[npinsker]

Yes, you can -- I believe the EV was around 3.47 for that. The "greedy" strategy (minimizing the worst-case size of the largest set) also ends up using at most 5 words.

Perhaps unsurprisingly, you can't guarantee at most 4 words.

[Sesse__]

You can get EV of 3.46393 with a guaranteed maximum of five tries. (I don't know whether this bound is tight.)

[pxx]

This bound is not tight. http://sonorouschocolate.com/notes/index.php?title=The_best_...

[Sesse__]

Good to know.

Another possible question is: What is the best strategy minimizing (at any point) _first_ the maximum number of tries, and second the EV (average number of tries over all possible words)? That's subtly different from either answer.