KQs
42.61%
Wins 42.34%, ties 0.54%
A4s
57.39%
Wins 57.12%, ties 0.54%
KQs against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQs | 42.338 | 0.543 | 57.119 | 42.609 |
| A4s | 57.119 | 0.543 | 42.338 | 57.391 |
Each side holds one of the suited hands: KQs and A4s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 14.78 point lead is real, and KQs still takes about 423 of every 1,000 deals outright. Ties are 0.54% of the outcomes here; each tied board gives both hands half the pot.
Among the 169 starting hands, KQs is number 16 and A4s is number 35 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQs | 11,599,000 | 149,000 | 15,649,000 |
| A4s | 15,649,000 | 149,000 | 11,599,000 |
The board total is exact, 16 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| KQs | 0.742 | 2.362 | 1.751 | 1.347 |
| A4s | 1.347 | 1.751 | 2.362 | 0.742 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
Break the boards down by their first three cards and A4s is strongest on low rainbow flops (nine high or lower) (75.72%) and weakest on rainbow flops topped by a ten or better (51.19%). A4s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | KQs wins | Ties | A4s wins | KQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 48.747 | 0.117 | 51.136 | 48.806 |
| Rainbow, nine or lower | 7.042 | 23.709 | 1.147 | 75.144 | 24.282 |
| Two-tone | 46.727 | 43.614 | 0.310 | 56.076 | 43.769 |
| Monotone | 5.273 | 43.526 | 3.447 | 53.027 | 45.250 |
| Paired | 17.091 | 37.209 | 0.629 | 62.162 | 37.524 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Relative to a random opponent, KQs changes by -20.79 points (baseline 63.40%) and A4s by -1.64 points (baseline 59.03%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQs, all flops | 42.609 | 63.400 | -20.791 | 0.67207 |
| KQs, rainbow, ten or higher | 48.806 | 63.400 | -14.594 | 0.76981 |
| KQs, rainbow, nine or lower | 24.282 | 63.400 | -39.118 | 0.38300 |
| KQs, two-tone | 43.769 | 63.400 | -19.631 | 0.69036 |
| KQs, monotone | 45.250 | 63.400 | -18.150 | 0.71372 |
| KQs, paired | 37.524 | 63.400 | -25.876 | 0.59186 |
| A4s, all flops | 57.391 | 59.034 | -1.643 | 0.97217 |
| A4s, rainbow, ten or higher | 51.194 | 59.034 | -7.840 | 0.86720 |
| A4s, rainbow, nine or lower | 75.718 | 59.034 | +16.684 | 1.28262 |
| A4s, two-tone | 56.231 | 59.034 | -2.803 | 0.95252 |
| A4s, monotone | 54.750 | 59.034 | -4.284 | 0.92743 |
| A4s, paired | 62.476 | 59.034 | +3.442 | 1.05831 |
Does a shared suit matter?
When the hands share a suit, A4s holds 59.32%; when they do not, it holds 56.75%. A4s does better with a shared suit, by 2.57 points.
| Deals | Specific deals | Share of deals | KQs wins | Ties | A4s wins | KQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 40.364 | 0.625 | 59.011 | 40.677 |
| No shared suit | 12 | 75.00 | 42.996 | 0.515 | 56.489 | 43.254 |
How often this matchup comes up
Counting specific cards, KQs against A4s appears in 16 of the 1,624,350 ordered heads-up deals (0.0010%), and in 32 when the seats are swapped too (0.0020%).
A worked example
Take a $200 pot built from $100 each. A4s' equity of 57.39% is worth $114.78, a $14.78 edge, and KQs' 42.61% is worth $85.22, which is $14.78 under its stake.
A thousand deals look like this: A4s takes 571, KQs takes 423, 6 are ties.
The same matchup from the other side
The reversed view, A4s against KQs, shows 57.39% for A4s and 42.61% for KQs. It is the same count, so it redirects here.
Keep exploring
The calculator link fills in KsQs against Ah4h, 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of KQs 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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