Defined model
Guess an Enigma M3 configuration with known rings
- Probability:
- 1.12 × 10⁻¹⁹%
- Odds:
- 1 to (8.9 × 10²⁰)
- dBan
- −209.5 dBan
Known ring settings still leave the naval Enigma M3’s rotors, starting positions, and plugboard hiding the correct setup among a vast field of possibilities. One guess has to find the exact combination.
Calculation
N = [26! / (6! × 10! × 2¹⁰)] × P(8, 3) × 26³ = 890,190,309,219,827,616,000. p = 1/N
Assumptions
The reflector, wiring, and ring settings are known. The counted configuration contains three ordered rotors from eight, one of 26 starting positions for each rotor, and exactly 10 plugboard cables that pair 20 letters. Six letters remain unplugged. All mechanically possible rotor orders count, regardless of historical operating restrictions. Effective cryptographic strength also depended on attack methods and message context. No fixed probability gain is assigned to the Bombe without defining the candidate set left by its tests.