Threat Matrix: A Fast Algorithm for Human–Machine Chinese Ludo Gaming

Abstract

Chinese Ludo, also known as Aeroplan Chess, has been a very popular board game for several decades. However, there is no mature algorithm existing for human–machine gambling. The major challenge is the high randomness of the dice rolls, where the algorithm must ensure that the machine is smarter than a human in order to guarantee that the owner of the game machines makes a profit. This paper presents a fast Chinese Ludo algorithm (named “Threat Matrix”) that we have recently developed. Unlike from most chess programs, which rely on high performance computing machines, the evaluation function in our program is only a linear sum of four factors. For fast and low-cost computation, we innovatively construct the concept of the threat matrix, by which we can easily obtain the threat between any two dice on any two positions. The threat matrix approach greatly reduces the required amount of calculations, enabling the program to run on a 32-bit 80 × 86 SCM with a 100 MHz CPU while supporting a recursive algorithms to search plies. Statistics compiled from matches against human game players show that our threat matrix has an average win rate of 92% with no time limit, 95% with a time limit of 10 s, and 98% with a time limit of 5 s. Furthermore, the threat matrix can reduce the computation cost by nearly 90% compared to real-time computing; memory consumption drops and is stable, which increases the evaluation speed by 58% compared to real-time computing.