ATo
74.17%
Wins 73.18%, ties 1.99%
KTo
25.83%
Wins 24.83%, ties 1.99%
ATo against KTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 73.178 | 1.993 | 24.829 | 74.174 |
| KTo | 24.829 | 1.993 | 73.178 | 25.826 |
Each side holds one of the offsuit hands: ATo and KTo. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
ATo is the clear favorite, though KTo gets there on roughly one board in 4. Of every 100 boards, about 1.99 are split pots, and the equity figures already include them.
By strength against a random hand, ATo holds place 19 of 169 and KTo holds place 33.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 135,327,000 | 3,686,000 | 45,916,000 |
| KTo | 45,916,000 | 3,686,000 | 135,327,000 |
The board total is exact, 108 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 | 2.872 | 1.367 | 4.028 | 0.348 |
| KTo | 0.348 | 4.028 | 1.367 | 2.872 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
By flop texture, ATo's equity runs from 68.49% on monotone flops up to 85.73% on low rainbow flops (nine high or lower). 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 | KTo wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.275 | 69.535 | 1.427 | 29.038 | 70.249 |
| Rainbow, nine or lower | 7.771 | 84.001 | 3.467 | 12.532 | 85.734 |
| Two-tone | 46.477 | 72.552 | 1.862 | 25.586 | 73.483 |
| Monotone | 5.144 | 67.153 | 2.671 | 30.176 | 68.489 |
| Paired | 17.333 | 76.681 | 2.242 | 21.077 | 77.802 |
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
Each hand has a baseline against a random hand: 62.72% for ATo, 59.74% for KTo. Here the change is +11.45 and -33.91 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 74.174 | 62.722 | +11.452 | 1.18258 |
| ATo, rainbow, ten or higher | 70.249 | 62.722 | +7.527 | 1.12001 |
| ATo, rainbow, nine or lower | 85.734 | 62.722 | +23.012 | 1.36689 |
| ATo, two-tone | 73.483 | 62.722 | +10.761 | 1.17157 |
| ATo, monotone | 68.489 | 62.722 | +5.767 | 1.09195 |
| ATo, paired | 77.802 | 62.722 | +15.080 | 1.24043 |
| KTo, all flops | 25.826 | 59.739 | -33.913 | 0.43231 |
| KTo, rainbow, ten or higher | 29.751 | 59.739 | -29.988 | 0.49802 |
| KTo, rainbow, nine or lower | 14.266 | 59.739 | -45.473 | 0.23881 |
| KTo, two-tone | 26.517 | 59.739 | -33.222 | 0.44388 |
| KTo, monotone | 31.511 | 59.739 | -28.228 | 0.52748 |
| KTo, paired | 22.198 | 59.739 | -37.541 | 0.37158 |
Does a shared suit matter?
Split by suits, the deals give ATo 74.28% when the hands overlap in a suit and 73.82% when they do not. ATo does better with a shared suit, by 0.46 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | KTo wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 73.267 | 2.018 | 24.715 | 74.276 |
| No shared suit | 24 | 22.22 | 72.865 | 1.905 | 25.230 | 73.818 |
How often this matchup comes up
Exactly 108 specific deals fit this matchup in one seat order, which is 0.0066% of 1,624,350; both orders together give 216, or 0.0133%.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. ATo is worth $148.34 on average (+$48.34); KTo is worth $51.66 (-$48.34).
A thousand deals look like this: ATo takes 732, KTo takes 248, 20 are ties.
The same matchup from the other side
KTo against ATo adds nothing new: it is 25.83% for KTo and 74.17% for ATo, the same figures reversed.
Keep exploring
Try AsTh against KdTc in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
Method: exact enumeration. The 108 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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