Min veninde gætter ikke bare hurtigt, men også rigtigt, når vi spiller kort sammen.

Veninde means female friend, while ven means friend and is often understood as male in contrast with veninde.

So:

• min ven = my friend / my male friend
• min veninde = my female friend

The sentence specifically says the speaker’s friend is female.

Danish possessives agree with the noun that follows.

• min is used with common gender singular nouns
• mit is used with neuter singular nouns
• mine is used with plural nouns

Veninde is a common gender singular noun, so you say min veninde.

Examples:

• min bog = my book
• mit hus = my house
• mine venner = my friends

Gætter is the present tense of the verb at gætte = to guess.

So:

• at gætte = to guess
• jeg gætter = I guess / I am guessing
• hun gætter = she guesses / she is guessing

In this sentence, Min veninde gætter ... means My friend guesses ...

Here, hurtigt and rigtigt are being used as adverbs, not adjectives. They describe how she guesses.

• hurtig = quick, fast
• hurtigt = quickly
• rigtig = correct
• rigtigt = correctly

So:

• gætter hurtigt = guesses quickly
• gætter rigtigt = guesses correctly

A very common pattern in Danish is that an adjective gets -t when used adverbially.

It means not just ..., but also ...

In this sentence:

• ikke bare hurtigt, men også rigtigt
• not just quickly, but also correctly

This structure is very common in Danish and works much like English.

Other examples:

• Han er ikke bare sjov, men også klog. = He is not just funny, but also smart.
• Det er ikke bare svært, men også dyrt. = It is not just difficult, but also expensive.

Because the fixed expression is ikke bare ... men også ...

It is treated as a unit:

• ikke bare = not just / not only

So you normally would not say bare ikke here if you want this meaning.
Ikke bare ... men også ... is the standard pattern.

Here it means correctly.

That is because it is connected to gætter:

• gætter rigtigt = guesses correctly

This is different from another common Danish word, rigtig/rigtigt, which can sometimes mean real, proper, or in some contexts act like really in informal speech. But in this sentence, the meaning is clearly correctly.

Når is used for when in the sense of something that happens repeatedly, generally, or whenever.

Here the idea is:

• whenever we play cards together
• when we play cards together

So når is the natural choice.

A useful contrast:

• når = when / whenever, for repeated or general situations
• da = when, for a specific event in the past

Examples:

• Når vi spiller kort, bliver hun altid ivrig. = When/Whenever we play cards, she always gets excited.
• Da vi spillede kort i går, vandt hun. = When we played cards yesterday, she won.

Because after a subordinating conjunction like når, Danish uses subordinate clause word order.

So you get:

• når vi spiller kort sammen

not

• når spiller vi kort sammen

In a subordinate clause, the subject normally comes right after the conjunction:

• når vi spiller
• fordi hun ved det
• hvis de kommer

This is one of the most important word-order patterns in Danish.

Because spille kort is a fixed idiomatic expression meaning to play cards.

So Danish usually says:

• spille kort = play cards
• not usually spille nogle kort if you mean the game/activity in general

This is similar to English, where we also say play cards without an article.

Sammen means together.

So:

• vi spiller kort = we play cards
• vi spiller kort sammen = we play cards together

It emphasizes that the speaker and the friend are participating together.

Sometimes it may feel optional in English, but in Danish it is very natural to include it when you want to stress shared activity.

The comma before når is especially easy to explain: når vi spiller kort sammen is a subordinate clause, and Danish normally uses commas to separate clauses.

The comma before men også helps mark the contrast between the two parts:

• ikke bare hurtigt
• men også rigtigt

In modern Danish punctuation, commas are strongly tied to clause structure, but commas can also help readability in coordinated phrases like this. You may see such punctuation used to make the sentence clearer.

Yes, but the meaning or emphasis would change.

• Min veninde gætter ikke hurtigt, men rigtigt ... This would sound like: she does not guess quickly, but correctly.
  That is a different meaning.

• Min veninde gætter ikke bare hurtigt, men rigtigt ... This is possible, but less balanced. Danish usually prefers men også after ikke bare.

The full pattern ikke bare ..., men også ... is the most natural way to express not just ..., but also ...

Either can work in English, depending on style.

• gætter hurtigt = guesses quickly
• gætter fast would be unnatural in English, but guesses fast is possible in casual speech

So hurtigt most directly corresponds to quickly, though in natural English translation people might also say fast.

Usually veninde means female friend, not girlfriend in the romantic sense.

If Danish wants to make the romantic meaning clear, it more often uses:

• kæreste = boyfriend/girlfriend/partner

So min veninde is normally understood as my female friend, not my girlfriend. Context can always matter, but the default meaning is female friend.