This is the reasoning behind 4 digit pins for cards: after three wrong attempts the atm will swallow the card (which gives an average (1/10000)+(1/9999)+(1/9998

This is the reasoning behind 4 digit pins for cards: after three wrong attempts the atm will swallow the card (which gives an average (1/10000)+(1/9999)+(1/9998) = 0.03% chance of guessing a random pin for a single card. But chances are obviously much higher if you want to guess the pin on a single card out of a batch of 10 000, or if users can pick their own pins).