Probability Calculation

Chance of winning 1000: 1 - 1/512 = 511/512

Betting Duration Analysis

Days 511000 can last without gambling: 511 days

To make this method useful, it needs to last more than 512 days

Probability Convergence

Probability calculation: (511/512)^512 ≈ 0.37 (37%)

Mathematical reference: lim n→∞ (1-1/n)^n = 1/e