Exact model

Guess a four-digit PIN

Probability:
0.01%
Odds:
1 to 10,000
dBan
−40 dBan

The probability that one random guess matches a PIN chosen uniformly from 0000 through 9999 is 1 in 10,000.

Calculation

p = 1 / 10,000

Assumptions

All 10,000 four-digit strings are equally likely, and the model covers one guess. Device and bank PIN systems commonly limit repeated attempts.

Security advice

Keep retry limits enabled on devices and bank accounts. For online accounts, use a passkey when available. Otherwise, use a unique password generated by a password manager and two-step verification.

Sources

  1. Uniform four-digit model
  2. NIST SP 800-63B: passwords and authentication