Learn Hardcore Danish: Hvis jeg var rig, ville jeg købe et lille hus i hver dal. - If I were rich, I would buy a small house in each valley.

Hvis jeg er rig = If I am rich (a real, present-time condition: maybe it’s true, maybe not).
Hvis jeg var rig = If I were rich (clearly hypothetical; I’m not rich, I’m just imagining it).

So var marks the condition as unreal or imaginary, not as a real situation in the present.

Why is the word order ville jeg købe and not jeg ville købe after the comma?

Danish is a V2 language in main clauses: the finite verb must be in second position.

In your sentence, the first clause is a subordinate clause:

Hvis jeg var rig, ...

After this, the next clause is a main clause, and in Danish that triggers inversion:

..., ville jeg købe et lille hus i hver dal.
1st element: (the whole previous clause Hvis jeg var rig)
2nd element: finite verb ville
3rd element: subject jeg

Compare:

Neutral main clause: Jeg ville købe et lille hus i hver dal. (subject first, then verb)
Main clause after a fronted element: Hvis jeg var rig, ville jeg købe ... (verb comes before the subject)

So ville jeg is required here because the main clause is coming after another element (the Hvis-clause).

Could I also say Hvis jeg var rig, jeg ville købe et lille hus…?

No, that would be wrong in standard Danish.

You either use:

Hvis jeg var rig, ville jeg købe et lille hus i hver dal.
(Subordinate clause + inverted main clause)

or (more informal, but common):

Hvis jeg var rig, så ville jeg købe et lille hus i hver dal.
(så acts as the first element, still followed by verb in second position: så ville jeg)

But you do not repeat jeg before ville without inversion:

✗ Hvis jeg var rig, jeg ville købe ... (incorrect)

The main clause after hvis must still follow V2 word order.

What is the difference between hvis and når? Why is it hvis here?

hvis = if, used for conditions that may or may not be true, or for unreal/hypothetical situations.
når = when, used for things that are expected to happen regularly or certainly.

Examples:

Hvis jeg var rig, ville jeg købe et lille hus…
→ Hypothetical; I am not rich.
Når jeg er rig, køber jeg et hus.
→ Suggests I expect to be rich at some point; it’s about a real future.

Your sentence expresses a purely hypothetical situation, so hvis is the correct conjunction.

Why do we use ville here? Is it like “would”?

Yes, ville here functions very similarly to English would in conditional sentences.

In this pattern:

Hvis + past tense, ville + infinitive

you get a hypothetical result:

Hvis jeg var rig, ville jeg købe et lille hus i hver dal.
= If I were rich, I would buy a small house in every valley.

Some contrasts:

Jeg vil købe et hus.
→ I want to / intend to buy a house or I will buy a house (more real intention or prediction).
Jeg ville købe et hus, hvis jeg var rig.
→ I would buy a house if I were rich (depends on a condition, not a real plan).

So ville + infinitive (købe) forms the conditional-like meaning.

Why is it et lille hus and not en lille hus?

In Danish, nouns have grammatical gender, and the article must match the noun:

en = common gender
et = neuter gender

The word hus is neuter, so you must use et:

et hus, et stort hus, et lille hus

Examples for contrast:

en dal, en stor dal, en dyb dal (common gender)
et hus, et smukt hus, et lille hus (neuter gender)

So: et lille hus is correct; en lille hus is wrong.

Why is the adjective lille and not something like lillet to agree with et hus?

The adjective lille is a bit irregular.

Singular indefinite (both genders): en lille dal, et lille hus
Plural (any gender): små dale, små huse

Notice:

You don’t add a -t to lille in neuter singular; it stays lille.
There is no form like lillet hus in standard Danish.

Compare with a regular adjective, e.g. stor:

en stor dal, et stort hus, store dale, store huse

So lille is special: in indefinite singular it’s just lille, regardless of gender.

Why is it i hver dal and not på hver dal?

The preposition depends on the type of place and the mental image of being inside or on something.

i is used for enclosed or 3D spaces: i dalen, i huset, i byen.
på is for surfaces, islands, floors, and some institutions: på bordet, på øen, på første sal, på arbejde.

A valley (dal) is seen as an area you are in, surrounded by higher land, so you say:

i dalen, i hver dal, i de danske dale

So i hver dal is the natural preposition choice here.

Why is it hver dal instead of alle dale? What’s the difference in meaning?

Both are about more than one valley, but the nuance differs:

hver dal = each / every valley, focusing on them individually
- i hver dal → in each valley (one house per valley)
alle dale = all valleys, focusing on them as a group
- i alle dale → in all valleys (could mean houses in all valleys, but doesn’t stress “one per valley”)

Your sentence:

et lille hus i hver dal strongly suggests one small house in each separate valley.

If you said:

et lille hus i alle dale, it would sound odd, because it’s singular (et), but refers to alle (all). You would normally say:
- små huse i alle dale (small houses in all valleys).

Why is it hver dal and not hver dale?

Because hver is always used with a singular noun, never with a plural:

hver dal (singular)
hver dag, hver uge, hver person

You must use:

hver
- singular
alle
- plural

So:

i hver dal = in each valley
i alle dale = in all valleys

Hver dale would be incorrect.

Why is it dal and not dalen in i hver dal?

Danish normally uses the indefinite form of the noun after hver:

hver dal, hver by, hver person

The definite form (dalen) is used in other contexts:

i dalen = in the valley (a specific valley)
husene i dalen = the houses in the valley

But with hver the pattern is:

hver + indefinite singular noun

So:

i hver dal (correct)
✗ i hver dalen (incorrect)

Why is the word order Hvis jeg var rig (subject before verb) and not something like Hvis var jeg rig?

In Danish:

Main clauses: verb is in second position (V2).
Subordinate clauses (after words like hvis, at, fordi, når): the order is conjunction – subject – verb – ...

So:

Main clause: Jeg er rig. (Subject–Verb–…)
Subordinate clause: Hvis jeg er rig, ... (Conjunction hvis
- subject jeg
  - verb er)

Your clause:

Hvis jeg var rig
→ hvis (conjunction) + jeg (subject) + var (verb) + rig (predicate)

The V2 rule does not apply inside subordinate clauses. That’s why you don’t say Hvis var jeg rig.

Can I add så and say Hvis jeg var rig, så ville jeg købe et lille hus i hver dal?

Yes. That’s very natural and common in spoken and informal Danish.

Hvis jeg var rig, ville jeg købe et lille hus i hver dal.
Hvis jeg var rig, så ville jeg købe et lille hus i hver dal.

Both are correct. Så works like a little linking word (“then”) and becomes the first element of the main clause:

..., så ville jeg købe ...
1st element: så
2nd element: ville (finite verb)
3rd element: jeg (subject)

It doesn’t change the meaning much; it just makes the connection between condition and result a bit more explicit.