QTs
63.69%
Wins 63.21%, ties 0.96%
53s
36.31%
Wins 35.83%, ties 0.96%
QTs against 53s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QTs | 63.209 | 0.964 | 35.827 | 63.691 |
| 53s | 35.827 | 0.964 | 63.209 | 36.309 |
This is a contest between two suited hands, QTs and 53s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 27.38 point lead is real, and 53s still takes about 358 of every 1,000 deals outright. The tie share is 0.96%: on those boards the pot is chopped and neither hand wins outright.
In the ranking of all 169 starting hands, QTs is number 34 and 53s is number 146.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QTs | 17,317,000 | 264,000 | 9,815,000 |
| 53s | 9,815,000 | 264,000 | 17,317,000 |
Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| QTs | 1.754 | 1.582 | 2.791 | 0.570 |
| 53s | 0.570 | 2.791 | 1.582 | 1.754 |
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
The flop changes the picture. QTs does best on rainbow flops topped by a ten or better, at 70.44%, and worst on low rainbow flops (nine high or lower), at 39.64%. 53s takes over on low rainbow flops (nine high or lower), so the favorite before the flop is the underdog on those boards.
| Flop | Share of flops | QTs wins | Ties | 53s wins | QTs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 70.202 | 0.475 | 29.323 | 70.440 |
| Rainbow, nine or lower | 6.314 | 39.242 | 0.786 | 59.972 | 39.635 |
| Two-tone | 46.727 | 62.864 | 0.496 | 36.640 | 63.112 |
| Monotone | 5.273 | 58.979 | 3.680 | 37.341 | 60.819 |
| Paired | 17.091 | 64.249 | 2.176 | 33.575 | 65.337 |
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
A random hand would give QTs 59.47% and 53s 39.69%. Against each other the change is +4.22 points for QTs and -3.38 for 53s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QTs, all flops | 63.691 | 59.468 | +4.223 | 1.07101 |
| QTs, rainbow, ten or higher | 70.440 | 59.468 | +10.972 | 1.18450 |
| QTs, rainbow, nine or lower | 39.635 | 59.468 | -19.833 | 0.66649 |
| QTs, two-tone | 63.112 | 59.468 | +3.644 | 1.06128 |
| QTs, monotone | 60.819 | 59.468 | +1.351 | 1.02272 |
| QTs, paired | 65.337 | 59.468 | +5.869 | 1.09869 |
| 53s, all flops | 36.309 | 39.693 | -3.384 | 0.91475 |
| 53s, rainbow, ten or higher | 29.560 | 39.693 | -10.133 | 0.74472 |
| 53s, rainbow, nine or lower | 60.365 | 39.693 | +20.672 | 1.52080 |
| 53s, two-tone | 36.888 | 39.693 | -2.805 | 0.92933 |
| 53s, monotone | 39.181 | 39.693 | -0.512 | 0.98710 |
| 53s, paired | 34.663 | 39.693 | -5.030 | 0.87328 |
Does a shared suit matter?
Two kinds of deal exist here. In 4 of them the hands share a suit and QTs holds 66.07%. In 12 they do not, and it holds 62.90%. QTs does better with a shared suit, by 3.17 points.
| Deals | Specific deals | Share of deals | QTs wins | Ties | 53s wins | QTs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 65.539 | 1.066 | 33.395 | 66.072 |
| No shared suit | 12 | 75.00 | 62.433 | 0.930 | 36.637 | 62.898 |
How often this matchup comes up
This page stands for 16 specific-card matchups (0.0010% of 1,624,350 ordered deals), or 32 once you count the seats both ways (0.0020%).
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. QTs is worth $127.38 on average (+$27.38); 53s is worth $72.62 (-$27.38).
Run 1,000 deals and the tally comes out near 632 for QTs, 358 for 53s and 10 ties.
The same matchup from the other side
If you came looking for 53s against QTs, the numbers are the same with the hands swapped: 36.31% and 63.69%.
Keep exploring
The calculator link fills in QsTs against 5h3h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of QTs against 53s, 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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