RISK Combat Dice

RISK

Combat Dice Simulator

Attacker

Rolls 2 dice

Defender

Rolls 2 dice

Battle Log

Win Probability — Current Armies

Attacker wins

—

Defender holds

—

AttackerDefender

Avg Left
if Atk Wins

—

Avg Left
if Def Holds

—

50/50
Break-even

—

Per-Round Dice Math

—

Campaign Math (Markov Chain)

P(win | a,d) =
Σ P(out) × P(win | a−ℓᵃ, d−ℓᵈ)

Each battle is a Markov chain: outcome depends only on current armies. Solved backwards via dynamic programming from base cases up.

P(win | a, 0) = 1.000

P(win | 1, d) = 0.000

Now: —

Win Probability Table ■ current

Win Probability Heatmap (1–20 armies each)

X-axis = defenders · Y-axis = attackers · Amber = current position

100%

Outcome Distribution

Attacker wins with N armies Defender holds with N armies