KQs
42.69%
Wins 42.42%, ties 0.55%
A3s
57.31%
Wins 57.03%, ties 0.55%
KQs against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQs | 42.415 | 0.554 | 57.031 | 42.692 |
| A3s | 57.031 | 0.554 | 42.415 | 57.308 |
Each side holds one of the suited hands: KQs and A3s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A3s is ahead, but KQs is far from dead: it takes 424 of every 1,000 deals outright. About 0.55% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
For context, KQs sits at number 16 of 169 starting hands and A3s at number 38 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQs | 11,620,000 | 152,000 | 15,625,000 |
| A3s | 15,625,000 | 152,000 | 11,620,000 |
Exact total: 16 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| KQs | 0.745 | 2.358 | 1.753 | 1.342 |
| A3s | 1.342 | 1.753 | 2.358 | 0.745 |
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
Low rainbow flops (nine high or lower) are the best for A3s (75.50%); rainbow flops topped by a ten or better are the worst (51.12%). A3s 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 | A3s wins | KQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 48.825 | 0.117 | 51.058 | 48.884 |
| Rainbow, nine or lower | 7.042 | 23.891 | 1.216 | 74.893 | 24.499 |
| Two-tone | 46.727 | 43.703 | 0.321 | 55.976 | 43.864 |
| Monotone | 5.273 | 43.593 | 3.452 | 52.955 | 45.319 |
| Paired | 17.091 | 37.209 | 0.633 | 62.158 | 37.526 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Each hand has a baseline against a random hand: 63.40% for KQs, 58.22% for A3s. Here the change is -20.71 and -0.91 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQs, all flops | 42.692 | 63.400 | -20.708 | 0.67338 |
| KQs, rainbow, ten or higher | 48.884 | 63.400 | -14.516 | 0.77104 |
| KQs, rainbow, nine or lower | 24.499 | 63.400 | -38.901 | 0.38642 |
| KQs, two-tone | 43.864 | 63.400 | -19.536 | 0.69186 |
| KQs, monotone | 45.319 | 63.400 | -18.081 | 0.71481 |
| KQs, paired | 37.526 | 63.400 | -25.874 | 0.59189 |
| A3s, all flops | 57.308 | 58.220 | -0.912 | 0.98434 |
| A3s, rainbow, ten or higher | 51.116 | 58.220 | -7.104 | 0.87798 |
| A3s, rainbow, nine or lower | 75.501 | 58.220 | +17.281 | 1.29682 |
| A3s, two-tone | 56.136 | 58.220 | -2.084 | 0.96420 |
| A3s, monotone | 54.681 | 58.220 | -3.539 | 0.93921 |
| A3s, paired | 62.474 | 58.220 | +4.254 | 1.07307 |
Does a shared suit matter?
Does suit overlap move the numbers? A3s has 59.23% when the hands share a suit and 56.67% when they do not. A3s does better with a shared suit, by 2.56 points.
| Deals | Specific deals | Share of deals | KQs wins | Ties | A3s wins | KQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 40.449 | 0.637 | 58.914 | 40.767 |
| No shared suit | 12 | 75.00 | 43.070 | 0.526 | 56.404 | 43.333 |
How often this matchup comes up
You will meet this exact matchup 0.0020% of the time in a random heads-up deal: 32 of 1,624,350, counting either seat order.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, A3s' average share is $114.62 (a gain of $14.62) and KQs' is $85.38 (a loss of $14.62).
In 1,000 deals of exactly this matchup, expect about 570 won outright by A3s, about 424 won outright by KQs and about 6 split.
The same matchup from the other side
Swap the hands and you get A3s with 57.31% against KQs with 42.69%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
The calculator link fills in KsQs against Ah3h, 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
Each figure is a complete count over boards. Take the 16 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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