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Dominion» Forums » Strategy

Subject: Constant, Quadratic, Linear, and Exponential Growth (Some math, No Strategy) rss

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Hans Scundal
United States
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In nature we see linear and exponential growth all the time. For linear growth, some variable grows about the same amount each time period. Trees grow wider almost linearly. If a variable doubles every x years, then we say that the variable is growing exponentially. The human population has been growing exponentially. I was wondering what kinds of growth are possible in Dominion if you had an infinite number of each card available. It turns out that you can get all of the following kinds of growth: Constant, Quadratic, Linear, and Exponential Growth. Here are some examples.

1) If a player was playing Dominion by himself and he/she used a big money strategy and did not buy victory point cards, then eventually he would have mostly gold in his deck. His maximum buying power would grow until it was nearly constant (15).

2) If we added new treasure cards, then we could exceed 15 buying power. Say there were an infinite list of treasure cards costing 9,12,15,.... Assume a treasure card costing D would have a buying power of D/3 + 1. If we now use the big money strategy, then the buying power grows, but less then linearly. (i.e. the average value of treasure cards in the deck divided by the number of cards in the deck tends toward 0.) (I think the average buying power of treasure cards is proportional to N^(2/3).)

3) If we keep the new treasure cards and used chapels to eliminate treasure cards that were below the deck average, then I am not sure how quickly the buying power of the deck increases, but I think it could be grow exponentially with proper play.

4) If instead the player buys 1/2 council rooms and 1/2 festivals, then his buying power would be a little less than N/2 where N is the number of cards in the deck. The number of cards in the deck would increase by about N/5 each turn. That leads to exponential growth in buying power.

5) If a player only buys the workshop and uses that workshop to get a 50/50 mix of gardens and workshops, then the number of victory points in the deck grows quadratically.


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