This Guy
United States Durham North Carolina

I'm working on a 2 player game about taking resources, each of which has 4 aspects with 23 values each: 123+abc+pdq+xy. So one resource might have the aspects 2bdx. This yields 54 unique resources. Players draw one resource to represent themselves during the game, leaving 52 resources up for grabs throughout the game. This is all good.
When trying to take a resource, I used to give you a bonus based on how many aspects you had in common with the resource: which meant you would get +0 to +3. When you won the resources, its point value was equal to the number of matches the resource had with your opponent. This calculation seemed to be too chunky, and some other nice mechanisms I've put in place have made bonuses too high.
Instead of a bonus, I am considering making it so you get a malus to your action which is equal to the number of misses you have with the resource, which is also the point value of the resource. So a resource with which you have no matches would give you 4 to your grab, but be worth 4 points if you succeed.
I need help verifying the number of maluses this system would create. Manually trying to do this, I came up with: 07 one point resources 17 two point resources 20 three point resources 09 four point resources (you and your opponent should both knock the same point value out of each other's pool)
I'd appreciate somebody posting the math, as I'm incredibly deficient there.
Thanks in advance.


Matt Davis
United States New Concord Ohio

I count:
7 1pointers 18 2pointers 20 3pointers 8 4pointers
To count these, you can think about what choices you have to make in building one of those things  and just count how many options you had along the way.
To count the 1pointers  each resource has 4 aspects, leaving 7 it doesn't have. To pick a 1pointer, you just pick one of the aspects it doesn't have and switch its corresponding aspect to that  7 ways to do that.
To count the 2pointers  There are two cases here. Maybe it matches the xy aspect and one of the others. Then you have to choose which other one it matches  3 ways to do that. And once you do that, you have 2 choices each for what the nonmatching aspects could be. So that's 3 x 2 x 2 = 12. If it matches two of the 3value aspects, it doesn't match the xy  but we have no choices to make there. So all we choose is which 3value aspect it doesn't match, and which of the two values it is. That's 3 x 2 = 6, for a total of 18.
To count the 3pointers  If it matches the xyaspect, then we get two choices each for the values of the other aspect, which is 2 x 2 x 2 = 8 ways. If it matches one of the 3value aspects, we get 3 choices of which one, and then we have to choose which of the two other values the other two nonmatching aspects should have. (Again, if the xy aspect doesn't match, we have no choice.) So that's 3 x 2 x 2 = 12, for a total of 20.
To count the 4pointers  Nothing matches, so we get to choose the other values for the 3value aspects  we have 2 choices for each of those. So that's 2 x 2 x 2 = 8 resources.


Christopher
Belgium De Panne Bachten de Kupe

Matt is correct , and faster than me . (I just finished my prepwork on a piece of paper and wanted to upload it, when I saw his answer.)


This Guy
United States Durham North Carolina

Thanks, gang.



