We usually recommend to perform one query (one API call) per keystroke starting from the first one. The actual number of calls depends a lot on the use-case. Our ranking takes into account both relevance and popularity to suggest the best result first which greatly reduces the number of letters you need to type.
In use-cases where there is a very strong popularity indicator, like the number of followers for TV shows, we usually get the correct result at the first keystroke (b -> breaking bad, d -> dexter). At the other extreme, you may need to type several words.