Dice mechanics beyond d6
Polyhedral sets map skill checks to different variance profiles: d20 for swingy checks, 2d6 for a bell curve toward seven. Naming the dice count and sides keeps remote sessions legible in chat logs.
Advantage and disadvantage
Rolling twice and keeping high or low shifts odds without changing the die itself. Document which rule you used—players remember outcomes, not mechanics.
Teaching probability
Empirical frequency approaches theory over many rolls. Compare predicted sums for 2d6 against a histogram from repeated clicks to bridge stats class and play.
House rules
Exploding dice, reroll ones, and botch thresholds change distributions. Agree before the session; the roller executes randomness, not rules lawyering.