From D&D 5e Advantage and 4d6 ability scores to Warhammer 40k wound pipelines and Catan 2d6 resource odds — calculate exact combinatorics instantly.
Explore PMF probabilities and bell curves in real-time
Calculate exact hit and success odds rolling 2d20 with Advantage (keep highest) or Disadvantage (keep lowest) against any Target Armor Class (AC) or DC.
Advantage: P(Success) = 1 - (1 - p)^2 | Disadvantage: P(Success) = p^2 (where p = normal success probability) Calculate → Calculate exact probability distribution for rolling 4d6 and dropping the lowest die for D&D 5e character generation.
PMF across all 1,296 permutations of 4d6 (sum of top 3 dice) Calculate → Calculate crit probability for standard attacks, Champion Fighter (19-20 / 18-20), Advantage, and Elven Accuracy (triple d20).
P(Crit) = 1 - (1 - CritRange / 20)^DiceCount Calculate → Compare the classic Greatsword (2d6) versus Greataxe (1d12) damage distributions, minimum damage, consistency, and Barbarian Brutal Critical synergy.
2d6: Triangular distribution (min 2, max 12, avg 7.0) vs 1d12: Uniform distribution (min 1, max 12, avg 6.5) Calculate → Calculate exact hit, miss, and critical hit percentage given your Attack Bonus and the target Armor Class (AC).
Target Roll = AC - AttackBonus; P(Hit) = clamp((21 - TargetRoll)/20, 0.05, 0.95) Calculate → Determine the probability of an enemy failing or succeeding on a saving throw against your Spell Save DC.
Target Roll = SpellSaveDC - SaveModifier; P(Save) = (21 - TargetRoll) / 20 Calculate → Calculate whether taking the -5 penalty to attack for +10 bonus damage increases or decreases your average expected damage per swing against any AC.
Expected Damage = P(Hit) * AvgDamage + P(Crit) * CritBonusDamage Calculate → Determine the exact odds of dying, stabilizing, or reviving with 1 HP on death saving throws across multiple rounds.
State-transition Markov chain across 3 successes vs 3 failures Calculate → Calculate hit and crit chances when rolling 3d20 and keeping the highest result with the Elven Accuracy half-feat.
P(Success) = 1 - (1 - p)^3 Calculate → Explore the bell curve, minimum (8), maximum (48), and average (28.0) damage distribution of the classic 3rd-level Fireball spell.
Convolution of 8 independent uniform discrete distributions on [1, 6] Calculate → Calculate expected wounds and unsaved damage through the complete 40k pipeline: Ballistic/Weapon Skill, Strength vs Toughness, and Armor/Invulnerable Save.
Expected Wounds = Attacks * P(Hit) * P(Wound) * (1 - P(Save)) * Damage Calculate → Calculate the probability of successfully making a charge roll on 2d6, with or without command re-roll or charge bonuses.
Cumulative P(2d6 >= ChargeDistanceInches) Calculate → Calculate how many wounds are ignored by Feel No Pain (5+++ or 6+++) rolls.
Ignored Wounds = WoundsSuffered * ((7 - FNP_Threshold) / 6) Calculate → Compare the damage output boost between Lethal Hits (crit auto-wounds) and Sustained Hits 1 or 2 (bonus hits on 6s).
Lethal bypasses wound roll; Sustained adds extra attacks Calculate → Calculate exact odds, pips, and resource yields for hex tile numbers in Settlers of Catan.
P(2d6 = N) based on 36 permutations; Pips = count of winning dice combinations Calculate → Calculate the probability of winning the come-out roll (7 or 11 = 22.22%), crapping out (2, 3, 12 = 11.11%), or hitting the point.
P(Win) = 8/36 + sum(P(Point) * P(Point before 7)) = 244/495 ≈ 49.29% Calculate → Calculate the exact odds of rolling a Yahtzee (five of a kind), Large Straight, Small Straight, or Full House across 1, 2, or 3 rolls.
Combinatorics over 3 roll cycles with optimal keeper strategy Calculate → Interactive bell curve distribution for the sum of two 6-sided dice, featuring exact fractional and percentage odds for all outcomes from 2 to 12.
P(N) = (6 - |7 - N|) / 36 Calculate → Calculate the probability of achieving hits (5s and 6s), normal glitches (>50% 1s), and critical glitches in Shadowrun.
Binomial distribution on p = 1/3 for hits, p = 1/6 for 1s Calculate → Calculate success and botch probabilities for Vampire: The Masquerade and Storyteller d10 dice pools.
Success count on d10 >= Target Number (TN) Calculate → Determine odds of Regular, Hard (half skill), Extreme (fifth skill), Critical (01), and Fumble (96-100) results on percentile dice.
Linear d100 breakdown against skill levels Calculate → Generate exact probability bell curves, PMF, and cumulative CDF for any roll from 1d4 to 10d20.
Polynomial convolution of discrete uniform random variables Calculate → Calculate the probability distribution for exploding dice (when rolling the maximum face grants another roll added to the total).
Geometric expansion of infinite series P(Sum = s) Calculate → Calculate probability distributions when rolling a pool of X dice and keeping only the top Y results.
Order statistics for discrete uniform distributions Calculate → Calculate damage distributions for Rogues combining weapon damage with 1d6 up to 10d6 Sneak Attack dice and critical hits.
Weapon Die + (Ceil(Level / 2)) * 1d6 + AbilityMod Calculate → Calculate how much a d6, d8, d10, or d12 Bardic Inspiration die boosts your chances of succeeding on near-miss d20 checks.
Convolution of 1d20 + 1dY against target DC Calculate → Determine the exact percentage hit boost when benefiting from abilities that allow rerolling hit rolls of 1.
P(Hit with Reroll 1s) = P(Normal Hit) + (1/6) * P(Normal Hit) Calculate → Calculate the probability of passing a Battleshock test rolling 2d6 against your unit Leadership characteristic.
P(2d6 >= Leadership) Calculate → Calculate win/loss probabilities for 3 attacking armies versus 2 defending armies in the classic board game Risk.
Order statistics across 3 attacker d6 vs 2 defender d6 (defender wins ties) Calculate → Calculate odds of rolling doubles, getting an extra turn, or rolling 3 consecutive doubles and going straight to jail in Monopoly.
P(1 Double) = 1/6; P(2 Doubles) = 1/36; P(3 Doubles / Jail) = 1/216 ≈ 0.463% Calculate → Complete probability distribution for 3d6 (sums 3 through 18), as used in GURPS, classic RPGs, and Hero System.
Trinomial expansion over 216 permutations Calculate → Calculate success (target 4) and raise (target 8) probabilities for Wild Cards rolling Trait Die + d6 Wild Die with exploding aces.
P(Success) = 1 - P(Trait Fails) * P(Wild Fails) Calculate → Calculate probabilities of Critical Success, Full Success (6), Mixed Success / Complication (4-5), and Bad Outcome (1-3) on d6 pools.
Roll Nd6 keep highest single die; multiple 6s = Critical Calculate → Try searching for generic terms like "dice", "d20", "crit", or "save".
Learn the exact mathematics behind D&D 5e Advantage vs Disadvantage, Greatsword 2d6 vs Greataxe 1d12 consistency, and the Warhammer 40k wound roll chart.