AA
86.87%
Wins 86.69%, ties 0.37%
K9o
13.13%
Wins 12.94%, ties 0.37%
AA against K9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 86.685 | 0.370 | 12.945 | 86.870 |
| K9o | 12.945 | 0.370 | 86.685 | 13.130 |
AA, a pocket pair, plays K9o, an offsuit hand. The pair outranks both of the other hand's cards, which is why the pair is a strong favorite.
AA is a big favorite here before anyone sees a flop. Ties are part of the picture: 0.37% of boards end in a split pot, and each side counts that as half a win.
By strength against a random hand, AA holds place 1 of 169 and K9o holds place 40.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 106,870,000 | 456,000 | 15,959,000 |
| K9o | 15,959,000 | 456,000 | 106,870,000 |
Exact total: 72 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) |
|---|---|---|---|---|
| AA | 6.616 | 1.154 | 7.725 | 0.151 |
| K9o | 0.151 | 7.725 | 1.154 | 6.616 |
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
If you know the kind of flop that came, the numbers shift: AA holds 90.19% on low rainbow flops (nine high or lower) and 81.53% on monotone flops. AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | K9o wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 86.249 | 0.168 | 13.583 | 86.333 |
| Rainbow, nine or lower | 7.042 | 89.663 | 1.059 | 9.278 | 90.193 |
| Two-tone | 46.485 | 86.411 | 0.355 | 13.234 | 86.589 |
| Monotone | 5.151 | 80.663 | 1.731 | 17.606 | 81.529 |
| Paired | 17.334 | 88.602 | 0.007 | 11.391 | 88.605 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
How much does the opponent matter? Compared with its random-hand 85.20%, AA changes by +1.67 points, and K9o, from 57.81%, by -44.68.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 86.870 | 85.204 | +1.666 | 1.01955 |
| AA, rainbow, ten or higher | 86.333 | 85.204 | +1.129 | 1.01325 |
| AA, rainbow, nine or lower | 90.193 | 85.204 | +4.989 | 1.05855 |
| AA, two-tone | 86.589 | 85.204 | +1.385 | 1.01626 |
| AA, monotone | 81.529 | 85.204 | -3.675 | 0.95687 |
| AA, paired | 88.605 | 85.204 | +3.401 | 1.03992 |
| K9o, all flops | 13.130 | 57.812 | -44.682 | 0.22712 |
| K9o, rainbow, ten or higher | 13.667 | 57.812 | -44.145 | 0.23640 |
| K9o, rainbow, nine or lower | 9.807 | 57.812 | -48.005 | 0.16964 |
| K9o, two-tone | 13.411 | 57.812 | -44.401 | 0.23198 |
| K9o, monotone | 18.471 | 57.812 | -39.341 | 0.31950 |
| K9o, paired | 11.395 | 57.812 | -46.417 | 0.19710 |
Does a shared suit matter?
Of the deals of this matchup, 60 share a suit (AA at 87.03%) and 12 do not (86.10%). AA does better with a shared suit, by 0.93 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | K9o wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 86.832 | 0.386 | 12.782 | 87.025 |
| No shared suit | 12 | 16.67 | 85.952 | 0.290 | 13.758 | 86.097 |
How often this matchup comes up
AA against K9o is made up of 72 specific-card matchups in one seat order, 0.0044% of the 1,624,350 ordered deals, and 144 counting both seat orders, 0.0089%.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. AA averages $173.74 from the $200, up $73.74; K9o averages $26.26, down $73.74.
Run 1,000 deals and the tally comes out near 867 for AA, 129 for K9o and 4 ties.
The same matchup from the other side
Read it from the other side: K9o against AA is the same matchup with the numbers swapped, so K9o holds 13.13% and AA holds 86.87%. That address sends you back to this page.
Keep exploring
AsAh against Kd9c 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 72 specific deals of AA against K9o, 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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