This paper shows card-based cryptographic protocols to calculate several Boolean functions with a standard deck of cards using private operations. They are multi-party secure computations executed by multiple semi-honest players without computers. The protocols use private operations that are executed by a player at a place where the other players cannot see. Most card-based cryptographic protocols use a special deck of cards that consists of many cards with two kinds of marks. Though these protocols are simple and efficient, the users need to prepare such special cards. Few protocols were shown that use a standard deck of playing cards, though the protocols with a standard deck of cards can be easily executed in our daily lives. It was shown that logical AND, logical XOR, and copy protocols can be executed with the minimum number of cards. However, the protocols for complicated functions are not known. This paper shows that by using private operations, all of the following Boolean functions can be calculated without additional cards other than the input cards: (1) any three input Boolean functions, (2) half adder and full adder, and (3) any n-input symmetric Boolean functions. The results show the effectiveness of private operations in card-based cryptographic protocols.