KJs
43.00%
Wins 42.73%, ties 0.54%
A3s
57.00%
Wins 56.73%, ties 0.54%
KJs against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KJs | 42.725 | 0.544 | 56.731 | 42.997 |
| A3s | 56.731 | 0.544 | 42.725 | 57.003 |
Here suited hands face each other, KJs on one side and A3s on the other. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. A split pot comes up on 0.54% of boards, so the wins and the equity differ by half of that.
Ranked by equity against a random hand, KJs is number 20 of the 169 starting hands and A3s is number 38.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KJs | 11,705,000 | 149,000 | 15,543,000 |
| A3s | 15,543,000 | 149,000 | 11,705,000 |
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) |
|---|---|---|---|---|
| KJs | 0.754 | 2.341 | 1.763 | 1.326 |
| A3s | 1.326 | 1.763 | 2.341 | 0.754 |
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
A3s prefers low rainbow flops (nine high or lower), where it holds 74.91%, and likes rainbow flops topped by a ten or better least, where it holds 50.80%. 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 | KJs wins | Ties | A3s wins | KJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 49.141 | 0.124 | 50.735 | 49.203 |
| Rainbow, nine or lower | 7.042 | 24.526 | 1.122 | 74.352 | 25.087 |
| Two-tone | 46.727 | 44.036 | 0.310 | 55.654 | 44.191 |
| Monotone | 5.273 | 43.824 | 3.447 | 52.729 | 45.548 |
| Paired | 17.091 | 37.339 | 0.637 | 62.024 | 37.658 |
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 KJs 62.57% and A3s 58.22%. Against each other the change is -19.57 points for KJs and -1.22 for A3s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KJs, all flops | 42.997 | 62.567 | -19.570 | 0.68722 |
| KJs, rainbow, ten or higher | 49.203 | 62.567 | -13.364 | 0.78640 |
| KJs, rainbow, nine or lower | 25.087 | 62.567 | -37.480 | 0.40096 |
| KJs, two-tone | 44.191 | 62.567 | -18.376 | 0.70630 |
| KJs, monotone | 45.548 | 62.567 | -17.019 | 0.72799 |
| KJs, paired | 37.658 | 62.567 | -24.909 | 0.60188 |
| A3s, all flops | 57.003 | 58.220 | -1.217 | 0.97910 |
| A3s, rainbow, ten or higher | 50.797 | 58.220 | -7.423 | 0.87250 |
| A3s, rainbow, nine or lower | 74.913 | 58.220 | +16.693 | 1.28672 |
| A3s, two-tone | 55.809 | 58.220 | -2.411 | 0.95859 |
| A3s, monotone | 54.452 | 58.220 | -3.768 | 0.93528 |
| A3s, paired | 62.342 | 58.220 | +4.122 | 1.07080 |
Does a shared suit matter?
Does suit overlap move the numbers? A3s has 58.90% when the hands share a suit and 56.37% when they do not. A3s does better with a shared suit, by 2.53 points.
| Deals | Specific deals | Share of deals | KJs wins | Ties | A3s wins | KJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 40.789 | 0.626 | 58.585 | 41.102 |
| No shared suit | 12 | 75.00 | 43.370 | 0.516 | 56.114 | 43.628 |
How often this matchup comes up
Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says A3s gets $114.00 of it on average and KJs gets $86.00.
Think in thousands: about 567 of 1,000 go to A3s, about 427 go to KJs, and about 6 are chopped.
The same matchup from the other side
A3s against KJs adds nothing new: it is 57.00% for A3s and 43.00% for KJs, the same figures reversed.
Keep exploring
Try KsJs against Ah3h in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
This is an exact count with no sampling. For the 16 ways to deal one KJs and one A3s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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