Three gives a strong advantage over two for the reasons I said. Those are really important reasons and need to be carefully understood by anyone with 1 or 2 cards. So I would make sure the person understands the ones I gave already to start with.
But in addition, there has been a less definable yet anecdotally confirmed advantage for having three cards. Aside from the scoring factors I mentioned earlier (e.g. number of zeroes on your open accounts), there seems to be a general but significant advantage to having three cards over two. FICO just seems to like it better. (4, 5, 6, cards etc. are also fine.)
I am not surprised that the models might work that way. Maybe this analogy will help. If you are applying for a position at a company, or for admission to a grad school program, they will likely ask for recomendations. If you can only find one person to attest to your great qualities, that's nice but also a little worrisome. Two would be a lot better -- but still if you can only find two colleagues or professors, that's also a bit of a concern. Three recomendations is often the number an admissions or HR office settles on. Once you are able to supply three really good ones, 4, 5, 6 etc. would be more like overkill and they don't require those.
Perhaps FICO works a bit that way. When a person has only one card, even if he's had it a long time, it's like only having one person who can attest to your great qualities (i.e. your ability to handle revolving credit). Having two different cards is a lot better. It shows you can manage two different cards, make payments, keep track of the charges. But still, that's only two. Three cards with a perfect track record would be significantly better still. Here you are are having three different ways you could have screwed up (lates, getting your balances way too high, etc.) -- and yet you are still showing you can handle those perfectly. Once you get beyond three, it's possible or even likely that FICO stops giving you a big advantage for a new card (though of course all new cards still affect the standard scoring factors).
I hope that helps. The bottom line is that there has been reported a significant advantage in the long term to having three cards over two. The evidence for this is anecdotal and what I might call "tribal lore." I give some guesses of my own for why FICO would work that way.
A final note: getting a third card is not ALWAYS the right thing to do. For example, if a person is preparing for a home purchase in the next six months, then getting a third card is probably the wrong thing to do, since it violates the stronger rule of avoiding opening new accounts (especially cards) in the run up to an important loan. Another reason that opening a third card would be wrong is if it would be a source of stress, anxiety, or worse still financial mismanagement for that person.
