In Risk-like games, players face off against each other on maps divided into territories. One player may conquer the territories of another by eliminating all of the other’s units from a said territory. Units can be eliminated with the throwing of the dice, and a unit is lost for every instance where the opposing player has a higher score on one cast die. The throwing of the die is governed by the following rules:
- The defender rolls a maximum of 2 dice (one per unit - contingent on the unit number on the attacked territory).
- The attacker rolls a maximum of 3 dice (one per unit - excluding the last unit and contingent on the unit number on the attacking territory).
- Only the top dice are considered if a player throws more dice than his opponent.
- Dice are paired with each other in an ordinal fashion.
There are already texts providing more wide-ranging whole-battle predictions (as for instance here), and closed-source (and in this particular case inaccurate) battle simulators. Here we try to offer a transparent formulaic reference and odds table for all single-attack scenarios.