After the main ball drop of a bingo game, a player may be given a free extra bingo number. A probability of awarding a free ball may be determined, at least in part, according to a desired paytable percentage for the bingo game (or vice versa). Some implementations of the invention provide multi-card bingo games. A player may be required to hit a predetermined pattern on more than one bingo card in order to obtain a progressive award. The number of hits in the pattern(s) and/or the number of bingo cards involved may be determined according to a desired progressive award size and/or a desired probability of obtaining the progressive award. Players may have an opportunity to purchase one or more additional bingo numbers after the main ball drop of a bingo game. A player may be provided the option of purchasing a block of more than one additional bingo number after the main ball drop. The player may be offered such a block at a discount, as compared to the price for purchasing the additional bingo numbers individually.