Probability Pattern

When a machine has a success rate (e.g., an 80% chance of producing the target item per craft), ordinary patterns cannot handle the uncertainty. This mod uses binomial distribution from statistics to calculate how many attempts are needed to reach the target output with sufficient confidence.

Core Principle The probability pattern models a machine''s probabilistic output as a binomial process:

Parameter Meaning Default Target amount (N) Desired final output quantity — Single-attempt success probability (p) Probability of success per attempt 80% Significance level (α) Allowed risk of underproduction 5% The system automatically computes the required number of attempts such that the probability of producing fewer than the target amount does not exceed α.

Computation Method Small targets (N ≤ 30): Uses the exact binomial lower-tail probability Large targets (N > 30): Uses a normal approximation for speed with sufficient accuracy Example Target: 1000 outputs, single-attempt success probability 80%, α = 0.05

The normal approximation calculates that 1286 attempts are needed. At this point, the probability of producing fewer than 1000 items is ≤ 5%.

当机器有成功率的概念（例如每次合成有 80% 概率产出目标物品）时，普通样板无法处理这种不确定性。这个 Mod 使用统计学中的二项分布来计算需要多少次尝试才能以足够高的置信度达到目标产出量。

核心原理 概率样板将机器的随机产出建模为二项过程：

参数 含义 默认值 目标数量 (N) 你想要获得的最终产出数 — 单次成功率 (p) 每次尝试产出成功的概率 80% 显著性水平 (α) 允许的产出不足风险 5% 系统自动计算所需尝试次数，使得产出低于目标数量的概率不超过 α。

计算方式 小目标（N ≤ 30）：使用精确的二项分布左尾概率计算 大目标（N > 30）：使用正态近似，计算速度快且精度足够 示例 目标：1000 个产物，单次成功率 80%，α = 0.05

正态近似计算出需要 1286 次尝试，此时产出不足 1000 个的概率 ≤ 5%。