Dice

There's no such thing as a three-sided die. To roll a D3, roll a D6 and halve the result, rounding up: 1-2 = 1, 3-4 = 2, 5-6 = 3.

Two special dice exist: the artillery die (faces of 2, 4, 6, 8, 10, and a Misfire result) and the scatter die (arrows plus a Hit! face). Both are mostly used for war machines such as cannons and stone throwers.

Except where a rule specifically says otherwise, neither the artillery die nor the scatter die can be re-rolled.

Whenever a dice result, characteristic, or other value has to be divided, any fraction is always rounded up. A 2D6 roll of 7, halved, is 4 (3.5 rounded up). 10% of a unit of 51 models, rounded up, is 6 models.

A modifier like D6+1 means roll the die and add (or subtract) that amount from the result. A number of dice like 2D6 or 3D6 means roll that many dice and add all of them together -- a 2D6 roll produces a total of 2-12. A multiplier like D6x5 means roll the die, then multiply the result by that amount.

Re-rolling means picking a die back up and rolling it again -- the second result stands even if it's worse than the first. No single die can ever be re-rolled more than once, no matter how many different sources of re-roll apply to it. Re-rolling a 2D6 or 3D6 roll means re-rolling every die in it, not just some of them, unless the rule granting the re-roll says otherwise.

If one side has a rule granting a re-roll and the other has a rule forcing a re-roll of successful results, the two cancel each other out entirely for as long as both apply -- no re-rolls happen at all. If the two abilities aren't equally powerful, the re-roll itself may be re-rolled once, so both still get to have an effect.

Each player rolls a die; whoever scores highest wins the roll-off. On a tie, both players re-roll (any modifiers that applied to the first roll apply again) until someone wins.

To randomly select between several things (models, magic items, spells, etc.), assign a D6 result to each option and roll to make the choice. With fewer than six options, simply re-roll any result that doesn't match one of the assigned numbers.