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This is objectively false.
On page 13 of the 5e PHB you'll find this:
"You generate your character's six ability scores randomly. Roll four 6-sided dice and record the total of the highest three dice on a piece of scratch paper. Do this five more times, so that you have six numbers. If you want to save time or don't like the idea of randomly determining ability scores, you can use the following scores instead: 15, 14, 13, 12, 10, 8."
Also on page 13 you will find this:
"VARIANT: CUSTOMIZING ABILITY SCORES
At your Dungeon Master's option, you can use this variant for determining ability scores. The method described here allows you to build a character with a set of ability scores you choose individually.
You have 27 points to spend on your ability scores. The cost of each scores is shown on the Ability Score Point Cost table."
If you want to talk about what's objectively true, you should probably know it first. The primary way to generate stats is to roll. Rolling may very well lead to a character with a rolled 18 + 2 for race bonus in a stat.
Lean'rd me real good to try and play a game of make believe with my friends without following a rigid strict guide!
And what are the normal limits?
^todays internetz winner!
Where are these normal limits written?
Evenly distribute the available points or distribute the available points according to your preferences? Those two are mutually exclusive.
Distributing the available points according to your preferences is OBVIOUSLY intended for the point buy system. You can find all this stuff in the first pages of the manual
Where would I go to find the math of the game itself?
Then why did you mention evenly distributing the available points?
I know what I can find in the first pages of the manual, I have it. It's why I was able to pull quotes directly from it. Which I must say is something you have yet to do.
People on both sides will say the DM can allow these things in a tabletop game. If they allow it then no on really cares about a house rule.
In this game TA is the DM. They are allowing
Point Buy
Unlimited Point Buy
Standard Array
Rolling with a reroll button you can push as many times as you want. It is even an achievement you can get.
So since they allow it then it is OK.