55
49.15%
Wins 48.81%, ties 0.67%
QJs
50.85%
Wins 50.52%, ties 0.67%
55 against QJs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 48.811 | 0.668 | 50.521 | 49.145 |
| QJs | 50.521 | 0.668 | 48.811 | 50.855 |
55 is a pocket pair and QJs is a suited hand. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.
This is close to even money, with QJs a little ahead. About 0.67% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
In the ranking of all 169 starting hands, 55 is number 27 and QJs is number 28.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 20,059,000 | 275,000 | 20,762,000 |
| QJs | 20,762,000 | 275,000 | 20,059,000 |
24 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| 55 | 0.966 | 2.049 | 1.979 | 1.035 |
| QJs | 1.035 | 1.979 | 2.049 | 0.966 |
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
Split by what the flop looks like, QJs peaks at 57.28% on rainbow flops topped by a ten or better and bottoms out at 24.22% on low rainbow flops (nine high or lower). 55 is ahead on low rainbow flops (nine high or lower) and paired flops, even though it trails QJs when every flop is counted.
| Flop | Share of flops | 55 wins | Ties | QJs wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 42.563 | 0.312 | 57.125 | 42.719 |
| Rainbow, nine or lower | 6.314 | 75.407 | 0.745 | 23.848 | 75.779 |
| Two-tone | 46.545 | 47.316 | 0.379 | 52.305 | 47.505 |
| Monotone | 5.212 | 48.019 | 2.669 | 49.312 | 49.353 |
| Paired | 17.334 | 52.245 | 1.319 | 46.436 | 52.905 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
A random hand would give 55 60.33% and QJs 60.26%. Against each other the change is -11.18 points for 55 and -9.41 for QJs.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 49.145 | 60.325 | -11.180 | 0.81467 |
| 55, rainbow, ten or higher | 42.719 | 60.325 | -17.606 | 0.70815 |
| 55, rainbow, nine or lower | 75.779 | 60.325 | +15.454 | 1.25618 |
| 55, two-tone | 47.505 | 60.325 | -12.820 | 0.78748 |
| 55, monotone | 49.353 | 60.325 | -10.972 | 0.81812 |
| 55, paired | 52.905 | 60.325 | -7.420 | 0.87700 |
| QJs, all flops | 50.855 | 60.259 | -9.404 | 0.84394 |
| QJs, rainbow, ten or higher | 57.281 | 60.259 | -2.978 | 0.95058 |
| QJs, rainbow, nine or lower | 24.221 | 60.259 | -36.038 | 0.40195 |
| QJs, two-tone | 52.495 | 60.259 | -7.764 | 0.87116 |
| QJs, monotone | 50.647 | 60.259 | -9.612 | 0.84049 |
| QJs, paired | 47.095 | 60.259 | -13.164 | 0.78154 |
Does a shared suit matter?
The suit split reads 50.70% for QJs with a shared suit and 51.01% without one. QJs does better with no shared suit, by 0.31 points.
| Deals | Specific deals | Share of deals | 55 wins | Ties | QJs wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 48.945 | 0.711 | 50.344 | 49.301 |
| No shared suit | 12 | 50.00 | 48.677 | 0.625 | 50.698 | 48.990 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are 55 against QJs, and 48 (0.0030%) if either hand may sit in either seat.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. QJs is worth $101.70 on average (+$1.70); 55 is worth $98.30 (-$1.70).
Per 1,000 deals: QJs wins about 505, 55 wins about 488, and about 7 end in a split pot.
The same matchup from the other side
One page covers both views. From QJs' side the equity is 50.85%, and from 55's side it is 49.15%.
Keep exploring
Open the calculator with 5s5h against QdJd 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
Method: exact enumeration. The 24 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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