Hi there,
First time posting here, since I ran into a tricky problem I haven't been able to solve myself. I quickly tried to search these forums for similar problems but couldn't find any. Any help is much appreciated.
We have three types of "chests" and three types of "gems". Lets call the chest types A, B and C and the gems red, blue and yellow.
A chest has always only one (1) gem inside it. Different chest types have different chances of yielding a certain coloured gem for each individual chest.
Lets say:
Chest A: 50% chance for RED gem, 30% chance for BLUE gem, 20% chance for YELLOW gem
Chest B: 20% chance for RED, 70% for BLUE, 10% for YELLOW
Chest C: 30% RED, 30% BLUE, 40% YELLOW
The actual problem:
Whats the optimal combination of chests to gain expected total of e.g. 30 RED gems, 45 BLUE gems and 40 YELLOW gems?
My progress so far:
We need 30+45+40 = 115 gems, and since each chest yields only 1 gem, the amount of chests we need is >= 115. Closer to 115 the better, since we want to find the optimal combination of chests.
We know that the expected yields for chests are (red/blue/yellow)
A: 0,5 / 0,3 / 0,2
B: 0,2 / 0,7 / 0,1
C: 0,3 / 0,3 / 0,4
I made a simple Excel to try to find the best solution manually and then try to determine a formula of sorts, but no success so far. The best manual result I could find was
0 amount of chest A (0 RED / 0 BLUE / 0 YELLOW)
24 of chest B (4.8 / 16.8 / 2.4)
94 of chest C (28.2 / 28.2 / 37.6)
= 118 chests with 33 RED gems, 45 BLUE gems and 40 YELLOW gems. Yes, I'm using fractions of gems here, even though I probably shouldn't, but this is the best answer I've been able to get so far. I tried to google for similar math problems, but the closest one I found was the Knapsack problem, which does seem to be somewhat similar, but not similar enough at least for me to form a new formula based on it. Oh, and instead of the actual answer, I'm more interested in finding a solution (or solutions?) to solve this and similar problems.
Thank you.
- Mike
First time posting here, since I ran into a tricky problem I haven't been able to solve myself. I quickly tried to search these forums for similar problems but couldn't find any. Any help is much appreciated.
We have three types of "chests" and three types of "gems". Lets call the chest types A, B and C and the gems red, blue and yellow.
A chest has always only one (1) gem inside it. Different chest types have different chances of yielding a certain coloured gem for each individual chest.
Lets say:
Chest A: 50% chance for RED gem, 30% chance for BLUE gem, 20% chance for YELLOW gem
Chest B: 20% chance for RED, 70% for BLUE, 10% for YELLOW
Chest C: 30% RED, 30% BLUE, 40% YELLOW
The actual problem:
Whats the optimal combination of chests to gain expected total of e.g. 30 RED gems, 45 BLUE gems and 40 YELLOW gems?
My progress so far:
We need 30+45+40 = 115 gems, and since each chest yields only 1 gem, the amount of chests we need is >= 115. Closer to 115 the better, since we want to find the optimal combination of chests.
We know that the expected yields for chests are (red/blue/yellow)
A: 0,5 / 0,3 / 0,2
B: 0,2 / 0,7 / 0,1
C: 0,3 / 0,3 / 0,4
I made a simple Excel to try to find the best solution manually and then try to determine a formula of sorts, but no success so far. The best manual result I could find was
0 amount of chest A (0 RED / 0 BLUE / 0 YELLOW)
24 of chest B (4.8 / 16.8 / 2.4)
94 of chest C (28.2 / 28.2 / 37.6)
= 118 chests with 33 RED gems, 45 BLUE gems and 40 YELLOW gems. Yes, I'm using fractions of gems here, even though I probably shouldn't, but this is the best answer I've been able to get so far. I tried to google for similar math problems, but the closest one I found was the Knapsack problem, which does seem to be somewhat similar, but not similar enough at least for me to form a new formula based on it. Oh, and instead of the actual answer, I'm more interested in finding a solution (or solutions?) to solve this and similar problems.
Thank you.
- Mike