Corrective connector (anzi)

The connector anzi has two distinct jobs: to correct a negative statement ("on the contrary") or to escalate an affirmative one ("or rather" / "better yet").

On the Contrary

When correcting a negative statement, use anzi to mean "on the contrary."

The dinner will not be modest, on the contrary, we are eating without thinking about the check!
La cena non sarà modesta, anzi, mangiamo senza pensare al conto!
We weren't going to the pub, on the contrary, we improvised and went to the casino.
Non stavamo andando al pub, anzi, abbiamo improvvisato e siamo andati al casinò.

The first half of each sentence sets up a negative expectation (non sarà modesta, non stavamo andando), and anzi introduces the correction.

Better Yet!

After an affirmative statement, anzi acts as an escalating connector. It dials up your original thought to mean "or rather," "in fact," or "better yet." It's perfect for when you change your mind mid-sentence and decide to go bigger:

Let's order the fish, or rather, I want the oysters and the sparkling wine!
Ordiniamo il pesce, anzi, voglio le ostriche e lo spumante!
There are oysters, better yet, we will also have caviar!
Ci sono le ostriche, anzi, avremo anche il caviale!
We can play a little, or rather, let's go to the casino and bet everything!
Possiamo giocare un po', anzi, andiamo al casinò e scommettiamo tutto!

Notice how the plans continually escalate: a simple fish dinner becomes oysters, and playing a little turns into betting everything!