55
50.33%
Wins 49.98%, ties 0.70%
Q9s
49.67%
Wins 49.32%, ties 0.70%
55 against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 55 | 49.978 | 0.704 | 49.318 | 50.330 |
| Q9s | 49.318 | 0.704 | 49.978 | 49.670 |
The first hand is a pocket pair; the second 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.
With only 0.66 points between them, the board decides this matchup far more than the cards in hand. Split pots make up 0.70% of the boards, and both equity figures count them as half a win each.
In the ranking of all 169 starting hands, 55 is number 27 and Q9s is number 43.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 55 | 20,539,000 | 289,000 | 20,267,000 |
| Q9s | 20,267,000 | 289,000 | 20,539,000 |
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 | 1.013 | 2.001 | 2.028 | 0.987 |
| Q9s | 0.987 | 2.028 | 2.001 | 1.013 |
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
Low rainbow flops (nine high or lower) are the best for 55 (61.26%); rainbow flops topped by a ten or better are the worst (48.48%). Q9s is ahead on rainbow flops topped by a ten or better and two-tone flops, even though it trails 55 when every flop is counted.
| Flop | Share of flops | 55 wins | Ties | Q9s wins | 55 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 48.293 | 0.370 | 51.337 | 48.478 |
| Rainbow, nine or lower | 5.689 | 60.910 | 0.709 | 38.381 | 61.264 |
| Two-tone | 46.545 | 48.536 | 0.409 | 51.055 | 48.741 |
| Monotone | 5.212 | 48.859 | 2.687 | 48.454 | 50.202 |
| Paired | 17.334 | 53.051 | 1.381 | 45.568 | 53.742 |
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, 55 changes by -10.00 points (baseline 60.33%) and Q9s by -7.99 points (baseline 57.66%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 55, all flops | 50.330 | 60.325 | -9.995 | 0.83431 |
| 55, rainbow, ten or higher | 48.478 | 60.325 | -11.847 | 0.80361 |
| 55, rainbow, nine or lower | 61.264 | 60.325 | +0.939 | 1.01557 |
| 55, two-tone | 48.741 | 60.325 | -11.584 | 0.80797 |
| 55, monotone | 50.202 | 60.325 | -10.123 | 0.83219 |
| 55, paired | 53.742 | 60.325 | -6.583 | 0.89087 |
| Q9s, all flops | 49.670 | 57.664 | -7.994 | 0.86137 |
| Q9s, rainbow, ten or higher | 51.522 | 57.664 | -6.142 | 0.89349 |
| Q9s, rainbow, nine or lower | 38.736 | 57.664 | -18.928 | 0.67175 |
| Q9s, two-tone | 51.259 | 57.664 | -6.405 | 0.88893 |
| Q9s, monotone | 49.798 | 57.664 | -7.866 | 0.86359 |
| Q9s, paired | 46.258 | 57.664 | -11.406 | 0.80220 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common 55 has 50.49% equity, and with none in common it has 50.17%. 55 does better with a shared suit, by 0.32 points.
| Deals | Specific deals | Share of deals | 55 wins | Ties | Q9s wins | 55 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 50.121 | 0.745 | 49.134 | 50.493 |
| No shared suit | 12 | 50.00 | 49.836 | 0.662 | 49.502 | 50.167 |
How often this matchup comes up
Counting specific cards, 55 against Q9s 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
With $100 from each side, the $200 pot is split on average as $100.66 for 55 and $99.34 for Q9s; the first side gains $0.66 per all-in and the second gives up $0.66.
Per 1,000 deals: 55 wins about 500, Q9s wins about 493, and about 7 end in a split pot.
The same matchup from the other side
Swap the hands and you get Q9s with 49.67% against 55 with 50.33%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
5s5h against Qd9d is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
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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