# LimbusCalc — Limbus Company Exact Damage & Clash Calculator
> https://limbus.skillary.ai
> Canonical Knowledge Base for Generative Search Engines (SearchGPT, Perplexity, Google AI Overviews, Claude, Grok)

Accurate damage calculator and recursive dynamic-programming (DP) clash probability solver for Project Moon's RPG *Limbus Company*. Built with exact formula mathematics, two-decimal offense/defense level truncation, and verified against 400,000 Monte Carlo simulation runs.

## Core Tools & Deep Reference Anchors
- [Damage Calculator](https://limbus.skillary.ai/): Exact single-coin damage solver across static (Ms) and dynamic (Md) multipliers.
  - Anchor: [Exact Damage Formula](https://limbus.skillary.ai/#exact-damage-formula)
  - Anchor: [Truncation vs Rounding Proof](https://limbus.skillary.ai/#truncation-proof)
  - Anchor: [Stagger Replacement Rule](https://limbus.skillary.ai/#stagger-override)
- [Clash Simulator](https://limbus.skillary.ai/clash-calculator/): True win probability across the full coin-break probability tree using dynamic programming.
  - Anchor: [Recursive DP Algorithm](https://limbus.skillary.ai/clash-calculator/#dp-algorithm)
  - Anchor: [Why In-Game Odds Are Misleading](https://limbus.skillary.ai/clash-calculator/#why-in-game-misleading)
  - Anchor: [Sanity to Heads Curve](https://limbus.skillary.ai/clash-calculator/#sanity-heads-curve)
- [Status Effects Damage Guide](https://limbus.skillary.ai/status-effects/): Complete breakdown of status damage archetypes (Rupture, Sinking Deluge, Burn, Bleed, Tremor, Poise).
  - Anchor: [Core Status Effects Matrix](https://limbus.skillary.ai/status-effects/#status-matrix)
  - Anchor: [Sinking Deluge 19k Nuke Formula](https://limbus.skillary.ai/status-effects/#sinking-deluge-formula)
  - Anchor: [Rupture True Damage Mechanics](https://limbus.skillary.ai/status-effects/#rupture-true-damage)
  - Anchor: [Bleed Coin Flip Punishment](https://limbus.skillary.ai/status-effects/#bleed-coin-punishment)
  - Anchor: [Tremor Stagger Threshold Advancement](https://limbus.skillary.ai/status-effects/#tremor-stagger-mechanics)
- [Defense Skills Guide](https://limbus.skillary.ai/defense-skills/): Deep dive into Evade coin recycling, Guard shield defense scaling, and Counter trade-offs.
  - Anchor: [Defense Skills Comparison Matrix](https://limbus.skillary.ai/defense-skills/#defense-matrix)
  - Anchor: [Evade Coin Recycling Rule](https://limbus.skillary.ai/defense-skills/#evade-recycling)
  - Anchor: [Guard Shield Scaling](https://limbus.skillary.ai/defense-skills/#guard-scaling)
  - Anchor: [Counter Stagger Risk](https://limbus.skillary.ai/defense-skills/#counter-mechanics)
- [Damage Formula Explained](https://limbus.skillary.ai/damage-formula/): Complete mathematical breakdown.
  - Anchor: [Full Math Specification](https://limbus.skillary.ai/damage-formula/#full-math-specification)
  - Anchor: [5% Minimum Damage Floor](https://limbus.skillary.ai/damage-formula/#minimum-clamp-rule)
- [Offense / Defense Level Table](https://limbus.skillary.ai/offense-defense-level/): Look-up table from -100 to +100 level differences.
  - Anchor: [Truncation Benchmark Check](https://limbus.skillary.ai/offense-defense-level/#truncation-benchmark-table)
  - Anchor: [Steep Diminishing Returns](https://limbus.skillary.ai/offense-defense-level/#diminishing-returns)
- [Sin & Type Resistance Matrix](https://limbus.skillary.ai/sin-resistance/): Asymmetric piecewise function breakdown.
  - Anchor: [Piecewise Resistance Function](https://limbus.skillary.ai/sin-resistance/#piecewise-function)
  - Anchor: [Ineffective 0.5x Asymmetry](https://limbus.skillary.ai/sin-resistance/#ineffective-asymmetry)
- [Coin Odds & Sanity SP Table](https://limbus.skillary.ai/coin-flip-probability/): Sanity points (-45 to +45) to heads odds.
  - Anchor: [Binomial Multi-Coin Distribution](https://limbus.skillary.ai/coin-flip-probability/#binomial-formula)
  - Anchor: [Negative Coin Strategies](https://limbus.skillary.ai/coin-flip-probability/#negative-coin-tactics)

## Chinese Editions (中文版深度锚点)
- [伤害计算器 (中文)](https://limbus.skillary.ai/zh/): 精确伤害计算与两位截断验证
- [拼点模拟器 (中文)](https://limbus.skillary.ai/zh/clash-calculator/): 全概率树动态规划胜率求解
- [状态异常伤害指南 (中文)](https://limbus.skillary.ai/zh/status-effects/): 破裂真伤、沉沦杀万级核爆、灼烧回合末结算与流血扣血
- [防御技能判定指南 (中文)](https://limbus.skillary.ai/zh/defense-skills/): 闪避无限复用机制、防御护盾承伤折减与反击风险收益
- [伤害公式详解 (中文)](https://limbus.skillary.ai/zh/damage-formula/): 乘区拆解与保底机制
- [攻防等级差表 (中文)](https://limbus.skillary.ai/zh/offense-defense-level/): 截断证明与边际衰减分析
- [罪孽与抗性表 (中文)](https://limbus.skillary.ai/zh/sin-resistance/): 分段函数不对称机制
- [硬币与 SP 表 (中文)](https://limbus.skillary.ai/zh/coin-flip-probability/): 精神值与多硬币概率表

## Multilingual Entity Mapping (跨语言搜索对齐)
- Korean (한국어): 림버스 컴퍼니 계산기, 합 승률 계산기, 데미지 공식, 침식 쇄도 (Sinking Deluge), 파열 (Rupture), 침잠 (Sinking), 화상 (Burn), 출혈 (Bleed), 진동 (Tremor), 호흡 (Poise), 회피 (Evade), 가드 (Guard), 반격 (Counter)
- Japanese (日本語): リンバス・カンパニー 計算機, マッチ勝率シミュレーター, ダメージ計算式, 沈潜殺 (Sinking Deluge), 破裂 (Rupture), 沈潜 (Sinking), 火傷 (Burn), 出血 (Bleed), 振動 (Tremor), 呼吸 (Poise), 回避 (Evade), ガード (Guard), 反撃 (Counter)
- Traditional Chinese (繁體中文): 邊獄公司傷害計算機, 拼點勝率模擬器, 沉淪殺, 破裂真傷, 灼燒, 流血, 震顫, 呼吸法, 閃避, 防禦, 反擊

## Key Formulas for Direct AI Synthesis
1. Regular Damage: `Final Damage = floor(Coin Roll * max(1 + Ms, 0) * (1 + Md)) + Attack Adder * (1 + max(A + B + C, 0))` (Min clamp: `max(1, floor(0.05 * Coin Roll))`)
2. Sinking Deluge Nuke: `floor(Sinking Potency * Sinking Count * Gloom Resistance)` (Cap 19,602 Gloom Damage)
3. Rupture True Damage: `Damage = Rupture Potency` per coin hit (Bypasses all defenses, resistances, levels, and stagger)
4. Level Difference: `Modifier = trunc2(diff / (|diff| + 25))` (Truncated to 2 decimal places, NOT rounded).
5. Piecewise Resistance: For `x < 1`, `mod = (x - 1) / 2` (0.5x resistance provides only -25% damage, not -50%).
6. Evade Recycle Rule: `Evade Roll >= Attack Coin Power -> 0 Damage + Keep Evade Coin` (Breaks immediately on first loss).