55
51.11%
Wins 50.78%, ties 0.67%
QTo
48.89%
Wins 48.55%, ties 0.67%
55 against QTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 50.777 | 0.669 | 48.554 | 51.111 |
| QTo | 48.554 | 0.669 | 50.777 | 48.889 |
The matchup pits a pocket pair against an offsuit hand. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.
55 leads by less than 3 points of equity, so the result of any one deal is close to a toss-up. Split pots make up 0.67% of the boards, and both equity figures count them as half a win each.
55 ranks number 27 of 169 starting hands, and QTo ranks number 47, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 62,601,000 | 825,000 | 59,860,000 |
| QTo | 59,860,000 | 825,000 | 62,601,000 |
The total is exact: 72 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) |
|---|---|---|---|---|
| 55 | 1.045 | 1.969 | 2.060 | 0.957 |
| QTo | 0.957 | 2.060 | 1.969 | 1.045 |
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
Break the boards down by their first three cards and 55 is strongest on low rainbow flops (nine high or lower) (76.43%) and weakest on rainbow flops topped by a ten or better (43.89%). On rainbow flops topped by a ten or better and monotone flops the numbers flip and QTo is the one ahead.
| Flop | Share of flops | 55 wins | Ties | QTo wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 43.710 | 0.365 | 55.925 | 43.892 |
| Rainbow, nine or lower | 6.314 | 76.071 | 0.710 | 23.219 | 76.426 |
| Two-tone | 46.485 | 50.099 | 0.422 | 49.479 | 50.310 |
| Monotone | 5.151 | 47.661 | 1.945 | 50.394 | 48.633 |
| Paired | 17.333 | 54.384 | 1.372 | 44.244 | 55.070 |
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
How much does the opponent matter? Compared with its random-hand 60.33%, 55 changes by -9.22 points, and QTo, from 57.29%, by -8.40.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 51.111 | 60.325 | -9.214 | 0.84726 |
| 55, rainbow, ten or higher | 43.892 | 60.325 | -16.433 | 0.72759 |
| 55, rainbow, nine or lower | 76.426 | 60.325 | +16.101 | 1.26690 |
| 55, two-tone | 50.310 | 60.325 | -10.015 | 0.83398 |
| 55, monotone | 48.633 | 60.325 | -11.692 | 0.80618 |
| 55, paired | 55.070 | 60.325 | -5.255 | 0.91289 |
| QTo, all flops | 48.889 | 57.291 | -8.402 | 0.85335 |
| QTo, rainbow, ten or higher | 56.108 | 57.291 | -1.183 | 0.97935 |
| QTo, rainbow, nine or lower | 23.574 | 57.291 | -33.717 | 0.41148 |
| QTo, two-tone | 49.690 | 57.291 | -7.601 | 0.86733 |
| QTo, monotone | 51.367 | 57.291 | -5.924 | 0.89660 |
| QTo, paired | 44.930 | 57.291 | -12.361 | 0.78424 |
Does a shared suit matter?
The suit split reads 51.02% for 55 with a shared suit and 51.56% without one. 55 does better with no shared suit, by 0.54 points.
| Deals | Specific deals | Share of deals | 55 wins | Ties | QTo wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 50.679 | 0.684 | 48.637 | 51.021 |
| No shared suit | 12 | 16.67 | 51.262 | 0.595 | 48.143 | 51.560 |
How often this matchup comes up
You will meet this exact matchup 0.0089% of the time in a random heads-up deal: 144 of 1,624,350, counting either seat order.
A worked example
With $100 from each side, the $200 pot is split on average as $102.22 for 55 and $97.78 for QTo; the first side gains $2.22 per all-in and the second gives up $2.22.
Scaled to 1,000 deals, that is roughly 508 wins for 55, 485 for QTo and 7 chopped pots.
The same matchup from the other side
If you came looking for QTo against 55, the numbers are the same with the hands swapped: 48.89% and 51.11%.
Keep exploring
Open the calculator with 5s5h against QdTc 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 72 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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