Chcę rozdawać karty.

Because Polish, like English, can use a verb meaning to want plus another verb in the infinitive.

• chcę = I want
• rozdawać = to deal / to hand out / to distribute

So the structure is:

• chcę + infinitive

Examples:

• Chcę iść. = I want to go.
• Chcę spać. = I want to sleep.
• Chcę rozdawać karty. = I want to deal cards.

In this sentence, rozdawać is the infinitive.

Chcieć is the dictionary form, meaning to want.
Chcę is the 1st person singular present tense form, meaning I want.

So:

• chcieć = to want
• chcę = I want

A few forms of chcieć:

• chcę = I want
• chcesz = you want
• chce = he/she/it wants
• chcemy = we want
• chcecie = you all want
• chcą = they want

Polish verbs change form depending on the subject, so you usually cannot leave them in the dictionary form in a normal sentence.

In Polish, the subject pronoun is often omitted because the verb ending already shows who is doing the action.

• chcę already means I want

So ja is not necessary.

You could say:

• Ja chcę rozdawać karty.

But that usually adds emphasis, for example:

• I want to deal the cards, not someone else.

In neutral speech, Chcę rozdawać karty is perfectly natural.

This is about aspect, which is very important in Polish.

• rozdawać = imperfective
• rozdać = perfective

Very roughly:

• rozdawać focuses on the process, repetition, or ongoing activity
• rozdać focuses on completing the action

With chcę, both can be possible, but they mean slightly different things:

• Chcę rozdawać karty.
  = I want to be dealing cards / I want to deal cards as an activity.

• Chcę rozdać karty.
  = I want to deal out the cards completely / get the dealing done.

If you are talking about being the dealer in a game, rozdawać karty is very natural.

Karty is in the accusative plural because it is the direct object of the verb rozdawać.

The singular noun is:

• karta = card

Plural nominative:

• karty

Plural accusative:

• karty

So here the form happens to look the same in nominative and accusative plural.

That is very common in Polish for many non-masculine-personal nouns.

Because kart is a different case form.

For karta:

• nominative plural: karty
• accusative plural: karty
• genitive plural: kart

In Chcę rozdawać karty, the cards are the thing being dealt, so you need the direct object, which takes the accusative.

You might see kart in different structures, for example:

• Nie mam kart. = I do not have any cards.
• Talia kart = a deck of cards

So kart is not wrong in general, just not right in this sentence.

In this sentence, yes, most naturally it means playing cards because of the verb rozdawać.

The noun karta can mean several things depending on context, for example:

• card
• ticket/card pass
• menu item
• sheet/page in some contexts
• map in some older or specialized uses

But rozdawać karty strongly suggests dealing cards in a card game.

It can also appear in an idiomatic sense:

• rozdawać karty = to call the shots / to hold power

Still, in a basic learning context, the ordinary meaning is to deal cards.

Yes. Polish word order is more flexible than English because case endings and verb forms carry a lot of grammatical information.

The neutral order here is:

• Chcę rozdawać karty.

You could also say:

• Karty chcę rozdawać.
• Rozdawać karty chcę.

But these alternatives usually sound marked, emphatic, or stylistic.

For everyday neutral speech, Chcę rozdawać karty is the best choice.

Yes, chcę is a tricky word for many learners.

A rough guide:

• ch in Polish sounds like the h in English hotel for most speakers
• c sounds like ts
• ę is a nasal vowel, but at the end of a word it is often pronounced more like e with some nasal coloring, and in everyday speech many speakers pronounce it very simply

So chcę is roughly like:

• hts-ehn or hts-eh

But do not expect an exact English equivalent.

The important thing is that:

• chc- is a tight consonant cluster
• the final ę is not the same as plain e, even if in fast speech the difference may be reduced

A rough pronunciation guide is:

• roz = like ross but with a Polish z that becomes voiceless here, so it sounds closer to ros
• da = dah
• wać = roughly vach or vahch, with ć being a soft consonant, not exactly English ch

Syllable stress in Polish usually falls on the second-to-last syllable, so here the stress is on da:

• roz-DA-wać

So very roughly:

• rohz-DAH-vach

Again, that is only an approximation.

No. Rozdawać can mean to hand out, to distribute, or to give out more generally.

Examples:

• rozdawać ulotki = to hand out leaflets
• rozdawać prezenty = to give out presents
• rozdawać jedzenie = to distribute food
• rozdawać karty = to deal cards

So the verb is broader than just card games.

• dawać = to give
• rozdawać = to give out / distribute / deal

The prefix roz- often adds the idea of spreading something around to multiple people or in multiple directions.

So:

• dawać kartę = to give a card
• rozdawać karty = to deal out the cards to everyone

This is why rozdawać is the natural choice for dealing cards in a game.

Yes. Rozdawać karty can also be idiomatic.

Literally:

• to deal cards

Figuratively:

• to be in control
• to decide how things happen
• to hold the power

For example, in politics or business, someone might say that a person or group rozdaje karty, meaning they are the ones making the important decisions.

So Chcę rozdawać karty could mean either:

• I want to deal the cards or
• I want to be the one in control

Context tells you which meaning is intended.