You're constructing an extremely unlikely scenario to rationalize thinking a die has memory. It does not.

The previous results don't affect future outcomes for a fair die, no matter what those previous results are or how unlikely that outcome was.

Let me toss that back at you: How many unlikely outcomes have to occur before it "begins to matter"? Is one enough to start ignoring the math? Ten? A thousand?

If the die is fair then it's fair, that's all she wrote. Rationally you should always follow the math. Constructing an absurdly unlikely scenario doesn't invalidate the math.

If the die is fair the odds don't change. The historical information is irrelevant as the die has no memory.

A long string of rolling the same number may indicate the die is not fair, in a non-hypothetical situation.

Dice have no memory. What happened in previous rolls in no way affects the outcome of future rolls. The odds of rolling a six don't change to "make up" for not rolling a six in a while.

Do you mean a ground?

The depicted yellow wire running to the switch is unnecessary. A single pole, single throw common switch will do fine with 2 conductor wire. Black from the always on receptacle to switch, red from switch to switched receptacle.