Collision Risk & Entropy Calculation

Accurately computing collision risk is essential when architecting scalable distributed systems. This module provides mathematically exact formulas based on the generalized Birthday Problem.

collisionRisk(alphabetLength, idLength, generatedCount)

Calculates the probability ($0 \le P \le 1$) of at least one collision occurring when generating $N$ identifiers of length $L$ over an alphabet of size $A$ using the formula $P \approx 1 - e^{-\frac{N^2}{2 \cdot A^L}}$:

import { collisionRisk } from '@readytools/id';

// Risk of collision when generating 10,000,000 NanoIDs (len: 21, alphabet: 64)
const risk = collisionRisk(64, 21, 10000000);
// Returns: ~2.32e-14 (virtually zero)

estimateIdLength(alphabetLength, expectedCount, maxRisk)

Computes the exact minimum character length required to keep collision probability below a maximum risk threshold:

import { estimateIdLength } from '@readytools/id';

// Calculate required length to generate 1 billion IDs with base62 alphabet at max 0.000001 (1 in a million) risk
const len = estimateIdLength(62, 1000000000, 0.000001);
// Returns: 16