AA
86.25%
Wins 86.06%, ties 0.38%
KTo
13.75%
Wins 13.56%, ties 0.38%
AA against KTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 86.055 | 0.379 | 13.566 | 86.245 |
| KTo | 13.566 | 0.379 | 86.055 | 13.755 |
We compare a pocket pair with 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. The tie share is 0.38%: on those boards the pot is chopped and neither hand wins outright.
AA ranks number 1 of 169 starting hands, and KTo ranks number 33, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 106,094,000 | 467,000 | 16,725,000 |
| KTo | 16,725,000 | 467,000 | 106,094,000 |
The total is exact: 72 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 | 6.270 | 1.162 | 7.371 | 0.159 |
| KTo | 0.159 | 7.371 | 1.162 | 6.270 |
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
The flop changes the picture. AA does best on low rainbow flops (nine high or lower), at 94.96%, and worst on monotone flops, at 80.92%. AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | KTo wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.260 | 83.488 | 0.165 | 16.347 | 83.570 |
| Rainbow, nine or lower | 7.771 | 94.441 | 1.032 | 4.527 | 94.957 |
| Two-tone | 46.485 | 85.638 | 0.365 | 13.997 | 85.820 |
| Monotone | 5.151 | 80.052 | 1.738 | 18.210 | 80.921 |
| Paired | 17.333 | 88.645 | 0.007 | 11.348 | 88.649 |
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
A random hand would give AA 85.20% and KTo 59.74%. Against each other the change is +1.05 points for AA and -45.99 for KTo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 86.245 | 85.204 | +1.041 | 1.01222 |
| AA, rainbow, ten or higher | 83.570 | 85.204 | -1.634 | 0.98082 |
| AA, rainbow, nine or lower | 94.957 | 85.204 | +9.753 | 1.11447 |
| AA, two-tone | 85.820 | 85.204 | +0.616 | 1.00723 |
| AA, monotone | 80.921 | 85.204 | -4.283 | 0.94973 |
| AA, paired | 88.649 | 85.204 | +3.445 | 1.04043 |
| KTo, all flops | 13.755 | 59.739 | -45.984 | 0.23025 |
| KTo, rainbow, ten or higher | 16.430 | 59.739 | -43.309 | 0.27503 |
| KTo, rainbow, nine or lower | 5.043 | 59.739 | -54.696 | 0.08442 |
| KTo, two-tone | 14.180 | 59.739 | -45.559 | 0.23737 |
| KTo, monotone | 19.079 | 59.739 | -40.660 | 0.31937 |
| KTo, paired | 11.351 | 59.739 | -48.388 | 0.19001 |
Does a shared suit matter?
The suit split reads 86.40% for AA with a shared suit and 85.49% without one. AA does better with a shared suit, by 0.91 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | KTo wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 86.199 | 0.395 | 13.406 | 86.396 |
| No shared suit | 12 | 16.67 | 85.339 | 0.299 | 14.362 | 85.489 |
How often this matchup comes up
How often does it happen? 72 of the 1,624,350 ordered deals (0.0044%) are AA against KTo, and 144 (0.0089%) if either hand may sit in either seat.
A worked example
With $100 from each side, the $200 pot is split on average as $172.50 for AA and $27.50 for KTo; the first side gains $72.50 per all-in and the second gives up $72.50.
A thousand deals look like this: AA takes 860, KTo takes 136, 4 are ties.
The same matchup from the other side
One page covers both views. From KTo's side the equity is 13.75%, and from AA's side it is 86.25%.
Keep exploring
The calculator link fills in AsAh against KdTc, 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 72 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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