238 |
| QQ, rainbow, nine or lower | 95.988 | 79.925 | +16.063 | 1.20098 |
| QQ, two-tone | 88.974 | 79.925 | +9.049 | 1.11322 |
| QQ, monotone | 80.833 | 79.925 | +0.908 | 1.01136 |
| QQ, paired | 90.532 | 79.925 | +10.607 | 1.13271 |
| QJo, all flops | 10.820 | 58.135 | -47.315 | 0.18612 |
| QJo, rainbow, ten or higher | 11.892 | 58.135 | -46.243 | 0.20456 |
| QJo, rainbow, nine or lower | 4.012 | 58.135 | -54.123 | 0.06901 |
| QJo, two-tone | 11.026 | 58.135 | -47.109 | 0.18966 |
| QJo, monotone | 19.167 | 58.135 | -38.968 | 0.32970 |
| QJo, paired | 9.468 | 58.135 | -48.667 | 0.16286 |
Does a shared suit matter?
Split by suits, the deals give QQ 89.46% when the hands overlap in a suit and 88.62% when they do not. QQ does better with a shared suit, by 0.84 points.
| Deals | Specific deals | Share of deals | QQ wins | Ties | QJo wins | QQ equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 88.625 | 1.668 | 9.707 | 89.459 |
| No shared suit | 12 | 33.33 | 87.837 | 1.568 | 10.595 | 88.621 |
How often this matchup comes up
Counting specific cards, QQ against QJo appears in 36 of the 1,624,350 ordered heads-up deals (0.0022%), and in 72 when the seats are swapped too (0.0044%).
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. QQ averages $178.36 from the $200, up $78.36; QJo averages $21.64, down $78.36.
Think in thousands: about 884 of 1,000 go to QQ, about 100 go to QJo, and about 16 are chopped.
The same matchup from the other side
QJo against QQ adds nothing new: it is 10.82% for QJo and 89.18% for QQ, the same figures reversed.
Keep exploring
The calculator link fills in QsQh 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 QQ 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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