KQo
39.81%
Wins 39.56%, ties 0.50%
A4s
60.19%
Wins 59.94%, ties 0.50%
KQo against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQo | 39.555 | 0.504 | 59.941 | 39.807 |
| A4s | 59.941 | 0.504 | 39.555 | 60.193 |
KQo, an offsuit hand, plays A4s, a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
The lead is steady rather than large, and the flop still has plenty of say in who wins. The tie share is 0.50%: on those boards the pot is chopped and neither hand wins outright.
KQo ranks number 23 of 169 starting hands, and A4s ranks number 35, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQo | 32,510,000 | 414,000 | 49,266,000 |
| A4s | 49,266,000 | 414,000 | 32,510,000 |
The total is exact: 48 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) |
|---|---|---|---|---|
| KQo | 0.661 | 2.528 | 1.668 | 1.512 |
| A4s | 1.512 | 1.668 | 2.528 | 0.661 |
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
The flop changes the picture. A4s does best on low rainbow flops (nine high or lower), at 78.22%, and worst on rainbow flops topped by a ten or better, at 52.51%. 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 | KQo wins | Ties | A4s wins | KQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 47.432 | 0.122 | 52.446 | 47.493 |
| Rainbow, nine or lower | 7.042 | 21.181 | 1.195 | 77.624 | 21.778 |
| Two-tone | 46.667 | 39.924 | 0.337 | 59.739 | 40.093 |
| Monotone | 5.212 | 42.020 | 2.419 | 55.561 | 43.229 |
| Paired | 17.091 | 34.313 | 0.628 | 65.059 | 34.627 |
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
A random hand would give KQo 61.46% and A4s 59.03%. Against each other the change is -21.65 points for KQo and +1.16 for A4s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQo, all flops | 39.807 | 61.456 | -21.649 | 0.64773 |
| KQo, rainbow, ten or higher | 47.493 | 61.456 | -13.963 | 0.77280 |
| KQo, rainbow, nine or lower | 21.778 | 61.456 | -39.678 | 0.35437 |
| KQo, two-tone | 40.093 | 61.456 | -21.363 | 0.65239 |
| KQo, monotone | 43.229 | 61.456 | -18.227 | 0.70341 |
| KQo, paired | 34.627 | 61.456 | -26.829 | 0.56344 |
| A4s, all flops | 60.193 | 59.034 | +1.159 | 1.01963 |
| A4s, rainbow, ten or higher | 52.507 | 59.034 | -6.527 | 0.88944 |
| A4s, rainbow, nine or lower | 78.222 | 59.034 | +19.188 | 1.32503 |
| A4s, two-tone | 59.907 | 59.034 | +0.873 | 1.01479 |
| A4s, monotone | 56.771 | 59.034 | -2.263 | 0.96167 |
| A4s, paired | 65.373 | 59.034 | +6.339 | 1.10738 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A4s has 59.86% equity, and with none in common it has 60.53%. A4s does better with no shared suit, by 0.67 points.
| Deals | Specific deals | Share of deals | KQo wins | Ties | A4s wins | KQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 39.869 | 0.545 | 59.586 | 40.142 |
| No shared suit | 24 | 50.00 | 39.242 | 0.463 | 60.295 | 39.473 |
How often this matchup comes up
You will meet this exact matchup 0.0059% of the time in a random heads-up deal: 96 of 1,624,350, counting either seat order.
A worked example
Take a $200 pot built from $100 each. A4s' equity of 60.19% is worth $120.38, a $20.38 edge, and KQo's 39.81% is worth $79.62, which is $20.38 under its stake.
Think in thousands: about 599 of 1,000 go to A4s, about 396 go to KQo, and about 5 are chopped.
The same matchup from the other side
A4s versus KQo is this same page seen from the other hand: 60.19% for A4s, 39.81% for KQo.
Keep exploring
The calculator link fills in KsQh against Ad4d, 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 figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 48 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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