Possible Chakra Draws

Jeuel's Chakra Guide for Dummies

There's always been this misconception about the chances of getting a certain chakra type on situations of 2v2 and 3v3.
Some say there's a 25% chance to get a certain type. But the truth is, it's only on 1v1.
I want to clarify everything about Chakra Math trough this guide. But there are prerequisites before reading my guide:
1. The ability to read
2. The ability to calculate for percentage ._.
3. The ability to count

If you are missing 1 one of these prerequisites, step out of this topic now. xD

3v3 Situation

In this situation, you get 3 chakra every turn. Since there are 4 chakra types then there should be 4^3 possible draws or 64.
But since there are draws which are mere rearrangements of another, this reduces the number of draws to 20 as listed below:






















Each chakra type appears in 10 draws (possibly more than once) out of 20. Basically, this means that there's a 50% chance to get at least 1 of a certain chakra type on a 3v3 situation.

How about if you want to get either a Tai or a Nin? If you count the possible draws which has either a tai or nin (not necessarily having both of them), you would end up with 16. Thus the chance of getting either a tai or a nin is 16/20 or 80% (Which is very high).

What if you want to get both a tai and a nin? Since 2 chakra out of the 3 you can get is fixed, then only 1 may vary. This 1 chakra can be either of the 4 chakra types. Thus you have 4/20 chance to get both a tai and a nin (that's 20%)

What are the chances of getting 3 gen chakra? By using common sense, there is only 1 draw with 3 gens in it. Thus the chance is 5%.

2v2 Situation

In this situation, you get 2 chakra every turn. Since there are 4 chakra types then there should be 4^2 possible draws or 16.
But since there are draws which are mere rearrangements of another, this reduces the number of draws to 10 as listed below:












Each chakra type appears in 4 draws (possibly more than once) out of 10. Basically, this means that there's a 40% chance to get at least 1 of a certain chakra type on a 2v2 situation.

In this situation, How about if you want to get either a Tai or a Nin? Similar to the 3v3 situation, if you count all draws which either have a tai or nin, you'll see that there are 7. Thus the chance is 7/10 or 70% to get either a tai or nin.

What if you want to get both a tai and a nin in 2v2? With this, you only have a 10% chance

A few clarifications:

nin-nin-tai = nin-tai-nin = tai-nin-nin

This is an example of why there is a reduction in the number of possible draws. A draw can be rearranged in many ways but only mean the same draw.

nin-tai-gen = nin-gen-tai = tai-gen-nin = gen-nin-tai = gen-tai-nin = tai-nin-gen

Similarly, this long chain is just a set of isomers of Gen, Nin and Tai.