I kdybych prohrál, chci hrát znovu.

Here, i does not mean and. In this sentence, i means even.

So i kdybych means even if. It adds a concessive idea: the speaker wants to play again despite the possibility of losing.

Kdybych is a conditional form meaning if I were to or if I did.

It is built from:

• kdyby = a conditional marker, roughly if
• -ch = the ending for I

Other common forms are:

• kdybys = if you
• kdyby = if he/she/it
• kdybychom = if we
• kdybyste = if you plural/formal
• kdyby = if they

So kdybych prohrál means if I lost / if I were to lose.

That is normal in Czech. After kdybych, Czech uses the l-participle form, which looks like the past tense form.

So:

• prohrál jsem = I lost
• kdybych prohrál = if I lost / if I were to lose

Even though prohrál looks past, the whole phrase is hypothetical, not simply past. English does something similar with if I lost, which also looks past but can describe a hypothetical situation.

Yes. In the singular, this form agrees with the speaker’s gender.

• kdybych prohrál = said by a male speaker
• kdybych prohrála = said by a female speaker

So the full sentence would be:

• I kdybych prohrál, chci hrát znovu. for a man
• I kdybych prohrála, chci hrát znovu. for a woman

Czech often leaves out subject pronouns when they are already clear from the verb form.

Here:

• kdybych already tells you I
• chci also means I want

So já is unnecessary unless the speaker wants extra emphasis:

• I kdybych prohrál, já chci hrát znovu.

That version is possible, but more emphatic.

These forms are similar, but not the same.

• i kdybych prohrál = even if I lost / even if I were to lose
• jestli prohraju = if I lose
• když prohraju = often when I lose or if I lose, depending on context

The sentence with i kdybych is stronger. It means the speaker wants to play again no matter what, even in the losing scenario.

So the nuance is:

• Jestli prohraju, chci hrát znovu. = If I lose, I want to play again.
• I kdybych prohrál, chci hrát znovu. = Even if I lost, I still want to play again.

Prohrát means to lose. It is a perfective verb, so it refers to a completed result: losing a game, match, round, and so on.

That fits well here, because the speaker is talking about the possibility of one complete loss. If you wanted an ongoing idea, such as even if I were losing, Czech would use a different verb form.

This is a very common Czech pattern:

• chtít + infinitive = to want to do something

So:

• chci = I want
• hrát = to play

Together, chci hrát means I want to play.

Znovu means again.

In chci hrát znovu, it modifies hrát: the speaker wants to play again. Putting znovu at the end is very natural in Czech.

You may also hear:

• chci znovu hrát

That is also possible, but chci hrát znovu is a very normal word order.

Because I kdybych prohrál is a subordinate clause placed before the main clause.

So Czech writes:

• I kdybych prohrál, chci hrát znovu.

The comma separates:

• the conditional subordinate clause
• the main clause

This is standard Czech punctuation.