Learn Romanian: Runda a început și mi-a acceptat pariul. - The round started and he accepted my bet.

Structurally, it could! Romanian frequently drops subject pronouns like el (he) or ea (she). Because the first clause's subject is Runda, a strict word-for-word reading might assume the round did the accepting. However, fluent speakers rely heavily on context: since a round cannot accept a bet, a new, unstated human subject is automatically understood for a acceptat.

Why does the sentence use the pronoun mi- (to me) instead of just saying pariul meu (my bet)?

This is a classic example of the Romanian "Dative of Possession." Instead of using a possessive adjective (pariul meu), Romanian often pairs a dative pronoun (mi-) with the definite form of the noun (pariul). Literally, it reads "he accepted the bet to me." This structure is extremely common in everyday speech and usually sounds more natural to natives than using the possessive adjective.

In English, the verb "start" can mean "to begin something" or "to begin by itself." Is it the exact same for a începe?

Yes, a începe is flexible and maps perfectly to "start" in English here. It can be used intransitively when an event begins on its own (as in Runda a început), or transitively when someone directly initiates an action (such as Arbitrul a început runda - The referee started the round).