What Randomness Actually Guarantees
Independence, small-sample variation, and why streaks are expected rather than suspicious.
Independent events carry no memory. A coin that has landed heads six times has exactly the same chance of heads on the seventh flip, and the intuition that tails is somehow due is the gambler’s fallacy.
Small samples stray a long way
Ten flips landing seven-three is unremarkable. It is only across hundreds or thousands of flips that the proportion settles near half, and even then it approaches rather than reaches it.
Streaks are expected
In any long random sequence, runs of the same outcome appear regularly. Their absence would be the genuinely surprising result — sequences invented by people to look random contain too few streaks.
Dice count changes the shape
Rolling 3d6 concentrates results near ten and eleven, while 1d18 is flat across its range. Same rough span, entirely different distribution, which matters when you design a game around it.