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

TL;DR

This study uses Monte Carlo simulations to analyze the stochastic dynamics of the Bhikar-Sawkar card game, focusing on game duration, hand-winning probabilities, and winning chances, highlighting differences from deterministic variants.

Contribution

It provides the first systematic statistical analysis of Bhikar-Sawkar's game duration and win probabilities using large-scale simulations, considering its unique rule-induced randomness.

Findings

Game duration varies significantly with rules and initial conditions.

Winning probabilities are influenced by hand sizes and game configurations.

Stochasticity leads to broader outcome distributions compared to deterministic games.

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.