Ok, we don't know the distribution, but even yesterday we were estimating a=50%, b=45%, c=5% which seems somewhat close to what it might be.
What I need help from math nerds (since I haven't done probability in over a decade) is how to figure out when it's better to buy than to roll.
I was running a simulation on how long it took to complete the emotes set, given a starting number of emotes for each category, but that didn't really tell me much other than that it takes a really long time to roll all the emotes
What I would like to figure out is the answer to OP's question. Which strategy requires less points? To answer that question I need to know when to stop rolling.
I've adjusted my simulation to just calculate how many 3xRolls (and therefore points) it would take to obtain just one emote, given a starting position.
Now obviously if you only have emotes of a single category left this is easily determined. If after running a simulation 10k times, the average cost to obtain 1 emote is greater than the cost of that emote, then it's probably better to buy.
But what if there are multiple types of emotes that you still have to unlock? Do you take the average cost of the missing emotes? e.g if you are missing 1 150pt emote and 1 300pt emote, do you set the costToBuy = 300 + 150 / 2 = 225?
Or am I going about this backwards trying to determine these things through simulation, when I could derive the same results using probability?
https://pastebin.com/raw/Qh8gXb2i 
