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. In some implementations providing multi-card bingo games, a player is 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 an additional bingo number or a block of a plurality of additional bingo numbers after the main ball drop. The block may be offered at a discount compared to the price of an individual additional bingo number.