I find these posts fascinating. Where do all the numbers come from?
X (the number of cards you'll need to draw to cycle through your deck reliably) = 18A. You start off with 10 cards.
B. In a "vanilla" setting (no +buy, no trashing/junking, no gaining), 8 is the maximum number of engine pieces you can buy (including treasure) before your deck is too slow to beat Big Money.
C. Add these two together and you get 18.
D. Note: the heuristic starts off by having you grab your +Actions first in order to ensure that you can't overload yourself on non-terminal draw.
Add 3 to Z if there is trashing.A. 1 turn to purchase your trasher.
B. Your trashers will cost you ~2 turns worth of productivity, either because you are trashing your entire hand (like with Chapel or Count) or you are limiting your buying power (a one-shot trashing takes two cards out of your hand).
Enough +Actions to equal X-5.A. This assumes that your +action source also provides +1 card, as is the case with almost all villages.
B. This assumes that if you take all your purchased terminals + treasure and average them together, it will amount to ~+2 cards each.
C. The statistics and simulations indicate that you need approximately +1.5 actions per terminal in your deck in order to reliably cycle every turn (assuming the conditions of A and B are accurate).
D. In a "vanilla" setting, the heuristic suggests you need +13 actions and +18 cards, which would require 9 terminal/treasures. Multiply that by 1.5, and you get 13.5 which is close enough to the 13 that the heuristic suggests.
E. In a "junking" setting, the heuristic suggests you need +18 actions and +23 cards, which would require 12 terminal/treasures. Multiply that by 1.5 and you get 18 which is equal to the 18 that the heuristic suggests.
F. In a "trashing" setting, the heuristic suggests you need +7 actions and +12 cards, which would require 6 terminal/treasures. Multiply that by 1.5 and you get 9, which is slightly more than the heuristic suggests.
Y = 10 represents the number of turns you have before a well-constructed Big Money deck can start greening. Most good BM decks can reach 4 provinces by turn 15. Which means if your deck can't start to go off consistently by turn 10, you will not consistently beat BM (10 turns plus 4 turns of province purchases).
Count one treasure for every 2 cards in your engine that cost 5 or more. Then count enough treasure cards to bring the total money in your deck up to 10.A. 1 treasure for every 2 cards that cost $5 or more in your engine is statistically optimal to ensure enough purchasing power to buy your components before the "time limit" imposed by Big Money.
B. Having $10 total in your deck ensures that you have ~95% chance to be able to buy a province in the event that your engine "goes off".
Start with Junk attacks. Count 1 if it's vanilla (e.g. Sea Hag/Maurauder), count 2 if it has effects (Mountebank, Witch, Ambassador, Masquerade). Add 5 to Y. A. If your Junk attack is vanilla, you typically only want 1 in your deck if you're running an engine. You'll be cycling enough to ensure that you'll at least tie them in the Junk race.
B. If your junk attack provides value like +cards or +coins, you typically want 2 to ensure that you can play one almost every turn in the early stages of the game.
B1. The risk of terminal collision if you purchase 2 junk attacks is a non-factor. Either your opponent purchases 2 terminal attacks as well, in which case he or she is subject to the same risk you are. Or, he or she only purchases 1, in which case on average you are going to be able to play your terminals ~60% more often and almost certainly win the Junk race.
C. Both the statistics and the simulators indicate that 5 curses/junk will mean your Big Money opponent will take 5 turns longer to reach 4 provinces, hence adding 5 to Y.
Set aside a maximum of 2 gainers. (If you already have gainers in your deck like trash-for-benefit, set aside a maximum of 1). Subtract 2 from Z for each "Pure" Gainer you have in your deck. Subtract 1 from Z for each "limited" Gainer you have in your deck. A. On average, each "gainer" will be played 3 times, but costs 1 turn to buy, for a net effect of 2 fewer turns needed to build your engine.
B. "Limited" gainers will on average get you something useful 2 times, and cost 1 turn to buy, for a net effect of 1 fewer turns needed to build your engine
C. More than 2 "pure" gainers is not helpful because of diminishing returns. (By the time you can buy your 3rd gainer, your cycling speed will be slower and you'll probably only get to play it twice, and the increased odds of terminal collision means that the net effect will be nearly 0).
Add 1 to Y for each discard attack you purchase.A. On average you'll get to play your discard attacks 2-3 times during the window when the discard will actually impact your opponent's speed. The net impact of these attacks will result in one additional turn required for Big Money to reach its goal.