The following table illustrates the probability of at least one collision occurring within a dataset of 15,000 unique inputs based on the hexadecimal character length.
| Hex Length | Total Combinations | Prob. of Collision | Risk Level | Safety Context |
|---|---|---|---|---|
| 8 | ~2.6% | 🔴 High | 1 in 38 chance; unsafe for production. | |
| 10 | ~0.01% | 🟡 Moderate | 1 in 10,000 chance; risky for primary keys. | |
| 12 | ~0.00004% | 🟢 Low | 1 in 2.5 million; very safe for most apps. | |
| 14 | < 0.0000001% | 🔵 Safe | 1 in 1 billion; negligible risk. | |
| 16 | ~$10^{-11}$ | 🛡️ Ultra | 1 in 80 trillion; industry standard. |
Risk calculated using the Birthday Paradox approximation: $P \approx 1 - e^{-n^2 / 2H}$ where $n=15,000$.