55
51.56%
Wins 51.24%, ties 0.65%
QJo
48.44%
Wins 48.11%, ties 0.65%
55 against QJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 51.236 | 0.654 | 48.110 | 51.563 |
| QJo | 48.110 | 0.654 | 51.236 | 48.437 |
We compare a pocket pair with an offsuit 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 55 a little ahead. Ties are 0.65% of the outcomes here; each tied board gives both hands half the pot.
By strength against a random hand, 55 holds place 27 of 169 and QJo holds place 39.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 63,167,000 | 806,000 | 59,313,000 |
| QJo | 59,313,000 | 806,000 | 63,167,000 |
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) |
|---|---|---|---|---|
| 55 | 1.065 | 1.952 | 2.079 | 0.939 |
| QJo | 0.939 | 2.079 | 1.952 | 1.065 |
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. 55 does best on low rainbow flops (nine high or lower), at 78.40%, and worst on rainbow flops topped by a ten or better, at 44.06%. The overall edge for 55 hides rainbow flops topped by a ten or better and monotone flops, where QJo comes out in front.
| Flop | Share of flops | 55 wins | Ties | QJo wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 43.900 | 0.324 | 55.776 | 44.062 |
| Rainbow, nine or lower | 6.314 | 78.006 | 0.782 | 21.212 | 78.397 |
| Two-tone | 46.485 | 50.623 | 0.405 | 48.972 | 50.826 |
| Monotone | 5.151 | 48.044 | 1.935 | 50.021 | 49.012 |
| Paired | 17.333 | 54.536 | 1.368 | 44.096 | 55.220 |
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
Each hand has a baseline against a random hand: 60.33% for 55, 58.14% for QJo. Here the change is -8.77 and -9.70 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 51.563 | 60.325 | -8.762 | 0.85475 |
| 55, rainbow, ten or higher | 44.062 | 60.325 | -16.263 | 0.73041 |
| 55, rainbow, nine or lower | 78.397 | 60.325 | +18.072 | 1.29958 |
| 55, two-tone | 50.826 | 60.325 | -9.499 | 0.84254 |
| 55, monotone | 49.012 | 60.325 | -11.313 | 0.81247 |
| 55, paired | 55.220 | 60.325 | -5.105 | 0.91538 |
| QJo, all flops | 48.437 | 58.135 | -9.698 | 0.83318 |
| QJo, rainbow, ten or higher | 55.938 | 58.135 | -2.197 | 0.96221 |
| QJo, rainbow, nine or lower | 21.603 | 58.135 | -36.532 | 0.37160 |
| QJo, two-tone | 49.174 | 58.135 | -8.961 | 0.84586 |
| QJo, monotone | 50.988 | 58.135 | -7.147 | 0.87706 |
| QJo, paired | 44.780 | 58.135 | -13.355 | 0.77028 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common 55 has 51.48% equity, and with none in common it has 52.00%. 55 does better with no shared suit, by 0.52 points.
| Deals | Specific deals | Share of deals | 55 wins | Ties | QJo wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 51.140 | 0.669 | 48.191 | 51.475 |
| No shared suit | 12 | 16.67 | 51.714 | 0.580 | 47.706 | 52.004 |
How often this matchup comes up
This page stands for 72 specific-card matchups (0.0044% of 1,624,350 ordered deals), or 144 once you count the seats both ways (0.0089%).
A worked example
Put $100 each into a $200 pot and deal every board once: 55 averages $103.12 back, ahead of its $100 by $3.12, while QJo averages $96.88, short of its $100 by $3.12.
A thousand deals look like this: 55 takes 512, QJo takes 481, 7 are ties.
The same matchup from the other side
QJo against 55 adds nothing new: it is 48.44% for QJo and 51.56% for 55, the same figures reversed.
Keep exploring
Open the calculator with 5s5h against QdJc 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 72 specific deals of 55 against QJo, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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