Squared Scoring in Games

February 22nd, 2012
Many games have squared scoring, like the Palace Guard in Guillotine:

Each Palace Guard is worth a number of points equal to the number of Palace Guards in your score pile (including this one)
In Seven Wonders the science cards work like the same way. In Dominion the "Duke/Duchy" combination is similar but more complex. [1] I've always thought just "oh, they're really good if you have a lot, but not so good if you only have a few". This is reasonable for the beginning of the game, but towards the end when deciding whether to take one of these or something else you need to look at the marginal benefits. How much better is one more? I made a table:
cards total value marginal value
1 1 1
2 4 3
3 9 5
4 16 7
5 25 9
6 36 11
7 49 13

[1] Each Duchy is 3 points. Each Duke is a point for each Duchy you have.

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