The formula
Each independent wheel multiplies the space: 26L × 10D. Three letters and four digits gives 26³ × 10⁴ = 175,760,000 codes. Adding just one more letter multiplies that by 26 — growth is exponential, not linear.
Why promos survive guessing
A human trying one code per Mr D checkout can't dent 175 million combos. But a script at 1,000 guesses/sec cracks it in ~1 day on average — which is why real promo systems add rate limiting, one-use codes, and account binding.
Same math as passwords
An 8-character lowercase password is 26⁸ ≈ 2×10¹¹ — only ~1,000× the promo code. Adding case, digits and symbols pushes each slot from 26 to ~94 options: 94⁸ ≈ 6×10¹⁵. Character variety beats length-by-one every time.
Average vs worst case
A brute-forcer finds the code after searching half the space on average (expected value of a uniform random position). The panel above shows N/2 ÷ rate. Worst case is double that.