A slot machine has a player selection bonus game where a player selects concealed gamepieces from a group to reveal the value of the gamepiece. The preferred game has a burger building theme in which the game rules are related to building one or more hamburgers, and the hidden gamepieces represent burger ingredients. A particular selection allows the player to win larger prizes for future selections. Other designated selections may modify future selections still further (2× and 3× multipliers for double-decker and triple-decker bun selections). Certain gamepieces may change their function based on the context or state of the bonus game.