AA
82.73%
Wins 82.53%, ties 0.39%
K9s
17.27%
Wins 17.08%, ties 0.39%
AA against K9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 82.532 | 0.390 | 17.078 | 82.727 |
| K9s | 17.078 | 0.390 | 82.532 | 17.273 |
The matchup pits a pocket pair against a suited hand. The pair outranks both of the other hand's cards, which is why the pair is a strong favorite.
A gap this wide means K9s is in trouble before the flop and has few good runouts. 0.39% of boards are ties, so the equity of each hand is its win rate plus half of that.
The hand ranking puts AA at 1 and K9s at 29 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 33,917,000 | 160,000 | 7,018,000 |
| K9s | 7,018,000 | 160,000 | 33,917,000 |
The total is exact: 24 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) |
|---|---|---|---|---|
| AA | 4.789 | 1.212 | 5.855 | 0.209 |
| K9s | 0.209 | 5.855 | 1.212 | 4.789 |
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
AA prefers low rainbow flops (nine high or lower), where it holds 87.42%, and likes monotone flops least, where it holds 76.67%. AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | K9s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 84.063 | 0.165 | 15.772 | 84.145 |
| Rainbow, nine or lower | 7.042 | 86.915 | 1.016 | 12.069 | 87.423 |
| Two-tone | 46.545 | 80.920 | 0.327 | 18.753 | 81.084 |
| Monotone | 5.212 | 75.464 | 2.410 | 22.126 | 76.669 |
| Paired | 17.334 | 85.097 | 0.007 | 14.896 | 85.101 |
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
Start from the random-hand figures, 85.20% for AA and 59.99% for K9s. This opponent changes them by -2.47 and -42.72 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 82.727 | 85.204 | -2.477 | 0.97093 |
| AA, rainbow, ten or higher | 84.145 | 85.204 | -1.059 | 0.98757 |
| AA, rainbow, nine or lower | 87.423 | 85.204 | +2.219 | 1.02604 |
| AA, two-tone | 81.084 | 85.204 | -4.120 | 0.95165 |
| AA, monotone | 76.669 | 85.204 | -8.535 | 0.89983 |
| AA, paired | 85.101 | 85.204 | -0.103 | 0.99879 |
| K9s, all flops | 17.273 | 59.988 | -42.715 | 0.28794 |
| K9s, rainbow, ten or higher | 15.855 | 59.988 | -44.133 | 0.26430 |
| K9s, rainbow, nine or lower | 12.577 | 59.988 | -47.411 | 0.20966 |
| K9s, two-tone | 18.916 | 59.988 | -41.072 | 0.31533 |
| K9s, monotone | 23.331 | 59.988 | -36.657 | 0.38893 |
| K9s, paired | 14.899 | 59.988 | -45.089 | 0.24837 |
Does a shared suit matter?
The suit split reads 83.37% for AA with a shared suit and 82.09% without one. AA does better with a shared suit, by 1.28 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | K9s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 83.151 | 0.432 | 16.417 | 83.367 |
| No shared suit | 12 | 50.00 | 81.913 | 0.348 | 17.739 | 82.087 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are AA against K9s, and 48 (0.0030%) if either hand may sit in either seat.
A worked example
With $100 from each side, the $200 pot is split on average as $165.46 for AA and $34.54 for K9s; the first side gains $65.46 per all-in and the second gives up $65.46.
Think in thousands: about 825 of 1,000 go to AA, about 171 go to K9s, and about 4 are chopped.
The same matchup from the other side
K9s versus AA is this same page seen from the other hand: 17.27% for K9s, 82.73% for AA.
Keep exploring
AsAh against Kd9d 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
Method: exact enumeration. The 24 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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