The reason I think you need to alternate I'd because you can gain cultists AND because you absolutely have to win the duchy war to make up for the fact your getting -10vp
Yeah, this doesn't make any sense. Let me try to say what Varsinor is saying about this in different terms.
Let's say that over the course of a game using your algorithm, the following Cultist/Duchy purchases take place:
Cultist - Duchy - Cultist - Duchy - Cultist - Duchy - Cultist - Duchy - Cultist - Duchy - Duchy - DuchyThen the game ends, and you have, hey look, 7 Duchies! That's awesome. 21 points for you. However, there is a price to pay for those Duchies beyond the money you spend on picking them up, and that is that the earlier Duchies clogged up your deck and appeared as dead cards in your hand
instead of Cultists, which could have been used to further slow down your opponent.
Let's replay that game, then,
keeping the same purchases but reordering them thusly:
Cultist - Cultist - Cultist - Cultist - Cultist - Duchy - Duchy - Duchy - Duchy - Duchy - Duchy - DuchyThere you go. 7 Duchies for the same 21 points. Only this time, with the Cultists entering your deck earlier, you got to play them more often, junking up your opponent's deck quicker and more, and the Duchies didn't slow you down as much, because they only started coming in at the end.
The hard part is figuring out when to stop buying Cultists and start buying Duchies. But a good player WILL know that, and will beat someone hedging his bets by alternating
every time.
This is a fundamental Dominion principle here, applicable in essentially every game. It's why Duchy/Estate openings aren't very good.