I Have A Question About Powders Involving Math.

So it takes 1024 T1 powders to make 1 T6 powder.

Suppose I had an equalish amount of every element in my pile of T1 powders,

Spoiler: Exact Numbers

208 Water, 204 Fire, 204 Earth, 204 Air, 204 Thunder

And that I wanted to end up with a T6 Water powder,
Would the chances of me ending up with a T6 Water powder increase if
I split up the powders so that in every powder combination there is at least 1 water powder in there

Spoiler: Example

Or would my odds be better if I just created pure powders?

Spoiler: Example

Oh yeah, you can assume whatever you need to assume to get it solved.

 

too hard 4 me

 

I think either way has the same chances

 

im pretty bad at math but i thoght it only took 256

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ohh crap nvm

 

A fixed amount of water powders always add up to the same amount of next-tier water powders.

 

OK here's some actual math.

Essentially, the final powder's color result can be determined by randomly selecting a starting powder.

Here's a simpler example: There are three blue powder I's and one red powder I. There is a 3/4 chance of getting a blue powder II and a 1/4 chance of getting a red powder II. Note that this result is identical to the result if you randomly picked one of the powders.
The same logic works in this case, just on a larger scale. So, if you only used those 1024 tier 1 powders, you have a 208/1024 chance of getting a blue tier VI no matter in which order you do it. Of course, if other powders came into play (i.e. you had, say, a tier III water that you could use if needed), the situation gets a little more complicated, but I don't feel like doing that.

 

Mfw I realized you need 1024 t1s to make a t6