Game Design & Balancing

Effective DPS from hit damage, attack speed, crit chance and crit multiplier — the core combat-balance number.

True survivability from raw HP plus damage reduction (armor/resist) — why 50% reduction doubles your effective health.

Probability of at least one drop in N tries, expected tries to get one, and the 'pity' attempt count.

XP required for a level and total cumulative XP under linear, polynomial or exponential progression curves.

Compare investing in crit chance vs crit damage to maximize expected damage — finds the better next point.

How long to kill a target from your DPS and its effective HP — the metric that defines a shooter's feel.

Expected pulls and currency to reach a target, accounting for soft/hard pity — for players and economy designers.

Convert a target FPS into a per-frame millisecond budget and check whether your subsystem timings fit.

Net currency inflow per player per day from your faucets and sinks — the inflation/deflation early-warning tool.

Probability of getting exactly K (or at least K) drops in N tries — the binomial answer for multi-drop farming.