Research on Optimizing the Profit Model of Live E-commerce Games Based on Mathematical Expectation

In recent years, the live broadcast e-commerce industry has risen rapidly. Especially driven by short video platforms such as Douyin, live broadcast has become one of the main sales methods for merchants. The traditional live broadcast sales method mainly relies on product introduction and price promotion. Users' purchasing decisions often depend on the cost-effectiveness of the product, which requires merchants to invest a lot of advertising costs to maintain sales. The emergence of live broadcast games, a live broadcast model with gamification design, has changed the traditional marketing model. This model allows consumers to "participate in the game" while shopping by constructing a probabilistic profit model, which increases the entertainment and uncertainty of shopping. Based on the principle of mathematical expectation, this study explores how to optimize the profit model of merchants by designing live broadcast games through theoretical research and case analysis, and verifies its commercial feasibility. The study shows that the reasonable application of mathematical expectation can help merchants design a live broadcast game model that can both stimulate users' desire to buy and ensure long-term profitability. However, this study has a certain degree of singularity. Future research can focus on the application of mathematical expectation in different industries.