In a primary or bonus game, single numerals are randomly generated in turn and assigned by the player to digit positions which determine an award. In a mechanical embodiment, Fig 14C, a spinner generates a numeral and the player selects a position for that numeral in an unfilled hundreds, tens or unit digit position, so that once all positions are filled, the award is delivered. In other embodiments, particularly those involving touch screen displays, the player selects a position for a masked numerical value which is only unmasked once the position has been selected, Figs 3A to 3D (not shown). Many alternative embodiments are suggested, including ones where the player can attempt to modify the reward before it is delivered, eg by requesting the unmasked numerals to be scrambled into different positions (Figs 8 and 9), the numerals to be completely regenerated (Fig 10), or an extra digit added (Fig 11); the masked numerals can be carried on the reels of a slot machine (Fig 7). The number of digit positions need not match the number of masked numerals, and when a single numeral value has been unmasked, the player may be allowed in some embodiments to use it in more than one position.