Thread: Eclipse:: Strategy:: Cannons vs computers?

by LetsGetTrivial

Which is better, adding cannon or computer?
I will tackle this question by using the probability of getting at least on hit. Typically this will be done by finding the probability of 0 hits, and subtracting this from 1, i.e., 1 - (misses)^#dice.

Start with one cannon (hits: 1/6)
+ cannon: 1 - (5/6)^2 = 1 - 25/36 = 11/36
+ computer: 2/6 = 12/36
VERDICT: get computer

Start with cannon and computer (hits: 2/6)
+ cannon: 1 - (4/6)^2 = 20/36
+ computer: 3/6 = 18/36
VERDICT: get cannon

Start with two cannons and computer (hits: 20/36)
+ cannon: 1 - (4/6)^3 = 1 - 64/216 = 152/216
+ computer: 1 - (3/6)^2 = 1 - 9/36 = 27/36 = 162/216
VERDICT: get computer

Start with two cannons and two computers (hits: 27/36)
+ cannon: 1 - (3/6)^3 = 1 - 27/216 = 189/216
+ computer: 1 - (2/6)^2 = 1 - 4/36 = 32/36 = 192/216
VERDICT: get computer

Start with two cannons and three computers (hits: 32/36)
+ cannon: 1 - (2/6)^3 = 1 - 8/216 = 208/216
+ computer: 1 - (1/6)^2 = 1 - 1/36 = 35/36 = 210/216
VERDICT: get computer

Further computers provide no benefit unless countered by shields.

Discussion:
I was surprised about how close the probabilities are. Even if an advantage is small, i will take it. The next analysis might us expected value to account for cannons with more damage.

Let me know of any errors.