With first half of the Hinamasturi tower over, and event helpers to be released this coming weekend, I’ve tried to answer the question, “How many copies of Snow White should I exchange?”

*Math warning

First, my assumptions and some possible systemic errors involved in the calculations:

All SE items will be spent after the exchange of the event drop rate helper, hereafter known as Snow Level ups are ignored, you will likely get more free SE from the level ups than the calculations assume, so your hishi mochi count would likely be higher 1 mochi (the normal kind) = 15 SE, via perks trading. 5 mochis can be exchanged for 15 perk up potions; ie 5 mochi = 75 SE, hence the 1:15 mochi:SE conversion I ignore the opportunity cost of trading mochis for helpers or perks; the main opportunity cost being trading for exchange daemons instead Spending SE items also gives XP, which gives soulstones and level ups. So spending on helpers means spending less SE, hence receiving less XP, less level ups, and less soulstones

Definitions

Let the rate of SE : Hishi Mochi conversion be r

Let the number of Hishi Mochi you need be h

Let the number of SE items in terms of mochi units (where 1 mochi = 15 SE) be m

Let the mochi cost of trading Snow be c

Let the total mochi expenditure in terms of SE items plus Snow exchanged be M

The total amount of free SE from regeneration in the last 3 days is 288×3=864

The Equation

With these terms defined, the number total number of mochi (M) required for any number of hishi mochi needed (h) would be :

M= (h – 864*r)/15*r + c

And where there are 2 different rates, r1 and r2, corresponding with different numbers of helpers hence different cost

M1= (h – 864*r1)/15*r1 + c1

M2= (h – 864*r2)/15*r2 + c2

And at hishi mochi acquisition levels where it is equally efficient to use different numbers of helpers (with corresponding different amounts of SE items),

M1=M2

[(h – 864*r1)/15*r1 ]+ c1 = [(h – 864*r2)/15*r2] + c2

And solving the equation for h (you can try this yourself)

h=(c2-c1)*r1*r2*15/(r2-r1)

The Rates

With a reasonably nice equation, let’s plug in numbers for r and c

As we know, the presence of event daemons increases the drop rate of hishi mochi (or at least that’s what Mitama says).

So here are some more assumptions:

Base drop rate without any helper or event daemon is 1SE:1 hishi mochi Event daemons that ‘slightly’ increase drop rate do so by 2% Event daemons that ‘moderately’ increase drop rate do so by 5% Snow increase drop rate by the stated %: 1 copy 33%, 2 copy 49.75%, 3 copy 66.5%, 4 copy 83.25%, 5 copy 100% Where multiple event daemons and helpers are present, their boosts are additive rather than multiplicative

Hence:

No Ohina, No Snow r=1.13, c=0

No Ohina, 1 Snow r=1.46, c=50

No Ohina, 2 Snow r=1.6275, c=100

No Ohina, 3 Snow r=1.795, c=150

No Ohina, 4 Snow r=1.9625, c=200

No Ohina, 5 Snow r=2.13, c=250

Ohina, No snow r=1.18, c=0

Ohina, 1 Snow r=1.51, c=50

Ohina, 2 Snow r=1.6775, c=100

Ohina, 3 Snow r=1.845, c=150

Ohina, 4 Snow r=2.0125, c=200

Ohina, 5 Snow r=2.18, c=250

Example

So in a case where you have 1 copy of Ohina, after ranking first half, and is considering exchanging 1 copy of Snow White, and would like to find the level at which the purchase of Snow with Mochis is redeemed by the number of items saved, you would use:

r1=1.18, c1=0

r2=1.51, c2=50

And plugging those numbers into this formulae h=(c2-c1)*r1*r2*15/(r2-r1)

h=(50-0)*1.18*1.51*15/(1.51-1.18)=4050 (rounded up to nearest whole number)

So what does this mean?

This h value means that at a target of 4050 hishi mochi to be farmed, you will spend equal amounts of mochis if you went and traded mochis for perks and spent SE items only, as with a scenario where you spent some of the mochi exchanging for 1 copy of Snow White and the remainder as SE items.

And because the more SE items you spend, the more significant the increase in drop rate is, any hishi mochi targeted above 4050, you would be definitely more efficient with the helper than without.

Results

So after crunching some numbers, the conclusion (assuming the SE:Hishi Mochi conversion rate listed above)

Number of Snow White recommended based on Hishi Mochi required:

In the case of No Ohina

No Snow: h<3750

1 Snow: 3750<h<10640

2 Snow: 10640<h<13081

3 Snow: 13081<h<15774

4 Snow: 15774<h<18717

5 Snow: h>18717

In the case of Ohina acquired

No Snow: h<4050

1 Snow: 4050<h<11342

2 Snow: 11342<h<12475

3 Snow: 12475<h<16626

4 Snow: 16626<h<19645

5 Snow: h>19645

Conclusion

So, there you are, the number of Snow Whites you should get would depend on your event farming goals and whether you have acquired Ohina as a drop rate helper from the first half or not.

Does that mean that everyone needing 15k hishi mochi should purchase 3 copies of Snow White? Of course not! If you are short on mochi but can afford to purchase more tonics, then you may well choose to spend the tonics instead of spending mochi. Conversely, if your target is merely 3k more hishi mochi, but you are item poor and have lots of mochi to spare, purchasing Snow in that case is not wrong either, just less efficient.

Generally, for reasonable levels of Hishi Mochi farming, you can’t go too wrong with the purchase of 1 copy of Snow White; after all, Snow White still functions as great bonding material for the Tower Boss, Ravenna.

And of course, the efficient levels of the number of helpers vary a great deal based on what I assume the conversion rate of SE to Hishi Mochi to be. If you find that you are getting much better (or much worse) rates than the numbers I’ve used, feel free to plug the rates that you’ve found from your own empirical data into the equation, and find your own efficient level of hishi mochi farming for the number of Snow White you plan to exchange for.

P.S. I’m not a mathematician, or even a math major. My last formal Math class was more than 10 years ago, and in the interim I have been using merely basic arithmetic for shopping, mainly. So there may well be errors in the equation or calculation.

Any comment or criticism of the mathematical methodology is welcome in comments below.