Mastermind is a famous two-player game, where the codemaker has to choose a secret code and the codebreaker has to guess it in as few questions as possible using information he receives from the codemaker after each guess. In Generalized Black-peg Mastermind for given arbitrary numbers p, c, the secret code consists of p pegs each having one of c colors, and the received information consists only of a number of black pegs, where this number equals the number of pegs matching in the corresponding question and the secret code. Let b ( p , c ) be the pessimistic number of questions for Generalized Black-peg Mastermind. By a computer program we compute several values b ( p , c ) . By introducing some auxiliary games and combining this program with theoretical methods, for arbitrary c we obtain exact formulas for b ( 2 , c ) , b ( 3 , c ) and b ( 4 , c ) and give upper and lower bounds for b ( 5 , c ) and a lower bound for b ( 6 , c ) . Furthermore, for arbitrary p, we present upper bounds for b ( p , 2 ) , b ( p , 3 ) and b ( p , 4 ) . Finally, we give bounds for the general case b ( p , c ) . In particular, we improve an upper bound recently proved by Goodrich.