QTs
62.43%
Wins 61.96%, ties 0.95%
54s
37.57%
Wins 37.09%, ties 0.95%
QTs against 54s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QTs | 61.957 | 0.954 | 37.089 | 62.434 |
| 54s | 37.089 | 0.954 | 61.957 | 37.566 |
This is a contest between two suited hands, QTs and 54s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Ties are 0.95% of the outcomes here; each tied board gives both hands half the pot.
QTs ranks number 34 of 169 starting hands, and 54s ranks number 136, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QTs | 16,974,000 | 261,000 | 10,161,000 |
| 54s | 10,161,000 | 261,000 | 16,974,000 |
16 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) |
|---|---|---|---|---|
| QTs | 1.662 | 1.614 | 2.696 | 0.602 |
| 54s | 0.602 | 2.696 | 1.614 | 1.662 |
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
Break the boards down by their first three cards and QTs is strongest on rainbow flops topped by a ten or better (69.17%) and weakest on low rainbow flops (nine high or lower) (37.54%). The lead reverses on low rainbow flops (nine high or lower): there 54s is the favorite even though QTs is ahead overall.
| Flop | Share of flops | QTs wins | Ties | 54s wins | QTs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 68.937 | 0.475 | 30.588 | 69.174 |
| Rainbow, nine or lower | 6.314 | 37.184 | 0.720 | 62.096 | 37.544 |
| Two-tone | 46.727 | 61.601 | 0.487 | 37.912 | 61.845 |
| Monotone | 5.273 | 58.036 | 3.668 | 38.296 | 59.870 |
| Paired | 17.091 | 63.243 | 2.172 | 34.585 | 64.329 |
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
Compared with a random opponent, this matchup shifts QTs from 59.47% by +2.96 points and 54s from 41.45% by -3.88 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QTs, all flops | 62.434 | 59.468 | +2.966 | 1.04988 |
| QTs, rainbow, ten or higher | 69.174 | 59.468 | +9.706 | 1.16321 |
| QTs, rainbow, nine or lower | 37.544 | 59.468 | -21.924 | 0.63133 |
| QTs, two-tone | 61.845 | 59.468 | +2.377 | 1.03997 |
| QTs, monotone | 59.870 | 59.468 | +0.402 | 1.00676 |
| QTs, paired | 64.329 | 59.468 | +4.861 | 1.08174 |
| 54s, all flops | 37.566 | 41.453 | -3.887 | 0.90623 |
| 54s, rainbow, ten or higher | 30.826 | 41.453 | -10.627 | 0.74364 |
| 54s, rainbow, nine or lower | 62.456 | 41.453 | +21.003 | 1.50667 |
| 54s, two-tone | 38.155 | 41.453 | -3.298 | 0.92044 |
| 54s, monotone | 40.130 | 41.453 | -1.323 | 0.96808 |
| 54s, paired | 35.671 | 41.453 | -5.782 | 0.86052 |
Does a shared suit matter?
The suit split reads 64.66% for QTs with a shared suit and 61.69% without one. QTs does better with a shared suit, by 2.97 points.
| Deals | Specific deals | Share of deals | QTs wins | Ties | 54s wins | QTs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 64.135 | 1.056 | 34.809 | 64.663 |
| No shared suit | 12 | 75.00 | 61.231 | 0.920 | 37.849 | 61.691 |
How often this matchup comes up
Counting specific cards, QTs against 54s appears in 16 of the 1,624,350 ordered heads-up deals (0.0010%), and in 32 when the seats are swapped too (0.0020%).
A worked example
Take a $200 pot built from $100 each. QTs' equity of 62.43% is worth $124.86, a $24.86 edge, and 54s' 37.57% is worth $75.14, which is $24.86 under its stake.
In 1,000 deals of exactly this matchup, expect about 620 won outright by QTs, about 371 won outright by 54s and about 9 split.
The same matchup from the other side
The mirror image, 54s against QTs, is 37.57% to 62.43%, and its address redirects to this page.
Keep exploring
Open the calculator with QsTs against 5h4h 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
Each figure is a complete count over boards. Take the 16 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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