I don't think three merchants is necessary at all, you rarely get three missions you want to use one on anyway. That's especially true after you maxed your stainless steel upgrades.
If a merchant wasn't worth having on your boat, you're probably done with the Ports in the first place.
Get 4 merchants, never let them leave any ships.
Thats just no.
If the voyage is sub-100% you don't want a merchant, better to have a different unit for 100%.
I can see Quy's point though I would be of the opinion when you have basically 'finished' ports presumably you'd be able to 100% most trade good missions (which are kinda the only reason to still be there) so surely you would be wanting a merchant on most voyages at that point.
Absolutely not. Let me give you probability 101 right now. Specific lesson: expected value.
Our goal is to maximize the expected return of each mission. There are two factors contributing to the expected value: the probability of success (p) and the amount returned if successful (x). The relationship between them is simple: the expected return on a voyage, E(V), is equal to the probability of success times the amount returned when successful. Thus, E(V) = px.
We have two scenarios to consider: one with a merchant, one without a merchant. Without a merchant, suppose the best success rate we can get is P, and the expected return is X. With a merchant, the return given success increases to 1.3X. How much does p decrease due to the lack of a merchant? Well, suppose you lose 2k of unit stats (conservative overestimate), and the mission has requirements of 16k (roughly typical, though it doesn't matter much if this changes). Then that changes p from P to 0.875P, and thus E(V) = 0.875P(1.3X) = 1.1375PX. This is a roughly 14% increase in expected return by using a merchant.
Note that as mission requirements increase, it actually becomes more beneficial to use a merchant, as the decrease in p becomes smaller while the increase in x becomes larger.
TLDR: ALWAYS use a merchant, on ALL your voyages, except for voyages for 3 or fewer trade goods, where the effect will be rounded down to nothing.
You wouldn't want to use a merchant if it decreased your success by more than 30% (roughly, 1/1.3 to be precise), but there are no such missions.
Edited by Thorgmir, 27 January 2013 - 08:00 PM.