Here's how we usually think of the life-cycle of a Big Money deck:
after building up its money density, BM gains Provinces quickly for a while, but soon it begins to choke on its green and slows down. Somewhere around 5-7 Provinces, it stalls out hard and has a very difficult time buying any more.For evidence of this claim, just look at some simulation results. Here Big Money Unimproved stalls out around 38 VP; Big Envoy around 44 VP:
Of course, this doesn't matter much for a matchup between them. Either BM deck will have essentially secured the win by the time it stalls hard. But it's very relevant if you're playing an alt-VP engine against BM. If you're running a little behind with Goons or Vineyards, then you'd be mad to help your opponent end the game by buying even one or two Provinces for him.
Right?
As it turns out, this stalling is a myth. The claim that BM chokes on its own green is wrong.
The apparent simulator evidence comes from the way the bots handle late game strategy and from the way humans naturally misinterpret the average VP graph.BM simulator strategies start buying Duchies and Estates like crazy when Provinces run low. That's the right play against another BM opponent, but it's no way to buy all 8 Provinces quickly. If we're contemplating an alt-VP only strategy, these sims don't really tell us anything about how quickly our BM opponent will be able to end the game.
Here's a version of BMU that never buys Duchies or Estates. I've matched it against a deck that just sits there:
Without Duchies or Estates, BMU gets to 5 Provinces around T19 and keeps right on going. There's no choking at that point at all. It still appears to be slowing towards the end though. Maybe BMU's hard stall comes around 8 Provinces instead of 5?
Nope. This is a misinterpretation of the average VP curve. We can't think of it as the performance of a single "average" deck. It's actually the average performance of a large number of decks, and the decks that make up that average are changing over time.
While all 1000 simulated decks are contributing to the average at T15, some of the luckiest ones drop out by T25 because they've bought all 8 Provinces and ended the game. The remaining decks are the ones that have been less lucky. That sample bias pulls the average VP curve down. The later it gets, the larger the bias gets.
BMU actually keeps buying Provinces at the same average rate indefinitely. It doesn't stall out at 5 Provinces, nor at 8, nor even much later. To demonstrate this, I altered dominiate to run with 80 Provinces instead of 8. Even the luckiest decks won't be removed from the average in 60 turns, so we can see what BMU does in the long run without that sample bias:
Et voilà. BMU gains at a constant rate up to 20 Provinces and beyond, a little more than two turns per Province.
So don't believe the myth that BM chokes in the long run and don't assume that you'll have tons of extra time against BM if you just keep your hands off the Provinces. Instead, expect your BM opponent to pick up another Province every two turns or so right up to the end.
