A three-player gambler's ruin problem: some extensions

For the expected ruin time of the classic three-player symmetric game, Sandell derived a general formula by introducing an appropriate martingale and stopping time. For the case of asymmetric game, the martingale approach is not valid to determine the ruin time. In general, the ruin probabilities for both cases, i.e. symmetric and asymmetric game and expected ruin time for asymmetric game are still awaiting to be solved for this game. The current work is also about three-player gambler’s ruin problem with some extensions as well. We provide expressions for the ruin time with (without) ties when all the players have equal (unequal) initial fortunes. Finally, the validity of asymmetric game is also tested through a Monte Carlo simulation study.

APPLICATION OF MARKOV CHAINS IN HUMAN RESOURCES MANAGEMENT IN OSUN STATE PUBLIC SECTOR

The purpose of this paper is to evaluate labour forecast and planning based on Markov chain model. The paper made use of improved Gray Markov model and collected data from information collected from a tertiary institution in Osun State, Nigeria. Markov chain was applied to predict the staff requirement between 2016 and 2019. The result revealed that Markov chain can be used to predict and forecast labour requirements which are very useful in labour planning. The study recommend the use of Markov chain model because it is able to forecast adequately the labour requirements and labour movement upward and downward the ladder of an organization. Keywords: Markov chain, planning, forecast, model, gambler’s ruin, human resource, management, strategic.

Understanding gambling behaviour and risk attitudes using cryptocurrency-based casino blockchain data

The statistical concept of gambler’s ruin suggests that gambling has a large amount of risk. Nevertheless, gambling at casinos and gambling on the Internet are both hugely popular activities. In recent years, both prospect theory and laboratory-controlled experiments have been used to improve our understanding of risk attitudes associated with gambling. Despite theoretical progress, collecting real-life gambling data, which is essential to validate predictions and experimental findings, remains a challenge. To address this issue, we collect publicly available betting data from a DApp (decentralized application) on the Ethereum blockchain, which instantly publishes the outcome of every single bet (consisting of each bet’s timestamp, wager, probability of winning, userID and profit). This online casino is a simple dice game that allows gamblers to tune their own winning probabilities. Thus the dataset is well suited for studying gambling strategies and the complex dynamic of risk attitudes involved in betting decisions. We analyse the dataset through the lens of current probability-theoretic models and discover empirical examples of gambling systems. Our results shed light on understanding the role of risk preferences in human financial behaviour and decision-makings beyond gambling.