Managing risk in a four-digit number game

The four-digit number game is a popular game of chance played in Southeast Asia. The players in this game choose a four-digit number and place their bets on it. In this paper, we study the design of a control mechanism for managing bets in this game. Our objective is to design a control mechanism to decide whether bets should be accepted or rejected. We propose a nonlinear optimization model for this problem and provide the mathematical justification for the control mechanism used by several operators in this region. We also suggest a simple improved control mechanism. Using data provided by a company in the region, we show that our control mechanism can accept more money per draw, while the risk exposure of the proposed mechanism can be considerably smaller than the current system.