Algorithmic Threshold Optimization: Quantitative Modeling of Multiplier Distributions in Crash Games

Abstract

Crash is a widely played casino game that blends strategic decision-making, probability, and computational analysis, particularly from the perspective of the house. This paper presents an optimization algorithm aimed at minimizing the casino's guaranteed positive earnings while simultaneously maximizing the number of players who win some amount during a given round. Since Crash is inherently a multiplayer game, players place random investment amounts at different points in time, which makes it difficult for any individual player to judge, before the round even begins, whether their intended investment is comparatively high or low, and consequently, how much risk they are actually taking on. The core objective of the proposed algorithm is to determine an optimal stopping multiplier that balances both the casino's and the players' interests. Notably, the algorithm remains unaffected by changes in the number of players or by variation in investment amounts, although in practice casinos typically impose a fixed range on permissible investments. Beyond this, the algorithm can help professional players make more informed decisions about how much to invest and how much risk they are comfortable accepting. We further analyze the algorithm's computational complexity and its stopping-multiplier statistics to give a fuller picture of how it behaves in practice.