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 *n*^{2} + *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 *n*^{2} + (*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

*n*^{2}/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?