Čak i ako izgubim, igraću još jedan krug.

In this sentence, čak i ako works as a set expression meaning even if.

The parts are:

• ako = if
• čak = even
• i adds emphasis and helps form the natural expression

So yes, in a sentence like this, it is best to learn čak i ako as one unit.

No. They look similar, but they mean different things.

• čak i ako = even if
• iako = although / even though

So:

• Čak i ako izgubim, igraću još jedan krug. = Even if I lose, I’ll play one more round.
• Iako sam izgubio, igrao sam još jedan krug. = Although I lost, I played another round.

This is a very common thing for learners to confuse.

Izgubim is the 1st person singular present form of the verb izgubiti.

Why this form?

• izgubiti is the dictionary form, meaning to lose in a completed sense
• izgubim = I lose / if I lose
• gubim comes from gubiti, the imperfective verb

The difference is mostly about aspect:

• izgubiti = perfective, one completed loss
• gubiti = imperfective, losing in progress, losing repeatedly, or generally

Here the speaker means if I end up losing this round/game, so ako izgubim is the natural choice.

If you said ako gubim, it would sound more like if I am losing.

Because Serbian usually uses the present tense after words like ako when talking about future conditions.

So:

• ako izgubim = if I lose
• not normally ako ću izgubiti

This is similar to English in a way:

• English: If I lose, I’ll play again
• Serbian: Ako izgubim, igraću ponovo

In Serbian, this is especially common with the perfective present, which often refers to a future completed event in subordinate clauses.

Igraću is future tense.

It is formed from:

• igrati = to play
• ću = I will

In standard Serbian, when the future clitic comes after an infinitive ending in -ti, they are written together:

• igrati + ću → igraću
• raditi + ću → radiću
• pisati + ću → pisaću

So igraću means I will play.

A different word order is also possible:

• Ja ću igrati još jedan krug.

That is also correct, but the structure is different.

Here još jedan means one more or another.

• još can mean still, yet, or more, depending on context
• before a numeral like jedan, it often means one more

So:

• još jedan krug = one more round

This is a very common pattern:

• još jedan minut = one more minute
• još jedna kafa = another coffee
• još jedno pitanje = one more question

In this sentence, krug is in the accusative singular because it is the direct object of igraću.

The speaker is going to play what?
→ još jedan krug

But krug is a masculine inanimate noun, and for many masculine inanimate nouns, the accusative singular looks the same as the nominative singular.

So:

• nominative: krug
• accusative: krug

The whole phrase još jedan krug is accusative singular.

The comma separates the subordinate clause from the main clause.

• Čak i ako izgubim = subordinate clause
• igraću još jedan krug = main clause

When the if-clause comes first, Serbian normally uses a comma before the main clause.

So the punctuation here is standard and expected.

A few letters here are especially important:

• č = roughly like ch in chocolate, but a bit crisper
• ć = a softer sound than č; English does not have a perfect equivalent
• š = sh in shoe
• j = y in yes

So roughly:

• Čak ≈ chak
• još ≈ yosh
• igraću ≈ ee-GRA-chyu, though the ć is softer than English ch

Also, Serbian spelling is generally very phonetic, so once you learn the letters, pronunciation becomes much easier.