Executive Summary:
There is game known as the “Dice game” (described below) where competitor try to score the most points they can while avoiding losing their points when a one is rolled. The analysis below considers the costs, benefits, probabilities and decisions facing each player. The optimal stopping point is when accumulated points in the turn reaches 20 points; at that time the costs of additional rolls are greater than the benefits. Though end-of-game standings may change objectives from maximizing expected value, rolling more or less will undoubtedly reduce the expected outcome of each turn. Stopping too early is low risk, low return; stopping later has higher potential return, but higher risk.
Problem Statement:
In the dice game, a die is rolled as many times as a player chooses in a turn, and the total points are tallied. If a one is rolled, all accumulated points for the turn is lost and the player’s turn is over. Each player must decide whether to roll the die again or not. If the die is not rolled, all the points are tallied for that round, and are ‘safe’. The objective is to score the most points in 10 turns.
Decision:
The key decision point occurs after each roll, whether to roll again or not. The number of rolls is irrelevant and not well stated; i.e., a player does not have to ‘choose’ how many times he/she will roll in a turn.
Objective:
The objective in this game is to ‘win’ – that is, score the most points of all the competitors. Though there may be some changes in strategy late in the game (take more risks if behind, take more risks if ahead), in general, the player does best when maximizing the expected value of each turn.
Analysis:
The decision is to decide when to stop rolling, which is a function of the costs and benefits of each roll. The benefits of each roll is the expected positive amount, which is 3.333 on each roll of die that is not a one (4 is the average of 2,3,4,5,6, equally weighted, with a 5/6 chance of not getting a 1: 5/6*4 = 3.33). Alternatively, the benefit of a roll could be viewed as the average of 0,2,3,4,5,6; rolling a one has a zero positive value.
A key input into this decision is the accumulated points in a turn, as that amount is at risk with each successive roll.
As each roll there is a 1/6 chance of losing all points, a player roll as long as:
the marginal expected benefit = 3.333 >= expected loss = 1/6* accumulated points.
Recommendation:
As shown in Table 1 and Figure 1, the benefits are constant (expected value of 3.33), but the costs rise with total accumulated points (1/6* total points).
The risks outstrip the benefits when the number of accumulated points are high. This occurs at a total of 20 points.
A player maximizing the expected points in a turn should pass the die after 20 points are accumulated. More risk averse players, or those who are ahead late in the game, may decide to pass the die sooner; risk neutral or loving players, or those behind late in the game may opt to roll after more than 20 points are accumulated.
CS 340 Milestone One Guidelines and Rubric Overview: For this assignment, you will implement the fundamental operations of create, read, update,
Retail Transaction Programming Project Project Requirements: Develop a program to emulate a purchase transaction at a retail store. This
7COM1028 Secure Systems Programming Referral Coursework: Secure
Create a GUI program that:Accepts the following from a user:Item NameItem QuantityItem PriceAllows the user to create a file to store the sales receip
CS 340 Final Project Guidelines and Rubric Overview The final project will encompass developing a web service using a software stack and impleme
