41 summons cost $80.

Those 41 summons give a 25% chance to get the limited ssr character in any given limited banner.

Heres the graph of the formula 1-(1-0.007)^x, which is the formula for the chance to get at least 1 of the featured ssr:

Heres the graph for at least 1 of any ssr unit(equation being 1-(1-0.01)^x:

As you can see, the 90% mark is at roughly 240 summons, aka 80*6 = $420. Bad luck here can still mean you get nothing.

Note though that this is the chances of *at least one summon*. Meaning that the chances of getting 2+ ssr units are included in here as well.

The chance of getting 2 or more ssr units would be the chance of getting 1 + chance of getting 2 + chance of 3 + chance of 4 etcâ€¦

In order to find the individual chances of 2 or more, then we would want a binomial distribution. The equation that helps us find out the chances for each particular outcome(number of ssrs = 0,1,2,3,4 etcâ€¦) would look like this:

Where p = chance of success, n = number of summons, and k = number of SSRs, and

(I shouldnâ€™t have to prove this, you can find the proof for it online or better, figure out how to prove it yourself).

From here we can plug in n = 41(given that that is how much $80 will get you), and then we can plug in k = 1,2,3,4,etcâ€¦

Hereâ€™s a graph of outputs for values of k at n = 41:

Most important conclusion is that if youâ€™re making 1 purchase, more often then not you are just straight up buying a 1/4 chance of getting 1 ssr unit, with a very small chance of buying 2. Donâ€™t expect too much.

If you wish to find out more about your specific situation, then feel free to use this(n = summons, k = ssrs, p = probability of obtaining what you want in 1 summon)

https://www.desmos.com/calculator/jnnwfbh1kn

Unfortunately due to this graphing calculator hating factorials, it only goes up to 169 summons(reason for this is because 170! = 7.257416e+306, a number with 306 digits.) Iâ€™ll see if I can find one that goes higher, but until then this one will be the most usable one.

Few more numbers:

For 50% chance to fully awaken a featured, chance up SSR it requires approximately 675 summons. (675/41)*80 = approximately $1317. If you want this to be 80% chance, youâ€™re going to need 1k summons, or $1951 for that.

A ~50% chance of Awakening all of the current SSRs is going to require an investment of 5500 summons, which is going to equal roughly $10731. Note though thatâ€™s the chance of getting them all completely awakened. At that level of spending youâ€™re probably going to get an uneven distribution with some extra duplicates and some ssrs unawakened fully.

In all in order to have a complete collection:

- $10.5k to spend up front.
- $1.6k for every new SSR after that.

@Admin (aka ryan) Iâ€™m not sure why there are priced this way, but itâ€™s your game, and apparently only pandering to the incredibly small number of people that want to spend this amount of money is the way you think is going to maximize profits. Canâ€™t say I agree, but up to you.