Credit cards use the Lhun Check Digit Algorithm. The main purpose of this algorithm is to catch data entry errors, but it does double here as a weak security tool.

For a card with an even number of digits, double every odd numbered digit and subtract 9 if the product is greater than 9. Add up all the even digits as well as the double-odd digits, and the result must be a multiple of 10 or it's not a valid card. If the card has an odd number of digits, perform the same addition doubling the even numbered digits instead.