Gamblers in the real world have been found to successfully navigate complex multivariate problems such as those of poker and the racetrack but also to misunderstand elementary problems such as those of roulette and dice. An account of gambling behaviour must accommodate both the strengths and weaknesses of decision making and yet neither of the dominating decision making traditions of heuristics and biases or Bayesian rational inference does. This thesis presents evidence supporting a model-based approach for studying gambling behaviour. The account is built on the premise that decision making agents hold a highly structured mental representation of the problem that is then refined through adjustments made by evaluating incoming evidence. In Study 1, roulette games played at a casino illustrate the range of tactics beyond simple data-driven strategies that are used in chance-based games. In Study 2, an experimental manipulation of the framing of a chance-based dice game highlights the role of prior beliefs about underlying outcome-generating processes. Studies 3 and 4 examine the impact of prior beliefs on subsequent information processing, using a laboratory-based slot machine paradigm. To complement these findings on a computational level, a modelling exercise in Study 5 shows indirectly that assuming a similarity mechanism of judgment is insufficient for predicting the impact of prior beliefs over time. Studies 6 and 7 used racetrack and poker betting experimental paradigms to show that, although priors were integrated into decisions without evaluation, incoming evidence underwent information search and hypothesis and data evaluation processes. Implications for users of gambling research and for future directions of the field are discussed.