KQs
45.27%
Wins 45.04%, ties 0.46%
A9o
54.73%
Wins 54.50%, ties 0.46%
KQs against A9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQs | 45.037 | 0.464 | 54.499 | 45.269 |
| A9o | 54.499 | 0.464 | 45.037 | 54.731 |
The first hand is a suited hand; the second is an offsuit hand. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
With only 9.46 points between them, the board decides this matchup far more than the cards in hand. Ties are part of the picture: 0.46% of boards end in a split pot, and each side counts that as half a win.
By strength against a random hand, KQs holds place 16 of 169 and A9o holds place 25.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQs | 37,016,000 | 381,000 | 44,793,000 |
| A9o | 44,793,000 | 381,000 | 37,016,000 |
The total is exact: 48 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) |
|---|---|---|---|---|
| KQs | 0.827 | 2.220 | 1.835 | 1.209 |
| A9o | 1.209 | 1.835 | 2.220 | 0.827 |
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
The flop changes the picture. A9o does best on low rainbow flops (nine high or lower), at 73.43%, and worst on rainbow flops topped by a ten or better, at 49.88%. Watch for rainbow flops topped by a ten or better: on those flops KQs holds the better equity.
| Flop | Share of flops | KQs wins | Ties | A9o wins | KQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 50.057 | 0.118 | 49.825 | 50.116 |
| Rainbow, nine or lower | 7.042 | 26.060 | 1.017 | 72.923 | 26.568 |
| Two-tone | 46.667 | 47.313 | 0.291 | 52.396 | 47.459 |
| Monotone | 5.212 | 46.138 | 2.380 | 51.482 | 47.328 |
| Paired | 17.091 | 39.260 | 0.608 | 60.132 | 39.564 |
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
Relative to a random opponent, KQs changes by -18.13 points (baseline 63.40%) and A9o by -6.04 points (baseline 60.77%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQs, all flops | 45.269 | 63.400 | -18.131 | 0.71402 |
| KQs, rainbow, ten or higher | 50.116 | 63.400 | -13.284 | 0.79047 |
| KQs, rainbow, nine or lower | 26.568 | 63.400 | -36.832 | 0.41905 |
| KQs, two-tone | 47.459 | 63.400 | -15.941 | 0.74856 |
| KQs, monotone | 47.328 | 63.400 | -16.072 | 0.74650 |
| KQs, paired | 39.564 | 63.400 | -23.836 | 0.62404 |
| A9o, all flops | 54.731 | 60.773 | -6.042 | 0.90058 |
| A9o, rainbow, ten or higher | 49.884 | 60.773 | -10.889 | 0.82083 |
| A9o, rainbow, nine or lower | 73.432 | 60.773 | +12.659 | 1.20830 |
| A9o, two-tone | 52.541 | 60.773 | -8.232 | 0.86455 |
| A9o, monotone | 52.672 | 60.773 | -8.101 | 0.86670 |
| A9o, paired | 60.436 | 60.773 | -0.337 | 0.99445 |
Does a shared suit matter?
Two kinds of deal exist here. In 24 of them the hands share a suit and A9o holds 55.21%. In 24 they do not, and it holds 54.26%. A9o does better with a shared suit, by 0.95 points.
| Deals | Specific deals | Share of deals | KQs wins | Ties | A9o wins | KQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 44.541 | 0.505 | 54.954 | 44.793 |
| No shared suit | 24 | 50.00 | 45.533 | 0.422 | 54.045 | 45.744 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 48 are KQs in one seat and A9o in the other (0.0030%); with the seats swapped too, 96 (0.0059%).
A worked example
Take a $200 pot built from $100 each. A9o's equity of 54.73% is worth $109.46, a $9.46 edge, and KQs' 45.27% is worth $90.54, which is $9.46 under its stake.
Over a long run, 1,000 deals split into about 545 for A9o, 450 for KQs and 5 tied.
The same matchup from the other side
One page covers both views. From A9o's side the equity is 54.73%, and from KQs' side it is 45.27%.
Keep exploring
KsQs against Ah9d 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 48 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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