One wants the home and the other wants the door left open. By the rule of elements, Cancer is water and Sagittarius is fire, and the rule rejects this pair. Keep that in mind and read on, because the rule answers far less than it seems to.

What's good about this pair is the contrast, used well. Sagittarius gets Cancer out of the house and makes it laugh at things it used to take far too seriously; Cancer gives Sagittarius a place to come back to, which it can't organise on its own and needs more than it admits. When it works, Cancer gets lighter and Sagittarius shows up more, and both notice the difference in themselves.

The table every magazine publishes is simple: fire matches fire and air, earth matches earth and water. It was not invented yesterday, and it has a geometric reason, signs of the same element sit 120 degrees apart, and allied elements sit 60 degrees apart. Those are the trine and the sextile, the two aspects that tradition calls harmonious. The compatibility table is the aspect table applied to a single planet.

It puts half the zodiac on each person's list, which already shows how little information that is. And it can be tested against the numbers. I drew a random sample of 600,000 pairs of birth dates between 1966 and 2025, using the same ephemeris that builds charts on this site, and asked: in the pairs the rule approves, do the other pieces follow along?

In the pairs the rule approves, the Moons match in 49.8% of cases; in the ones it rejects, in 50.0%. There is contact between one person's Sun and the other's Moon in 46.4% of both groups, and contact between Venus and Mars in 46.1% and 46.2%. Between the two charts there are, on average, 26.7 contacts in the approved pairs and 26.6 in the rejected ones.

The columns are the same. Knowing that the rule approves or fails your pair tells you nothing about the other person's Moon, nothing about desire, and nothing about how many contacts the two charts have. And 50.0% is exactly what a coin toss would give you.

That does not make the table false. It makes it small: it describes a trait of temperament, read from a single point on the chart. Using it to decide who to date is reading a book by its title's first letter.

They're 150 degrees apart, the quincunx, and it's the angle of mismatch. There's no declared opposition, there are two ways of being that don't fit together and never become a topic. Sagittarius says what it thinks out loud and moves on; Cancer takes in the whole sentence and holds onto it for the rest of the week. Sagittarius doesn't even remember saying it. And there's a mismatch over presence: for Cancer, the person who loves you is close by; for Sagittarius, the person who loves you doesn't need to keep watch. Each proves its own affection in a way the other doesn't count as proof.

What holds this pair together is Sagittarius's Venus, in Scorpio or in Capricorn, it knows about commitment, and Cancer's Moon, which decides whether Cancer can be alone on a Friday night without it turning into abandonment.

What usually unblocks things: Sagittarius giving notice and making repairs. Giving notice before changing the plan costs ten seconds and saves Cancer's whole week, because what hurts isn't the changed plan, it's the shock. And making repairs when a sentence came out too harsh: a "that came out harsh, sorry" said the same day undoes what would otherwise sit there for months. Cancer, for its part, gains by saying it got hurt instead of going cold, Sagittarius reads no mood at all, and fixes at once whatever it actually hears.

The element rule reads one thing only: the element. Each sign carries two other labels the table ignores, and in both cases they say more about the day-to-day than the element does. The modality, cardinal, fixed or mutable, is the way a person goes into a subject: cardinal starts it, fixed holds it, mutable changes it. And the ruler is the planet that gives the sign its vocabulary.

Cancer is cardinal and ruled by the Moon; Sagittarius is mutable and ruled by Jupiter.

Cardinal with mutable, and the imbalance is large: Cancer starts things that require staying and Sagittarius doesn't stay out of obligation. The arrangement that tends to be left standing is Cancer holding down the base and Sagittarius having room to move, and it works as long as Cancer doesn't start feeling like the home base for someone who only drops by.

The Moon and Jupiter: one piece that protects and one that expands. Jupiter enlarges everything it touches, including speech, and Cancer weighs words by how much they'd weigh if Cancer had said them. It's the root of almost every hurt feeling in this pair, Sagittarius exaggerates out of enthusiasm and Cancer reads the sentence as if it had been measured out.

And there's a similarity few people notice: both are optimists, in opposite ways. Sagittarius thinks it'll work out; Cancer thinks you keep at it until it does. That's why this pair handles a crisis better than it handles routine.

There is one exception to "the table tells you nothing", and it comes down to pure geometry. Venus never moves more than 47.2 degrees from the Sun, it is an inner planet, and from Earth's point of view it stays tied to the Sun's light. Given your sun sign, your Venus can only fall in five signs.

So the distance between two sun signs decides the odds that both Venuses land in the same sign. Measured across the same 600,000 pairs:

When both are of the same sign, which is the conjunction, the two Venuses fall in the same sign in 24.3% of pairs; one sign apart, the semi-sextile, in 19.2%; two apart, the sextile, in 12.9%; three apart, the square, in 5.5%; four apart, the trine, in 0.8%; and five or six apart, the quincunx and the opposition, never.

Cancer and Sagittarius are 150° apart, a quincunx, and that puts this pair in the 0.0% bracket. In other words: your two Venuses almost never land together, and that is the only thing the distance between your Suns actually determines.

Notice what the table does with the element rule: it cannot follows the rule. Pairs the rule fails come out on top of the list, and pairs it approves come out at the bottom. The Venus link is real, and it is geometric, and it is why the compatibility table sometimes seems to work. It works a little, and not for the reason it claims to.

Four pieces that change everything, and that no sun-sign table can reach:

• Each person's Moon. It is the way you feel, need and settle down, the piece that most decides day-to-day life together. It changes sign every two and a half days.
• The Ascendant. It changes every two hours and depends on the city. Two Cancers born on the same day can arrive at a party in opposite ways.
• The house each one falls into on the other's chart. The same Venus in your house 5 and your house 12 is passion in one case and a private matter in the other. This layer needs both people's birth time.
• What each one has already lived. Age, past relationships and the timing of the meeting weigh more than any aspect, and none of it is in anyone's chart.

This crossing is what's called synastry, and it needs both people's date, time and city of birth. Comparing sun signs is what's left when you don't have that.

And the limit stated out loud still holds: astrology decides nothing for anyone, doesn't tell you to stay or leave, and doesn't replace conversation or therapy. It gives you vocabulary. A couple who discover that one Moon needs routine and the other needs novelty have gained a better question than they had before.

And the questions that come up most on this subject, with the short answer: