Freemium Funnel & Cohort LTV Simulator

Every mobile app's monetization strategy — freemium, subscription, hybrid — ultimately reduces to the same chain of conditional probabilities: installs who see a paywall, paywall viewers who start a trial, trial users who convert to paid, and paid subscribers who stick around month after month. This simulator renders that chain as a real 3D particle funnel — a fresh cohort of 10,000 installs streams downward through three conversion gates you control, visibly thinning at each one — while a 24-month retention bar chart shows the geometric decay N(t) = N₀·(1−churn)ᵗ that determines subscriber lifetime. Live readouts compute the install-to-paid conversion rate, ARPU, the standard LTV = price / churn perpetuity formula, and the CAC payback period, so you can see exactly how tightening a paywall, cutting churn or raising price moves the underlying unit economics.