![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
EVE: Combinations and probabilities.
Nov. 9th, 2005 02:30 pmI have a bit of a puzzle that I'm trying to figure out.
It's EVE related, but a little more ... annoying.
The problem is this.
When building a starbase, one deploys sentry guns as defenses.
You have a choice of small, medium or large (in a mix if necessary).
A small gun does 1 point of damage, a medium 2, and a large 4.
Each gun uses a certain amount of power. A small uses 1, a medium 2, a large 4.
The problem is this. An attacking ship requires at least 5 points damage to destroy it. (It might be more, but a single large gun cannot do the job). (Otherwise it can run away and repair, come back and repeat).
Against a single ship, there's no difference at all in damage dealt. However, when one is faced by an attacking fleet of 10, 20, 30, 40 or 50, is having 40 small guns doing 1 point each, better than 10 large doing 4 each.
Each gun selects a target entirely at random.
Now, the first stage, is figuring out how many different 'sets' there are. Which is fairly easy, it's number of ships to the power of the number of guns. Easy enough really.
The thing I'm having trouble figuring out is how many 'sets' the same ship is picked multiple times.
I started on permutations (N!/(N!-K!)) in the hopes of excluding all the permutations where multiple aren't picked, however that doesn't really help when I'm trying to fit the cases where '3 or more the same' are picked.
To take the simple case, with 3 guns, and 3 ships, and 2 on the same target needed to destroy:
( Read more... )
The purpose of the puzzle, is to figure out if a starbase populated entirely with 'small' guns is 'better' than a starbase populated with 'large' guns. (Intuitively I'm thinking yes, because 'efficiency' of distribution is better, but if more guns will probably lead to evening out of damage, and I need 'spikes' to destroy ships)
It's EVE related, but a little more ... annoying.
The problem is this.
When building a starbase, one deploys sentry guns as defenses.
You have a choice of small, medium or large (in a mix if necessary).
A small gun does 1 point of damage, a medium 2, and a large 4.
Each gun uses a certain amount of power. A small uses 1, a medium 2, a large 4.
The problem is this. An attacking ship requires at least 5 points damage to destroy it. (It might be more, but a single large gun cannot do the job). (Otherwise it can run away and repair, come back and repeat).
Against a single ship, there's no difference at all in damage dealt. However, when one is faced by an attacking fleet of 10, 20, 30, 40 or 50, is having 40 small guns doing 1 point each, better than 10 large doing 4 each.
Each gun selects a target entirely at random.
Now, the first stage, is figuring out how many different 'sets' there are. Which is fairly easy, it's number of ships to the power of the number of guns. Easy enough really.
The thing I'm having trouble figuring out is how many 'sets' the same ship is picked multiple times.
I started on permutations (N!/(N!-K!)) in the hopes of excluding all the permutations where multiple aren't picked, however that doesn't really help when I'm trying to fit the cases where '3 or more the same' are picked.
To take the simple case, with 3 guns, and 3 ships, and 2 on the same target needed to destroy:
( Read more... )
The purpose of the puzzle, is to figure out if a starbase populated entirely with 'small' guns is 'better' than a starbase populated with 'large' guns. (Intuitively I'm thinking yes, because 'efficiency' of distribution is better, but if more guns will probably lead to evening out of damage, and I need 'spikes' to destroy ships)
