I kdyby bylo skóre stejné, chci hrát znovu.

Here i adds the sense of even.

So:

• kdyby = if
• i kdyby = even if

This is a very common combination in Czech. The word i can mean also, too, or even, depending on context. In this sentence, even if is the natural interpretation.

Because kdyby introduces a hypothetical or unreal condition, while když usually introduces a real, factual, or repeated situation.

Compare:

• Když je skóre stejné, chci hrát znovu.
  = When/if the score is the same, I want to play again.
  This sounds more factual or general.

• I kdyby bylo skóre stejné, chci hrát znovu.
  = Even if the score were the same, I want to play again.
  This is hypothetical.

So kdyby is the right choice because the speaker is talking about a possibility, not a known fact.

After kdyby, Czech uses a conditional-type form, not an ordinary present or future tense.

So:

• je = is
• bude = will be
• bylo in kdyby bylo = part of a hypothetical structure, roughly were / was

In this sentence:

• kdyby bylo skóre stejné
  literally behaves like if the score were the same

This use can feel strange to English speakers because Czech uses forms that look a bit like past tense here, but the meaning is not past. It is hypothetical.

Bylo agrees with skóre.

The noun skóre is treated as neuter singular in Czech, so:

• verb: bylo = neuter singular
• adjective: stejné = neuter singular

That is why you get:

• skóre bylo stejné

and not:

• byl stejné
• byla stejná
• byli stejní

Everything is matching the neuter singular noun skóre.

Because it is agreeing with skóre, which is neuter singular.

The adjective stejný changes by gender and case:

• masculine: stejný
• feminine: stejná
• neuter: stejné

Since skóre is neuter singular, the correct form is:

• stejné skóre
• skóre je stejné
• kdyby bylo skóre stejné

So stejné is just the neuter singular form of stejný.

In normal usage, skóre is usually treated as an indeclinable noun, so its form often stays the same in different grammatical roles.

For example, you will commonly see:

• to skóre
• bez skóre
• ke skóre

Even though the endings around it change, skóre itself usually does not.

What matters here is that it is still grammatically treated as neuter singular, which is why the verb and adjective agree with it as bylo and stejné.

Because i kdyby bylo skóre stejné is a subordinate clause, and in Czech subordinate clauses are normally separated by commas.

So the structure is:

• I kdyby bylo skóre stejné, = subordinate clause
• chci hrát znovu. = main clause

This comma is standard Czech punctuation.

Yes. Czech word order is flexible, and this sentence could be rearranged.

For example:

• Chci hrát znovu, i kdyby bylo skóre stejné.

This means basically the same thing.

The version with the subordinate clause first:

• I kdyby bylo skóre stejné, chci hrát znovu.

puts more emphasis on the even if idea right away. It sounds natural and often slightly more dramatic or contrastive.

Because the speaker is stating a real present इच्छा/wish/intention in the main clause:

• chci hrát znovu = I want to play again

Only the condition is hypothetical:

• i kdyby bylo skóre stejné = even if the score were the same

So the sentence mixes:

• a hypothetical subordinate clause
• with a normal present-tense main clause

That is completely normal in Czech.

If you said:

• I kdyby bylo skóre stejné, chtěl bych hrát znovu.

that would mean something more like:

• Even if the score were the same, I would want to play again.

That is possible too, but it is a different nuance.

Yes, both are possible, but they are not always identical in feel.

• znovu = again
• ještě jednou = one more time

So:

• chci hrát znovu = I want to play again
• chci hrát ještě jednou = I want to play one more time

In many contexts, they are very close.
Znovu is a direct match for again, while ještě jednou can sound a bit more like once more.

Yes, hrát is natural here.

Hrát is imperfective and means to play in a general sense. With znovu, it expresses repeating the activity:

• hrát znovu = to play again

There is no common perfective partner used here in the same straightforward way. Czech often uses the imperfective verb with words like znovu when talking about repeating an activity.

So chci hrát znovu is perfectly normal Czech.

Yes, that is possible, but the meaning changes slightly.

• Kdyby bylo skóre stejné, chci hrát znovu.
  = If the score were the same, I want to play again.

• I kdyby bylo skóre stejné, chci hrát znovu.
  = Even if the score were the same, I want to play again.

The version with i is stronger. It emphasizes that the speaker would still want to play again despite that condition.

Yes, it is natural and grammatical.

It has a very standard structure:

• I kdyby... = Even if...
• ..., chci... = main statement

A native speaker would understand it immediately. A very similar sentence with slightly different word order would also be natural:

• Chci hrát znovu, i kdyby bylo skóre stejné.

Both are good Czech.