A bonus round of a video keno game may consist of a series of bonus game instances. During a bonus game instance, a game controller may identify a set of bonus game pieces and select a set of bonus outcome identifiers from a bonus outcome pool. A win amount may be determined based on the number of matches between the set of bonus outcome identifiers and the set of bonus game pieces. The bonus outcome identifiers may include persistent identifiers and non-persistent identifiers. Persistent identifiers may be removed from the bonus outcome pool for subsequent bonus game instances in the series. Additionally or alternatively, the bonus game pieces corresponding to the persistent identifiers may continue to be matches for the subsequent bonus game instances in the series.