Inputs

Methodology and assumptions

Method: weighted random selection over a per-player weight vector. w_C = k_vip * k_cat, w_T = k_vip * k_thomas. P(Cat) = w_C / (w_C + S*1.0). P(Thomas) = w_T / (w_T + S*1.0). Expected rounds to first occurrence = 1 / p. Assumptions: the Roblox API description '2x Chance' is treated as a literal 2.0x multiplier (advanced sliders expose k_cat, k_thomas, k_vip for re-calibration). VIP overrides single passes (multiplier caps at 2x). Applicability: use to compare single 2x passes vs VIP bundle; verify the actual selection algorithm in-game before committing Robux.

Sources