Abstract: A pyramid game randomly assigns integers to players of the game, and arranges the player positions corresponding to those integers in a pyramidal hierarchy having a geometric progression of the powers of two, from a single number at the apex to multiple numbers in a base row. Provision is made for redistribution of player positions forming only a fraction of a row, proportionally to other rows to ensure that the base row or level contains no more than half of the total player positions. The integers of the player positions are arranged in numerical order, with the highest number at the apex and other numbers distributed to the remaining player positions in descending order. Alternatively, an apex number may be randomly selected, with the remaining lower numbers positioned in descending order therebelow and any higher numbers positioned following the lower numbers.