Pearz's Chakra distribution Guide (Chakra God Approved :O) - Page 15

That's a wonderful metaphor for explaining multiple instances occurring at the same time... except that we're not pulling the entire combination out of thin air all at once.
The game is not randomly generating all three results at the same time, it's generating them one at a time. One at a time. One at a time, one per draw. Generate, add. Generate, add. Generate, add.
Your "bag" in this case now contains four stones and we draw three times. Their formation afterwards is completely negligible.
Now, my chance of getting the same ones twice in a row? Not as good. Why? The chance of my getting something ELSE is what modifies this. That's IT. This is seen how? This is seen that the chance of my getting it- 1/3, 1/4, 1/5, etc. changes with the /amount of stones in the bag/. The amount of stones in the bag is also expressed as the chance of getting something else.

There are only four possible results for the 1 in 4 draw. A, B, C, or D.
However:
Your expressions are correct if the game is generating the chances in exactly what you have described, a solid list. If the game is doing that then yes, the chances of getting each combination are how you describe using the 64 bag method.

If the game is generating them one at a time as I'm saying than each draw is treated individually as a 1 in four chance and there's no distinction between X and Y where X is what you get on the first draw and Y is the other types because as I said before- dice have no memory, and your chance of getting the same one twice in a row is the same as getting a different one on the second draw. There is no distinction between X and Y when you hit draw two because the random generation has no modifier on it to do so.

If I put the 4 chakra stones in the bag, and take one out, what was my chance of getting that color? 1 in 4. Let's say I picked up red.
I put the red back and shake the bag up. There are now two outcomes.
I draw and don't get a red one. I get another color. What was my chance of getting that color? 1 in 4.
I draw and I get the red again. What was my chance of getting that color? 1 in 4.


We won't solve this argument unless we can be sure of the game's random generation mechanic.

Well.
The only reason this is defying conventional logic in the "one in four" system is because when you attempt a varied draw like that you're changing your chance to a 1 in 2.

For 1 draw of ABC or D, and I only want A, it's a 1 in 4.
For 1 draw of ABC or D, and I want either A or B, it's a 1 in 2.

For 2 draws of ABC or D, and I want an A and an A, my chance is 1/4 into 1/4.
Possible solutions are:
A on draw 1, A on draw 2.

For 2 draws of ABC or D, and I want an A and a B, my chance is 1/2 into 1/4.
Possible solutions are:
A on draw 1, B on draw 2.
B on draw 1, A on draw 2.

What I said before about far reaching probability still applies when you look at the big picture: I.E. Over the entire game. Over the entire game, you will usually see an even spread of chakra.
(For 16 draws, this is most likely.
4 Tai, 4 Nin, 4 Blood, 4 Gen.)

However, your probability of "mixed results occur more" counts when you isolate a draw from the rest of the game/picture.
(For 2 draws, Tai/Nin is more likely than Tai/Tai.)

The longer the game goes on, the more even of a spread you'll see. For one short burst however, for just one draw, that probability is what occurs.

So technically, your probability numbers should decrease as the game goes on right? It doesn't matter that your chance of getting Nin/Tai is whatever on turn 12 because if during the entire game you've gotten more Nin than Tai in a large amount, that's going to throw the count off.

Now, if we take this and link every game and every draw you've made together, doesn't it continue influencing your later games?

Glad to see I've stimulated some more growth in the guide. I'm mentally implementing the idea of influence in my games now- I'm using those percents to plan actual teams (Sadly, Kabuto is now no longer as awesome as he used to be in my eyes) and I''m using the idea of say "If I've got more Tai/Nin than Blood/Gen these last 4 turns I'll try for the blood/gen maneuvers/combos" mid-game now.

Ok, someone that was keeping up with the character changes will have to tell me if my mind is deceiving me or not.

Did they really boost Kakashi(S) by changing his attack maneuver from Red/Red to Red/White? If so, wow. Ya'll are making an impact.

If not, please disregard.