QTs
44.45%
Wins 44.19%, ties 0.53%
A3s
55.55%
Wins 55.28%, ties 0.53%
QTs against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QTs | 44.188 | 0.526 | 55.286 | 44.451 |
| A3s | 55.286 | 0.526 | 44.188 | 55.549 |
Here suited hands face each other, QTs on one side and A3s on the other. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
The lead is steady rather than large, and the flop still has plenty of say in who wins. Ties are part of the picture: 0.53% of boards end in a split pot, and each side counts that as half a win.
For context, QTs sits at number 34 of 169 starting hands and A3s at number 38 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QTs | 12,106,000 | 144,000 | 15,147,000 |
| A3s | 15,147,000 | 144,000 | 12,106,000 |
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 | 0.800 | 2.263 | 1.809 | 1.250 |
| A3s | 1.250 | 1.809 | 2.263 | 0.800 |
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 A3s is strongest on low rainbow flops (nine high or lower) (71.93%) and weakest on rainbow flops topped by a ten or better (49.46%). QTs takes over on rainbow flops topped by a ten or better, so the favorite before the flop is the underdog on those boards.
| Flop | Share of flops | QTs wins | Ties | A3s wins | QTs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 50.467 | 0.152 | 49.381 | 50.543 |
| Rainbow, nine or lower | 7.042 | 27.617 | 0.898 | 71.485 | 28.066 |
| Two-tone | 46.727 | 45.547 | 0.288 | 54.165 | 45.691 |
| Monotone | 5.273 | 44.925 | 3.438 | 51.637 | 46.644 |
| Paired | 17.091 | 38.305 | 0.645 | 61.050 | 38.627 |
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 -15.02 points and A3s from 58.22% by -2.67 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QTs, all flops | 44.451 | 59.468 | -15.017 | 0.74748 |
| QTs, rainbow, ten or higher | 50.543 | 59.468 | -8.925 | 0.84992 |
| QTs, rainbow, nine or lower | 28.066 | 59.468 | -31.402 | 0.47195 |
| QTs, two-tone | 45.691 | 59.468 | -13.777 | 0.76833 |
| QTs, monotone | 46.644 | 59.468 | -12.824 | 0.78435 |
| QTs, paired | 38.627 | 59.468 | -20.841 | 0.64954 |
| A3s, all flops | 55.549 | 58.220 | -2.671 | 0.95412 |
| A3s, rainbow, ten or higher | 49.457 | 58.220 | -8.763 | 0.84948 |
| A3s, rainbow, nine or lower | 71.934 | 58.220 | +13.714 | 1.23555 |
| A3s, two-tone | 54.309 | 58.220 | -3.911 | 0.93282 |
| A3s, monotone | 53.356 | 58.220 | -4.864 | 0.91645 |
| A3s, paired | 61.373 | 58.220 | +3.153 | 1.05416 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A3s has 57.27% equity, and with none in common it has 54.98%. A3s does better with a shared suit, by 2.29 points.
| Deals | Specific deals | Share of deals | QTs wins | Ties | A3s wins | QTs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 42.425 | 0.607 | 56.968 | 42.728 |
| No shared suit | 12 | 75.00 | 44.775 | 0.499 | 54.726 | 45.025 |
How often this matchup comes up
Counting specific cards, QTs against A3s 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
Put $100 each into a $200 pot and deal every board once: A3s averages $111.10 back, ahead of its $100 by $11.10, while QTs averages $88.90, short of its $100 by $11.10.
Run 1,000 deals and the tally comes out near 553 for A3s, 442 for QTs and 5 ties.
The same matchup from the other side
A3s versus QTs is this same page seen from the other hand: 55.55% for A3s, 44.45% for QTs.
Keep exploring
QsTs against Ah3h 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
Nothing here is simulated. The 16 deals of QTs against A3s fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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