An American native speaker would certainly understand and not raise an eyebrow at using “both” in this context, even though technically it means two not three.

An American native speaker would certainly understand and not raise an eyebrow at using “both” in this context, even though technically it means two not three. Using “thrice” is sort of archaic and formal (like you mentioned) and people would maybe make a good natured joke about being “fancy” if you used the word “thrice” often in conversation. Oddly though twice has none of the baggage of thrice, and is used all the time. My four year old knows and uses twice, but doesn’t know what thrice means.