so if for example my can is umbued and has elements earth water and wind. if i use five natures again on the same ninja tool will i get other random elements? or i would need to get a new cane ninja tool and use five natures on it to get different elements?
so if for example my can is umbued and has elements earth water and wind. if i use five natures again on the same ninja tool will i get other random elements? or i would need to get a new cane ninja tool and use five natures on it to get different elements?
the li
so i dont need to change the ninja tool i already have? but keep on trying to get the elements that i want right?
if that tool have better stat u should keep it . and just tryiing to get the elements you want.
While it is true that you can just keep refreshing the one you have, to have a complete matching set, it is easier if you had multiple tools. Specifically, if you haven't reforged tools and have no legacy super tools that you have to keep (if you don't know what I mean, you don't and don't need to worry about it), you are far more likely to have a full cycle or close to it if you have 4-5 of EACH tool with a single elemental roll. Then you should try to pick out a set from them... using some kind of graph because it's gonna be confusing af.
Read below if you care about the math behind it.
Consider, for the simple example, of four tools forming a square.
To have a perfect match, you can start with a corner(any corner), 1 will do. The chance of a neighbor one matching to it is 1/5 (only the connecting element matters, the other can be whatever), so on average, you need 5.
The chance that its second neighbor match is also 1/5, but it comes with another condition that the OTHER element of this second neighbor cannot be the same as the 1st neighbor, or the fourth one cannot match both (as it would need same element on both).
The chance that it is NOT the same is 3/4. Ergo, the chance of getting an acceptable result is 1/5 * 3/4, or 3/20, on average you need 6.66 stones to finish this.
And finally, the last stone must have a specific result, which is 1/20, ergo requiring 20.
Overall, this method, on average, requires 32.66 sets of stones. (I know it takes 3 per try, but that unnecessarily complicates the matter, so we talk in sets)
Now, if you take 16 stones and make 4 of each, the chance that you do not have a cycle is tiny.
Specifically, we should consider the sample space:
There exists 20x20x20x20 different possible combinations, 160,000.
How many cycles are there? The first connection have 5 choices, its neighboring connections 4 each. The last is a bit tricky, since depending on if the neighboring connections are the same, could be 3 or 4. Overall, it is: 5*4*3*4 + 5*4*1*3=300
Therefore, the chance of a random set of stone having a cycle is 3/1600, or about 1/500.
Now, go back to the "4 of each", this is actually 4x4x4x4 possible combinations of stone, or 256, half of the "required amount" So you have a pretty good chance. Granted, this is a biased subset, as you have specific pieces, but it's not a huge difference.
And if you were to use 20 sets, 5 each, you are exploring 5*5*5*5 = 625 of the sample space, so on average you'd get a cycle.
So using this method, the amount that you are expected to use is around 20.
There is actually a bigger difference in the real 10-tool world. Specifically, due to 3 connections on most of the tools, the amount required to get a particular one connected is often times 1/20 or so. Ergo the entire thing will take around 150 sets on average.
On the other hand, "x of each" will cover roughly the same proportion of sample space--as it is a covering of possible outcome and not affected by the connections, therefore 5 or 6 of each, 50 or 60 set respectively, will get you close to the result you desire.
So yes, you can keep trying to reroll the same thing. But if you haven't started "working" the tools yet, there are better alternatives.
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