77.49%
Wins 77.27%, ties 0.45%
54s
22.51%
Wins 22.28%, ties 0.45%
QQ against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77.265 | 0.447 | 22.288 | 77.488 | |
| 54s | 22.288 | 0.447 | 77.265 | 22.512 |
The matchup pits a pocket pair against a suited hand. The pair outranks both of the other hand's cards, which is why the pair is a strong favorite.
QQ is well ahead, and 54s needs a specific kind of board to catch up. Of every 100 boards, about 0.45 are split pots, and the equity figures already include them.
By strength against a random hand, QQ holds place 3 of 169 and 54s holds place 136.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 31,752,000 | 184,000 | 9,159,000 | |
| 54s | 9,159,000 | 184,000 | 31,752,000 |
The total is exact: 24 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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) |
|---|---|---|---|---|
| 3.442 | 1.294 | 4.487 | 0.291 | |
| 54s | 0.291 | 4.487 | 1.294 | 3.442 |
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
Rainbow flops topped by a ten or better are the best for QQ (82.81%); low rainbow flops (nine high or lower) are the worst (63.06%). 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 | 54s wins | QQ equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 82.704 | 0.213 | 17.083 | 82.810 |
| Rainbow, nine or lower | 6.314 | 62.534 | 1.044 | 36.422 | 63.056 |
| Two-tone | 46.545 | 75.289 | 0.360 | 24.351 | 75.469 |
| Monotone | 5.212 | 71.302 | 2.509 | 26.189 | 72.556 |
| Paired | 17.334 | 82.011 | 0.176 | 17.813 | 82.099 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
A random hand would give QQ 79.93% and 54s 41.45%. Against each other the change is -2.44 points for QQ and -18.94 for 54s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QQ, all flops | 77.488 | 79.925 | -2.437 | 0.96951 |
| QQ, rainbow, ten or higher | 82.810 | 79.925 | +2.885 | 1.03610 |
| QQ, rainbow, nine or lower | 63.056 | 79.925 | -16.869 | 0.78894 |
| QQ, two-tone | 75.469 | 79.925 | -4.456 | 0.94425 |
| QQ, monotone | 72.556 | 79.925 | -7.369 | 0.90780 |
| QQ, paired | 82.099 | 79.925 | +2.174 | 1.02720 |
| 54s, all flops | 22.512 | 41.453 | -18.941 | 0.54307 |
| 54s, rainbow, ten or higher | 17.190 | 41.453 | -24.263 | 0.41469 |
| 54s, rainbow, nine or lower | 36.944 | 41.453 | -4.509 | 0.89123 |
| 54s, two-tone | 24.531 | 41.453 | -16.922 | 0.59178 |
| 54s, monotone | 27.444 | 41.453 | -14.009 | 0.66205 |
| 54s, paired | 17.901 | 41.453 | -23.552 | 0.43184 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and QQ holds 78.04%. In 12 they do not, and it holds 76.93%. QQ does better with a shared suit, by 1.11 points.
| Deals | Specific deals | Share of deals | QQ wins | Ties | 54s wins | QQ equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 77.799 | 0.489 | 21.712 | 78.043 |
| No shared suit | 12 | 50.00 | 76.731 | 0.406 | 22.863 | 76.934 |
How often this matchup comes up
Counting specific cards, QQ against 54s appears in 24 of the 1,624,350 ordered heads-up deals (0.0015%), and in 48 when the seats are swapped too (0.0030%).
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. QQ averages $154.98 from the $200, up $54.98; 54s averages $45.02, down $54.98.
Per 1,000 deals: QQ wins about 773, 54s wins about 223, and about 4 end in a split pot.
The same matchup from the other side
54s against QQ adds nothing new: it is 22.51% for 54s and 77.49% for QQ, the same figures reversed.
Keep exploring
Try QsQh against 5d4d in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 24 specific deals of QQ against 54s, 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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