So, the typical Dominion card, if you play
n copies of it, you get its benefit
n times. Monument is a good example. Play one Monument, get $2 and 1 VP; play two, get $4 and 2 VP; and so on.
Some cards have diminishing returns from multiple copies. With Margrave, each one you play gives you +3 cards and +1 buy, but while the first one you play attacks your opponents, the additional copies actually on average help them. So the benefit of playing
n Margraves is less than
n times the benefit of playing one Margrave.
But a few cards have benefits that not only increase if you play multiple copies of them, but increase
quadratically. A couple of these are obvious and fairly well-known:
- If you play one Goons, you can get 2 VP if you use both your buys. If you play two Goons, you can get 6 VP. If you play n Goons, then if you use all your buys you get n2 + Bn VP, where B is the number of buys you have from other sources than Goons.
- If you play one Bridge, then if you use both your buys your total purchasing power increases by $3 in face value. (I.e., you get +$1, buy one card at a $1 discount, and buy a second card at a $1 discount.) But if you play n Bridges, your face-value purchase power increases by n2 + (B+1)n coins.
These are quadratic cards because they give you both an extra buy
and some other bonus
that operates on a per-buy basis. Thus playing more of them both increases the number of times you get the bonus and the amount each instance of the bonus is worth.
A less obvious quadratic card is Bank: playing
n Banks gives you
n2/2 + (
T+1/2)
n coins. This one is less useful because
T is usually substantially larger than
n, whereas for Goons and Bridge
B is usually 1. But it's quadratic for the same reason: it both puts a Treasure into play and gives you a per-Treasure bonus.
What other cards have quadratically increasing effects?