KJo
40.22%
Wins 39.97%, ties 0.50%
A3s
59.78%
Wins 59.53%, ties 0.50%
KJo against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KJo | 39.966 | 0.504 | 59.530 | 40.218 |
| A3s | 59.530 | 0.504 | 39.966 | 59.782 |
We compare an offsuit hand with a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. The tie share is 0.50%: on those boards the pot is chopped and neither hand wins outright.
Among the 169 starting hands, KJo is number 26 and A3s is number 38 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KJo | 32,848,000 | 414,000 | 48,928,000 |
| A3s | 48,928,000 | 414,000 | 32,848,000 |
48 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| KJo | 0.673 | 2.502 | 1.680 | 1.486 |
| A3s | 1.486 | 1.680 | 2.502 | 0.673 |
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
A3s prefers low rainbow flops (nine high or lower), where it holds 77.39%, and likes rainbow flops topped by a ten or better least, where it holds 52.10%. 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 | KJo wins | Ties | A3s wins | KJo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 47.839 | 0.129 | 52.032 | 47.904 |
| Rainbow, nine or lower | 7.042 | 22.023 | 1.167 | 76.810 | 22.606 |
| Two-tone | 46.667 | 40.382 | 0.334 | 59.284 | 40.549 |
| Monotone | 5.212 | 42.339 | 2.416 | 55.245 | 43.547 |
| Paired | 17.091 | 34.451 | 0.637 | 64.912 | 34.769 |
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
A random hand would give KJo 60.57% and A3s 58.22%. Against each other the change is -20.35 points for KJo and +1.56 for A3s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KJo, all flops | 40.218 | 60.569 | -20.351 | 0.66400 |
| KJo, rainbow, ten or higher | 47.904 | 60.569 | -12.665 | 0.79090 |
| KJo, rainbow, nine or lower | 22.606 | 60.569 | -37.963 | 0.37323 |
| KJo, two-tone | 40.549 | 60.569 | -20.020 | 0.66947 |
| KJo, monotone | 43.547 | 60.569 | -17.022 | 0.71897 |
| KJo, paired | 34.769 | 60.569 | -25.800 | 0.57404 |
| A3s, all flops | 59.782 | 58.220 | +1.562 | 1.02683 |
| A3s, rainbow, ten or higher | 52.096 | 58.220 | -6.124 | 0.89481 |
| A3s, rainbow, nine or lower | 77.394 | 58.220 | +19.174 | 1.32934 |
| A3s, two-tone | 59.451 | 58.220 | +1.231 | 1.02114 |
| A3s, monotone | 56.453 | 58.220 | -1.767 | 0.96965 |
| A3s, paired | 65.231 | 58.220 | +7.011 | 1.12042 |
Does a shared suit matter?
Split by suits, the deals give A3s 59.44% when the hands overlap in a suit and 60.12% when they do not. A3s does better with no shared suit, by 0.68 points.
| Deals | Specific deals | Share of deals | KJo wins | Ties | A3s wins | KJo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 40.285 | 0.545 | 59.170 | 40.557 |
| No shared suit | 24 | 50.00 | 39.648 | 0.463 | 59.889 | 39.879 |
How often this matchup comes up
How often does it happen? 48 of the 1,624,350 ordered deals (0.0030%) are KJo against A3s, and 96 (0.0059%) if either hand may sit in either seat.
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. A3s averages $119.56 from the $200, up $19.56; KJo averages $80.44, down $19.56.
Think in thousands: about 595 of 1,000 go to A3s, about 400 go to KJo, and about 5 are chopped.
The same matchup from the other side
A3s against KJo adds nothing new: it is 59.78% for A3s and 40.22% for KJo, the same figures reversed.
Keep exploring
The calculator link fills in KsJh against Ad3d, 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
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 48 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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