ATo
55.40%
Wins 55.17%, ties 0.46%
QJs
44.60%
Wins 44.37%, ties 0.46%
ATo against QJs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 55.172 | 0.456 | 44.372 | 55.400 |
| QJs | 44.372 | 0.456 | 55.172 | 44.600 |
The matchup pits an offsuit hand against a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
The lead is steady rather than large, and the flop still has plenty of say in who wins. A split pot comes up on 0.46% of boards, so the wins and the equity differ by half of that.
The hand ranking puts ATo at 19 and QJs at 28 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 45,346,000 | 375,000 | 36,470,000 |
| QJs | 36,470,000 | 375,000 | 45,346,000 |
The total is exact: 48 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) |
|---|---|---|---|---|
| ATo | 1.242 | 1.813 | 2.254 | 0.805 |
| QJs | 0.805 | 2.254 | 1.813 | 1.242 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
The flop changes the picture. ATo does best on low rainbow flops (nine high or lower), at 71.93%, and worst on rainbow flops topped by a ten or better, at 50.60%. ATo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | ATo wins | Ties | QJs wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.260 | 50.548 | 0.110 | 49.342 | 50.603 |
| Rainbow, nine or lower | 7.770 | 71.480 | 0.908 | 27.612 | 71.934 |
| Two-tone | 46.667 | 53.212 | 0.282 | 46.506 | 53.353 |
| Monotone | 5.212 | 52.177 | 2.375 | 45.448 | 53.364 |
| Paired | 17.091 | 60.314 | 0.612 | 39.074 | 60.620 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
The table below sets each hand against its own random-hand baseline: a change of -7.32 points for ATo, from 62.72%, and -15.66 for QJs, from 60.26%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 55.400 | 62.722 | -7.322 | 0.88326 |
| ATo, rainbow, ten or higher | 50.603 | 62.722 | -12.119 | 0.80678 |
| ATo, rainbow, nine or lower | 71.934 | 62.722 | +9.212 | 1.14687 |
| ATo, two-tone | 53.353 | 62.722 | -9.369 | 0.85063 |
| ATo, monotone | 53.364 | 62.722 | -9.358 | 0.85080 |
| ATo, paired | 60.620 | 62.722 | -2.102 | 0.96649 |
| QJs, all flops | 44.600 | 60.259 | -15.659 | 0.74014 |
| QJs, rainbow, ten or higher | 49.397 | 60.259 | -10.862 | 0.81974 |
| QJs, rainbow, nine or lower | 28.066 | 60.259 | -32.193 | 0.46576 |
| QJs, two-tone | 46.647 | 60.259 | -13.612 | 0.77411 |
| QJs, monotone | 46.636 | 60.259 | -13.623 | 0.77393 |
| QJs, paired | 39.380 | 60.259 | -20.879 | 0.65351 |
Does a shared suit matter?
Split by suits, the deals give ATo 55.85% when the hands overlap in a suit and 54.95% when they do not. ATo does better with a shared suit, by 0.90 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | QJs wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 55.602 | 0.496 | 43.902 | 55.850 |
| No shared suit | 24 | 50.00 | 54.741 | 0.416 | 44.843 | 54.949 |
How often this matchup comes up
You will meet this exact matchup 0.0059% of the time in a random heads-up deal: 96 of 1,624,350, counting either seat order.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, ATo's average share is $110.80 (a gain of $10.80) and QJs' is $89.20 (a loss of $10.80).
Run 1,000 deals and the tally comes out near 552 for ATo, 444 for QJs and 4 ties.
The same matchup from the other side
QJs versus ATo is this same page seen from the other hand: 44.60% for QJs, 55.40% for ATo.
Keep exploring
The calculator link fills in AsTh against QdJd, 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
We counted every case. Each suit pattern of the 48 specific ATo against QJs deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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