Win Probabilities, Hand Sizes, and Game Duration Analysis in the Bhikar-Sawkar Card Game

Abstract

We present a Monte Carlo simulation study of the Bhikar-Sawkar card game, a non-deterministic game structurally similar to the classic Beggar-My-Neighbour, which is fully deterministic. Although both games share a common setup, key differences in their rules, particularly the reshuffling of cards after each won hand in Bhikar-Sawkar, introduce stochasticity and significantly increase the space of possible game evolutions. This inherent randomness raises a range of interesting statistical questions regarding the duration of the game, the hand-winner distributions, and the probability of winning the game for a given player. These questions are systematically investigated through large-scale simulations across multiple game configurations.