AJo vs KQo ace-jack offsuit against king-queen offsuit
All-in before the flop, ace-jack offsuit wins 59.5% of boards, king-queen offsuit wins 40.0%, and 0.5% split the pot. AJo is a 1.49 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 7 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.
Interleaved ranks
One hand has the highest card, the other has the two middle ones. The high card wins most boards where nothing pairs, but either middle card pairing beats it unless the high card pairs too, which keeps these closer than the top card suggests.
Suits change it by 0.68 points
There are 144 ways to deal AJo against KQo without the two hands sharing a card, and they fall into 7 patterns once you ignore which suit is which. Best case for AJo is 60.10% (for example A♣J♦ against K♣Q♥), worst is 59.42% (A♣J♦ against K♥Q♦). The headline number is the average over all 144, weighted by how many deals share each pattern.
| Example deal | Suits in common | Deals like it | AJo wins | Split | KQo wins | AJo equity |
|---|---|---|---|---|---|---|
| A♣J♦ vs K♣Q♥ | A–K | 24 of 144 | 1,025,133 | 8,010 | 679,161 | 60.10% |
| A♣J♦ vs K♥Q♣ | A–Q | 24 of 144 | 1,025,091 | 8,010 | 679,203 | 60.10% |
| A♣J♦ vs K♦Q♣ | A–Q, J–K | 12 of 144 | 1,020,076 | 9,369 | 682,859 | 59.85% |
| A♣J♦ vs K♣Q♦ | A–K, J–Q | 12 of 144 | 1,020,075 | 9,370 | 682,859 | 59.85% |
| A♣J♦ vs K♥Q♠ | none | 24 of 144 | 1,018,521 | 6,652 | 687,131 | 59.68% |
| A♣J♦ vs K♦Q♥ | J–K | 24 of 144 | 1,013,506 | 8,011 | 690,787 | 59.42% |
| A♣J♦ vs K♥Q♦ | J–Q | 24 of 144 | 1,013,463 | 8,012 | 690,829 | 59.42% |
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. AJo wins most often with pair (26.0% of boards); KQo with pair (15.4%). Splits happen when both hands play the same five cards or make the same hand, mostly straights.
| Made hand | AJo wins with it | KQo wins with it | Split with it |
|---|---|---|---|
| High card | 6.43% | 0.00% | – |
| Pair | 26.03% | 15.39% | – |
| Two pair | 16.56% | 14.40% | – |
| Three of a kind | 3.98% | 3.11% | – |
| Straight | 2.78% | 3.39% | 0.29% |
| Flush | 1.44% | 1.44% | 0.07% |
| Full house | 2.16% | 2.16% | 0.10% |
| Four of a kind | 0.14% | 0.12% | 0.00% |
| Straight flush | 0.01% | 0.01% | 0.00% |
| Total | 59.53% | 40.00% | 0.47% |
When calling with KQo is right
If you call an all-in of S with KQo and know you are up against exactly AJo, you win 40.24% of a pot that holds 2S plus whatever dead money D was already in the middle (blinds, antes, earlier bets). Calling breaks even when 40.24% × (2S + D) = S, so D ÷ S = 1 ÷ 0.4024 − 2 = 0.485. A 10 bb shove needs at least 4.9 bb of dead money before calling it with KQo 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: KQo (dealt as K♣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 AJo. 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 AJo or KQo
| Matchup | First hand | Split | Second hand | Equity bar |
|---|---|---|---|---|
| AJo vs TT | 43.0% | 0.4% | 57.0% | |
| KQo vs JJ | 43.5% | 0.4% | 56.5% | |
| JJ vs AJo | 69.4% | 1.7% | 30.6% | |
| QQ vs AJo | 71.6% | 0.4% | 28.4% | |
| AKo vs AJo | 74.1% | 4.7% | 25.9% | |
| AKo vs KQo | 74.8% | 1.2% | 25.2% | |
| AQo vs AJo | 73.9% | 5.8% | 26.1% | |
| AJo vs ATo | 72.8% | 8.0% | 27.2% |
Other interleaved matchups
| Matchup | First hand | Split | Second hand | Equity bar |
|---|---|---|---|---|
| A5s vs KQo | 60.3% | 0.5% | 39.7% | |
| A2o vs KQs | 54.4% | 0.6% | 45.6% | |
| AQo vs KJs | 59.2% | 0.5% | 40.8% |
- 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 144 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 AJo at 59.70% here, 0.07 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: ajo-vs-kqo.json and the summary matchups.json, built by
tools/build-matchups.mjs.