That article really overcomplicated matters with its math. However, the results were correct in that you want three more Duchys compared to Dukes.
That said, the biggest flaw I have seen in people who try to execute this strategy (besides them being too slow) is that they attempt to keep that "+3" ratio the entire game. That is not needed and in some cases very bad. You should buy your Duchys first, then buy your Dukes. Duchys will run out much more quickly than Dukes if two people are attempting to do this, and since you want three more, they become much more important.
If you happen to split the Duchys 4/4, you both want one Duke, so there are plenty. If you happen to snag a fifth Duchy, then you want a second Duke, still plenty. Basically, you still want to end the game with a "+3" Duchy to Duke ratio, but get your Duchys first.
There are many other problems with this strategy too. If you want to pull off a successful Duke strategy in a 2P game, here are some things to keep in mind.
1. Is your opponent going Dukes as well? If so, you will most likely tie in "Duke" points and you'll need to change your plan to include Provinces.
2. Are there Colonies in play? If so, Dukes will never (practically) at up to enough points to beat out Colonies... unless...
3. How do you plan to end the game? It is usually bad for you if the game ends by Province or Colony, so you need to figure out the three piles you are going to empty and how you will do so. Duchy should always be one of them, and the other two will most likely cost four or less (exceptions being piles your opponent really likes). Are there any cards that will help you empty those piles such as Bridge, Ironworks, etc. For example, using an Ironworks to get other Ironworks. It doesn't eat up your action and it actually serves a purpose of trying to end the game more quickly for you.
4. How do you plan to actually buy your Duchys? Buying one each turn is too slow if yo start at the same time as your opponent (lets say round
. This means you will either need to start buying early or find a way to get more than one a turn. If you start early, support from Kingdom cards like Scout can make or break your game. Your strategy here should really be based on what your table looks like.
5. Last, but not least, what other Kingdom Victory cards are on the table? It would be really lame for you to pull off your Duke game just to lose to Gardens.
To many players the Duke seems like a mysteriously powerful card if they can just figure out how to use it properly. The problem is, there actually isn't a great way to use it. Most other Kingdom Victory cards are better (some just because they are easier to use) and many times big money is faster with provinces. In my experience, Dukes can win, but it is not because the Dukes are good, it is because what the other player did ended up being bad.