KK vs AQo pocket kings against ace-queen offsuit
All-in before the flop, pocket kings wins 71.6% of boards, ace-queen offsuit wins 28.0%, and 0.4% split the pot. KK is a 2.54 to 1 favourite. These are not samples: the engine dealt every one of the 1,712,304 possible five-card boards for each of the 4 ways the suits can line up, and the working is below.
Equity counts a split pot as half a win for each side, which is why the two equities add to 100% and the two win rates do not.
A pair against one higher and one lower card
Only the higher card beats the pair by pairing. The lower card has to make two pair, trips or better to get there, so this is closer to pair against pair than to a coin flip.
Suits change it by 0.74 points
There are 72 ways to deal KK against AQo without the two hands sharing a card, and they fall into 4 patterns once you ignore which suit is which. Best case for KK is 72.16% (for example K♣K♦ against A♥Q♣), worst is 71.42% (K♣K♦ against A♣Q♥). The headline number is the average over all 72, weighted by how many deals share each pattern.
| Example deal | Suits in common | Deals like it | KK wins | Split | AQo wins | KK equity |
|---|---|---|---|---|---|---|
| K♣K♦ vs A♥Q♣ | K–Q | 24 of 72 | 1,231,930 | 7,228 | 473,146 | 72.16% |
| K♣K♦ vs A♣Q♦ | K–A, K–Q | 12 of 72 | 1,228,029 | 8,600 | 475,675 | 71.97% |
| K♣K♦ vs A♥Q♠ | none | 12 of 72 | 1,223,243 | 5,855 | 483,206 | 71.61% |
| K♣K♦ vs A♣Q♥ | K–A | 24 of 72 | 1,219,342 | 7,227 | 485,735 | 71.42% |
Click any deal to run it in the equity calculator, which counts the same boards in your browser, or add a third hand, a flop or a dead card to it.
How each hand wins
The made hand the winner shows down with, as a share of all boards. KK wins most often with two pair (27.4% of boards); AQo with two pair (10.9%). Splits happen when both hands play the same five cards or make the same hand, mostly straights.
| Made hand | KK wins with it | AQo wins with it | Split with it |
|---|---|---|---|
| Pair | 22.10% | 8.92% | – |
| Two pair | 27.41% | 10.94% | – |
| Three of a kind | 10.80% | 2.62% | – |
| Straight | 0.64% | 2.07% | 0.34% |
| Flush | 1.44% | 1.35% | 0.07% |
| Full house | 8.29% | 1.95% | – |
| Four of a kind | 0.89% | 0.14% | 0.00% |
| Straight flush | 0.01% | 0.01% | 0.00% |
| Total | 71.58% | 28.00% | 0.42% |
When calling with AQo is right
If you call an all-in of S with AQo and know you are up against exactly KK, you win 28.21% of a pot that holds 2S plus whatever dead money D was already in the middle (blinds, antes, earlier bets). Calling breaks even when 28.21% × (2S + D) = S, so D ÷ S = 1 ÷ 0.2821 − 2 = 1.545. A 10 bb shove needs at least 15.4 bb of dead money before calling it with AQo stops losing chips. Nobody shows you their hand, though: against a real shove you are calling a range, and the push/fold charts already account for it.
Open this as a spot: AQo (dealt as A♥Q♣, the most common suit pattern) facing a 10 bb all-in with 2.5 bb already in the middle, against a range of exactly KK. The calculator samples runouts rather than dealing all of them, so expect its equity to land within a few tenths of a point of the exact figure for that deal. Change the pot, the bet or the range and it reprices.
Each hand has its own page with its equity against all 169 starting hands and its push/fold range at every stack depth.
More with KK or AQo
Other pair vs one overcard matchups
- Exhaustive, not sampled. With four cards dealt, 48 remain, and there are C(48, 5) = 1,712,304 five-card boards. For each suit pattern our Rust engine (the same WebAssembly file the trainer runs) evaluated both seven-card hands on every board and counted wins, splits and losses. The board counts in the suit table are exact; anyone with an enumerator can reproduce them digit for digit.
- Suit patterns. Two deals are the same pattern when one becomes the other by renaming suits (clubs to hearts, say), which cannot change who wins. Each pattern is enumerated once and weighted by how many of the 72 deals it stands for.
- Cross-check. The site's independent Monte Carlo matrix (200,000 random boards per matchup, used on the starting-hand pages) has KK at 71.92% here, 0.13 points from the exact figure. The build fails if any matchup disagrees by more than 0.4 points.
- All-in preflop only. This is the equity when the money goes in before the flop and five cards are dealt with no more decisions. It says nothing about how the hands play when there is betting left.
- Raw data: kk-vs-aqo.json and the summary matchups.json, built by
tools/build-matchups.mjs.