QJs
51.92%
Wins 51.43%, ties 0.98%
33
48.08%
Wins 47.59%, ties 0.98%
QJs against 33: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QJs | 51.434 | 0.979 | 47.587 | 51.924 |
| 33 | 47.587 | 0.979 | 51.434 | 48.076 |
We compare a suited hand with a pocket pair. 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. 0.98% of boards are ties, so the equity of each hand is its win rate plus half of that.
For context, QJs sits at number 28 of 169 starting hands and 33 at number 66 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QJs | 21,137,000 | 402,000 | 19,556,000 |
| 33 | 19,556,000 | 402,000 | 21,137,000 |
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 | 1.080 | 1.944 | 2.101 | 0.926 |
| 33 | 0.926 | 2.101 | 1.944 | 1.080 |
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
The flop changes the picture. QJs does best on rainbow flops topped by a ten or better, at 57.75%, and worst on low rainbow flops (nine high or lower), at 25.69%. 33 is ahead on low rainbow flops (nine high or lower), even though it trails QJs when every flop is counted.
| Flop | Share of flops | QJs wins | Ties | 33 wins | QJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 57.530 | 0.441 | 42.029 | 57.750 |
| Rainbow, nine or lower | 6.314 | 25.149 | 1.083 | 73.768 | 25.690 |
| Two-tone | 46.545 | 52.864 | 0.538 | 46.598 | 53.133 |
| Monotone | 5.212 | 49.763 | 3.343 | 46.894 | 51.434 |
| Paired | 17.334 | 49.025 | 2.174 | 48.801 | 50.112 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
Relative to a random opponent, QJs changes by -8.34 points (baseline 60.26%) and 33 by -5.61 points (baseline 53.69%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QJs, all flops | 51.924 | 60.259 | -8.335 | 0.86168 |
| QJs, rainbow, ten or higher | 57.750 | 60.259 | -2.509 | 0.95836 |
| QJs, rainbow, nine or lower | 25.690 | 60.259 | -34.569 | 0.42633 |
| QJs, two-tone | 53.133 | 60.259 | -7.126 | 0.88174 |
| QJs, monotone | 51.434 | 60.259 | -8.825 | 0.85355 |
| QJs, paired | 50.112 | 60.259 | -10.147 | 0.83161 |
| 33, all flops | 48.076 | 53.693 | -5.617 | 0.89539 |
| 33, rainbow, ten or higher | 42.250 | 53.693 | -11.443 | 0.78688 |
| 33, rainbow, nine or lower | 74.310 | 53.693 | +20.617 | 1.38398 |
| 33, two-tone | 46.867 | 53.693 | -6.826 | 0.87287 |
| 33, monotone | 48.566 | 53.693 | -5.127 | 0.90451 |
| 33, paired | 49.888 | 53.693 | -3.805 | 0.92913 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common QJs has 51.77% equity, and with none in common it has 52.08%. QJs does better with no shared suit, by 0.31 points.
| Deals | Specific deals | Share of deals | QJs wins | Ties | 33 wins | QJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 51.262 | 1.010 | 47.728 | 51.767 |
| No shared suit | 12 | 50.00 | 51.607 | 0.948 | 47.445 | 52.081 |
How often this matchup comes up
The class pair covers 24 combinations of specific cards in a fixed seat order, 0.0015% of 1,624,350, and 48 (0.0030%) in either order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. QJs is worth $103.84 on average (+$3.84); 33 is worth $96.16 (-$3.84).
Out of 1,000 deals you should see around 514 outright wins for QJs, 476 for 33, and 10 split pots.
The same matchup from the other side
33 versus QJs is this same page seen from the other hand: 48.08% for 33, 51.92% for QJs.
Keep exploring
Open the calculator with QsJs against 3h3d already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 24 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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