User blog:OceanSushi/A Mini Research on the Optimal Maruyu Batch Size

Note: Am not the original author, the original author wishes to stay anonymous so I am posting this on his behalf.

TL;DR for people who are confused or too lazy to read: FEEDING-MARUYUS-IN-BATCHES-OF-TWO MASTER RACE. If you are risk-adverse, feel free to feed in batches of 5 as per normal.



Given five different "methods" to feed remodelled Maruyus, each with different success and failure values of giving luck, as can be seen here ( http://kancolle.wikia.com/wiki/Modernization#Luck), assuming success and failure rates of 50% each, the distribution of likely luck obtained from feeding a total of 60 Maruyus using  the same method the entire time, with 60 being the LCM of 1, 2, 3, 4 and 5.



There are five different ways you can feed remodelled Maruyus. You can feed them one by one (you get 1 luck on failure and 2 luck on success, so assuming success rate of 50% that's 1.5 luck per Maruyu). You can feed them in batches of 2 (4 per success, 3 per failure, so average of 1.75 luck per Maruyu). Likewise, you can feed them in threes (5 per success, 4 per failure, 1.5 luck per Maruyu), in fours (7 per success, 6 per failure, 1.625 luck per Maruyu), or in fives (guaranteed 8 luck, 1.6 per Maruyu).

The graph is a distribution of the probability of how much luck you would get if you have sixty Maruyus, and you feed them all in batches of a fixed quantity. The x-axis shows the amount of luck obtained (so those on the right are better as you want more luck out of it), whereas the y-axis shows the probability (as can be seen, there is an equal 19.64% chance of getting 97 and 98 luck if you feed in batches of 4). As the chance of you getting 96 luck by feeding in batches of 5 is always 100%, the graph gets vertically cut off at 20% (the maximum value among the four other charts is 19.64%).

Distribution is applied using the Pascal's triangle.