ATo
59.86%
Wins 59.63%, ties 0.46%
KQo
40.14%
Wins 39.91%, ties 0.46%
ATo against KQo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 59.628 | 0.455 | 39.917 | 59.855 |
| KQo | 39.917 | 0.455 | 59.628 | 40.145 |
Both hands are offsuit hands: ATo and KQo. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
ATo is ahead, but KQo is far from dead: it takes 399 of every 1,000 deals outright. Split pots make up 0.46% of the boards, and both equity figures count them as half a win each.
In the ranking of all 169 starting hands, ATo is number 19 and KQo is number 23.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 147,026,000 | 1,122,000 | 98,424,000 |
| KQo | 98,424,000 | 1,122,000 | 147,026,000 |
The board total is exact, 144 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| ATo | 1.491 | 1.677 | 2.505 | 0.671 |
| KQo | 0.671 | 2.505 | 1.677 | 1.491 |
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
Low rainbow flops (nine high or lower) are the best for ATo (76.19%); rainbow flops topped by a ten or better are the worst (53.43%). 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 | KQo wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.381 | 53.368 | 0.117 | 46.515 | 53.426 |
| Rainbow, nine or lower | 7.771 | 75.671 | 1.039 | 23.290 | 76.190 |
| Two-tone | 46.606 | 58.695 | 0.332 | 40.973 | 58.861 |
| Monotone | 5.151 | 55.992 | 1.712 | 42.296 | 56.848 |
| Paired | 17.091 | 64.541 | 0.604 | 34.855 | 64.843 |
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 ATo from 62.72% by -2.86 points and KQo from 61.46% by -21.32 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 59.855 | 62.722 | -2.867 | 0.95429 |
| ATo, rainbow, ten or higher | 53.426 | 62.722 | -9.296 | 0.85179 |
| ATo, rainbow, nine or lower | 76.190 | 62.722 | +13.468 | 1.21473 |
| ATo, two-tone | 58.861 | 62.722 | -3.861 | 0.93844 |
| ATo, monotone | 56.848 | 62.722 | -5.874 | 0.90635 |
| ATo, paired | 64.843 | 62.722 | +2.121 | 1.03382 |
| KQo, all flops | 40.145 | 61.456 | -21.311 | 0.65323 |
| KQo, rainbow, ten or higher | 46.574 | 61.456 | -14.882 | 0.75784 |
| KQo, rainbow, nine or lower | 23.810 | 61.456 | -37.646 | 0.38743 |
| KQo, two-tone | 41.139 | 61.456 | -20.317 | 0.66941 |
| KQo, monotone | 43.152 | 61.456 | -18.304 | 0.70216 |
| KQo, paired | 35.157 | 61.456 | -26.299 | 0.57207 |
Does a shared suit matter?
Two kinds of deal exist here. In 120 of them the hands share a suit and ATo holds 59.87%. In 24 they do not, and it holds 59.77%. The two rows differ by only 0.10 points, so suits barely change this matchup.
| Deals | Specific deals | Share of deals | ATo wins | Ties | KQo wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 120 | 83.33 | 59.638 | 0.470 | 39.892 | 59.873 |
| No shared suit | 24 | 16.67 | 59.580 | 0.375 | 40.045 | 59.768 |
How often this matchup comes up
ATo against KQo is made up of 144 specific-card matchups in one seat order, 0.0089% of the 1,624,350 ordered deals, and 288 counting both seat orders, 0.0177%.
A worked example
Take a $200 pot built from $100 each. ATo's equity of 59.86% is worth $119.72, a $19.72 edge, and KQo's 40.14% is worth $80.28, which is $19.72 under its stake.
A thousand deals look like this: ATo takes 596, KQo takes 399, 5 are ties.
The same matchup from the other side
The mirror image, KQo against ATo, is 40.14% to 59.86%, and its address redirects to this page.
Keep exploring
The calculator link fills in AsTh against KdQc, 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
Method: exact enumeration. The 144 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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