This study investigates the relevance of behavioural finance to decision making. Studies suggest that human decision making is not always rational. This paper examines three behavioural financial theories: expected utility, optimal expectation, and cumulative prospect theory, to test financial decision-making when facing skewed distribution in Vietnam. A survey was conducted using lottery tickets, with six questions divided into three pairs. Each pair was aligned with one set of theories, and the questions selected allowed conclusions to be drawn to explain participants' behaviour. The experiment tested 321 people from a variety of age ranges, genders and occupations. Findings show that gender and ages do not significantly impact the decision-making process. However, they explain the preference of participants who appear to be behaving irrationally but do show some rationality when facing the skewed distribution of return. Decision-makers look for all the possible probability payoffs and choose the best outcome with the low-frequency distribution. They follow optimal expectation and cumulative prospect theory ranking the increasing order payoff valued by the parameter and support the cumulative prospect theory set out by Tversky and Kahneman (1992), showing "cognitive biases" and demonstrating that individuals routinely make decisions that contradict reasonable logic The behavioural finance theory is again proven to be crucial. It strongly complements the standard financial theory. Individuals show heuristic behaviour when decision making in random situations especially when facing skewed distribution.