Introduction Hello! I have been playing on this server for about 3.5 weeks and in that time I have noticed a decent number of people ask about whether to sell AP resets or to gacha for something profitable. Nonetheless, I thought about it during my class lecture and I have decided to put some theoretical analysis on the matter. Although, this can be obvious or nonsense to many but it wouldn't hurt to shed some light on the curious so constructive feedback is appreciated. Now, if you are wondering whether to sell AP resets or attempt to gacha and sell a White Scroll as a means of profit, then allow me to provide you the math and explanation on the odds! Preconditions To start off, there needs to be some assumptions before we start the math to keep it simple and accurate. Assume you and I are noobs and broke ones at best. However, there is the one power that you and I do have, voting for NX. Assume that we are voting exactly every 24 hours. Exclude bossing or other forms of obtaining NX cash as those are continuous variables. Prices will change due to a free market economy but the margin of error shouldn't be too far off. Calculation (Open Spoiler tabs to see calculations) Our main goal is to find the chance to gacha at least one White Scroll and compare it to selling AP resets alone. A White Scroll is sold for 290m on average and an AP reset sells 9m on average. So we need to know how many AP resets needs to be sold to equal the amount of profit of selling a single White Scroll. Spoiler: AP resets to While Scrolls 290m / 9m = 32.222 AP resets = 32 AP resets (rounded cause you cant have 0.22 of an AP reset) We know it takes 32 AP resets to be worth 1 white scroll. Each AP reset is bought is the cash store for 3,100 NX. Spoiler: Total cost of 32 AP resets 32 AP resets * 3,100 NX each = 99,200 NX It cost 99,200 NX to buy 32 AP resets. We can find how many votes it takes by dividing the total 99,200 NX by 8,000 NX we get per vote. Spoiler: Total days it takes to get total cost of NX 99,200 NX / 8,000 NX = 12.4 votes = 13 days of voting (rounded up to 13 because it is the minimum required to achieve 99,200 NX) It takes 13 days of voting to sell as much AP resets to match the profit of selling a single White Scroll. With 13 days of voting we can find how much actual NX we get. Spoiler: Total gachas from total votes 13 votes * 8,000 NX each vote = 104,000 NX 104,000 / 1,000 = 104 Gacha tickets From 13 days of voting, you can purchase up to 104 Gacha tickets. Moving onto probability, we can use binomial distribution to calculate the chances of obtaining at least 1 white scroll out of a 104 attempts. Spoiler: Binomial Distribution Formula N = number of gacha tickets to attempt. x = number of times we get a white scroll. In this case, we want to get at least one. p = The probability that a White Scroll is obtained from Gacha. I do not know the percentage, so in a worst-case scenario, I will assume it is 1% (although it is might likey that it is higher). Probability of 1 White Scroll out of 104 attempts: (104 attempts choose 1 White Scroll) * (.01)^1 White Scroll) * (1 - .01)^(104 attempts - 1 White Scroll) = 0.369 for x = 1 and 0.648 for x equal or greater then 1 Therefore, if we assume the chance to get a White Scroll is from a gacha is 1% then you have a 37% to get EXACTLY 1 White Scroll or 65% to get more then 1 white Scrolls out of 104 Gachas.Conclusion From my calculations, you have a pretty good chance of obtaining 1 or more White Scroll if the worst-case scenario chance is 1% which I personally doubt is that low due to the number of WS in FM. Even if all 104 attempts were not a White Scroll then there is still plenty of other great items obtained from Gacha. I personally would just always gacha and I encourage everybody to try your luck at gacha unless you are in immediate need of money. I would like to appreciate the time you spent reading my first tread and I hope it has enlightened you in some form or way.
Ah I see, I chose 1% because I based it off the amount I would see a WS in the FM so I was under the assumption it was higher. Thanks. Can you clarify what do you mean by that? If I understood correctly, I used WS as a prime example and excluded other gachas. Of course I concluded that other then WS, u can still get other great things. Yeah, woops I forgot about the bundle deal, that just adds all the more reason why Gacha is more effective. sorry about that!
Yeah think about how many people gach everyday. Rough back-of-the-envelope calculation: we have, but maybe 2500? players, all voting for 8k, = 20M NX = ~24000 gach tickets per day. Even if you assume only a third of those get spent at NLC, thats still 8000 tix, and you see maybe 2~3 ws per hour (60ish a day), so < 1%. @Plenty's observations seem in line with this as well. I for one have spent ~300 at NLC with 1 white scroll.
tl;dr SELL RESETS: 9m/reset * 1reset/3100NX = 2900 mesos/1NX GACH (with your assumptions of 1% white scroll, everything else worth 0, which as someone mentioned is unrealistic, but whatevs): 35tix/30kNX * 290M/100tix = 3400 mesos/1NX The biggest benefit of selling resets is if you are under lv50, you cant gach. Also, you could argue it is less variance. Edit: my original post came off as really condescending for some reason lol sorry
Basing off of Plenty's statistic of 7 WS per 1000 gacha tickets and the calculations done by OP, the probability of gaining at least 1 WS is .3531 or 35.31%, which isn't far off from the hypothetical 36.9%. Now, basing off of knuckle's statistic of approximately 1 WS per 300 gacha tickets, the probability of gaining at least 1 WS is .2457 or 24.57%, which is substantially smaller than OP and Plenty's statistic. If we take into account bundle deals (I'm just taking the data directly from sillend; have not confirmed it myself), the calculations from Plenty and knuckle's statistic is: Plenty: 36.41% knuckle: 26.88% It doesn't make too much of a difference from 104 gacha tickets. Of course, who cares right? Gacha > AP resets still hold if you take into account the possibility of obtaining other valuables from gacha.
Hopefully once you get settled more into the community, you can determine which Gachapon is worth going to more than the other.
Would it maybe make a difference if the tix were turned in consecutively? I think @Plenty did all 1000 in 1 run? @knuckle Did u do all 300 in 1 run aswell? Hope that makes sense haha
As best I can tell, everyone who has done large runs of gach tickets (800 tickets or more) turns back about a 1/150 rate of white scrolls, or about a 0.67% rate rather than 1%. White scrolls are also commonly 270-280m atm and are still dropping (they're nearly in freefall - they were 350m a month ago) TLR AP resets are slightly smaller returns than gacha but they're much easier to sell than getting rid of all the random stuf gach is going to turn out. Nothing new here.
