KK
67.03%
Wins 66.80%, ties 0.45%
A4s
32.97%
Wins 32.75%, ties 0.45%
KK against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KK | 66.801 | 0.448 | 32.751 | 67.025 |
| A4s | 32.751 | 0.448 | 66.801 | 32.975 |
KK and A4s are a pocket pair and a suited hand, in that order. The pair is ahead of one card and behind the other, so the board decides how that plays out.
That is a clear edge, 67.03% to 32.97%, but A4s still wins often enough that one hand proves nothing. Split pots make up 0.45% of the boards, and both equity figures count them as half a win each.
Among the 169 starting hands, KK is number 2 and A4s is number 35 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KK | 27,452,000 | 184,000 | 13,459,000 |
| A4s | 13,459,000 | 184,000 | 27,452,000 |
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) |
|---|---|---|---|---|
| KK | 2.033 | 1.497 | 3.053 | 0.492 |
| A4s | 0.492 | 3.053 | 1.497 | 2.033 |
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
The flop changes the picture. KK does best on low rainbow flops (nine high or lower), at 72.65%, and worst on monotone flops, at 62.72%. KK stays ahead on all five textures.
| Flop | Share of flops | KK wins | Ties | A4s wins | KK equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 66.979 | 0.198 | 32.823 | 67.078 |
| Rainbow, nine or lower | 7.042 | 72.033 | 1.226 | 26.741 | 72.646 |
| Two-tone | 46.545 | 64.975 | 0.397 | 34.628 | 65.173 |
| Monotone | 5.212 | 61.491 | 2.459 | 36.050 | 62.720 |
| Paired | 17.334 | 70.930 | 0.010 | 29.060 | 70.935 |
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
The table below sets each hand against its own random-hand baseline: a change of -15.37 points for KK, from 82.40%, and -26.06 for A4s, from 59.03%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KK, all flops | 67.025 | 82.396 | -15.371 | 0.81345 |
| KK, rainbow, ten or higher | 67.078 | 82.396 | -15.318 | 0.81409 |
| KK, rainbow, nine or lower | 72.646 | 82.396 | -9.750 | 0.88167 |
| KK, two-tone | 65.173 | 82.396 | -17.223 | 0.79097 |
| KK, monotone | 62.720 | 82.396 | -19.676 | 0.76120 |
| KK, paired | 70.935 | 82.396 | -11.461 | 0.86090 |
| A4s, all flops | 32.975 | 59.034 | -26.059 | 0.55858 |
| A4s, rainbow, ten or higher | 32.922 | 59.034 | -26.112 | 0.55768 |
| A4s, rainbow, nine or lower | 27.354 | 59.034 | -31.680 | 0.46336 |
| A4s, two-tone | 34.827 | 59.034 | -24.207 | 0.58995 |
| A4s, monotone | 37.280 | 59.034 | -21.754 | 0.63150 |
| A4s, paired | 29.065 | 59.034 | -29.969 | 0.49234 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, KK has 67.31%; looking only at deals where they do not, 66.74%. KK does better with a shared suit, by 0.57 points.
| Deals | Specific deals | Share of deals | KK wins | Ties | A4s wins | KK equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 67.066 | 0.489 | 32.445 | 67.310 |
| No shared suit | 12 | 50.00 | 66.537 | 0.407 | 33.056 | 66.740 |
How often this matchup comes up
The class pair covers 24 combinations of specific cards in a fixed seat order, 0.0015% of 1,624,350, and 48 (0.0030%) in either order.
A worked example
Take a $200 pot built from $100 each. KK's equity of 67.03% is worth $134.06, a $34.06 edge, and A4s' 32.97% is worth $65.94, which is $34.06 under its stake.
Scaled to 1,000 deals, that is roughly 668 wins for KK, 328 for A4s and 4 chopped pots.
The same matchup from the other side
A4s versus KK is this same page seen from the other hand: 32.97% for A4s, 67.03% for KK.
Keep exploring
KsKh against Ad4d 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 24 specific deals of KK against A4s, 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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