How drop rates work
Exact probability first. Simulation only when you ask for it.
Every live update uses the exact binomial formula P(at least 1 success) = 1 - (1 - p)^n. The pack drop rate is the success value, and the number of expected box opens comes from your tokens divided by either the standard box cost or the pack's static effective cost.
Duplicate refund mode never simulates recursive sell-back loops. Instead, each pack ships with a precomputed effective cost constant. That keeps the slider path fast, hydration-safe, and stable under load. Full simulation runs separately in a Web Worker with 5,000 iterations.