To explore the structure of gambling participation and its association with problem gambling, we draw upon Caillois's distinction between games based on competition (i.e. "agon") and those based on chance (i.e. "alea"). The idea that "alea" and "agon" are socially patterned and associated with differing levels of problem gambling, as measured by the Canadian Problem Gambling Index (CPGI), was empirically tested using data from the 2005 Northern Territory Gambling Prevalence Survey (Australia). This survey collected information on gambling participation, problem gambling, and a range of socio-demographic variables from a representative sample of the Northern Territory adult population. Principal Components Analysis of participation in eight different gambling activities was used to explore the underlying structure of participation. Subsequently, regression was used to identify associations between dimensions of participation, social characteristics, and problem gambling. While a two-factor solution supported a basic distinction between "agonistic" and "aleatory" games, the third factor of a three-factor solution combined the two categories, indicating that activity preferences are more complex than the "agon-alea" duality would suggest. There were significant associations between the two-factor solution and socio-demographic variables including geographic remoteness, age, gender, and household type. No association was found between "alea," "agon" and the CPGI, suggesting that it is the configuration of specific games, rather the broad structure of activities, that influence problem gambling risk. In terms of harm minimisation, strategies that target specific gambling games may be more effective than those that cover a range of gambling modes.