Gambling Example

Abstract

This chapter highlights an example of Bayesian Belief Network (BBN) in a gaming scenario by evaluating the variables of “Die Randomness” and “Fair Die.” Here, the balance between winning and losing has great utility in a casino’s ability to remain profitable while hedging risk to maintain their reputation as a gaming establishment. It also provides the experimental protocol for conducting the BBN, which includes the following 11-Steps: (a) Step 1: identify a population of interest, (b) Step 2: slice through this population and identify at a minimum two mutually exclusive or disjoint (unconditional) events, which are the subsets of our population, (c) Step 3: determine prior (a priori) or unconditional probabilities, (d) Step 4: identify the conditional event and its subset of mutually exclusive or disjoint (unconditional) elements, (e) Step 5: conduct the random experiment, (f) Step 6: determine frequency counts, (g) Step 7: determine likelihood/conditional probabilities (relative frequencies), (h) Step 8: determine joint probabilities, (i) Step 9: determine posterior probabilities, (j) Step 10: draw a tree diagram, and (k) Step 11: run a Netica replication. In addition, it provides a conclusion, which includes a discussion of posterior and inverse probabilities as they pertain to this scenario.