In a game of repeated die rolls, a player is allowed to roll a standard die up to n times, where n is determined prior to the start of the game. On any roll except the last, the player may choose to either keep that roll as their final score, or continue rolling in hopes of a higher roll later on. If the player rolls all n times, then after the nth roll, the player must keep that roll as their final score. A player always acts to maximize their expected final score. Finally, let Vn denote the final score in a game with a max of n rolls allowed. a) Compute E[V2] with justification. b) Compute E[V3] with justification. c) Find the smallest n such thatE[Vn] ≥5. d) Find the smallest n such that E[Vn] ≥5.999. Hint:try finding a closed-form expression for E[Vn] .
In a game of repeated die rolls, a player is allowed to roll a standard die...
The game of Pig is a simple two-player dice game in which the first player to reach 100 or more points wins. Players take turns. On each turn, a player rolls a six-sided die: If the player rolls a 1, then the player gets no new points and it becomes the other player’s turn. If the player rolls 2 through 6, then he or she can either ROLL AGAIN or HOLD: At this point, the sum of all rolls...
Players A and B each roll a fair 6-sided die. The player with the higher score wins ¤1 from the other player. If both players have equal scores, the game is a draw and no one wins anything. i. Let X denote the winnings of player A from one round of this game. State the probability mass function of X. Calculate the expectation E(X) and variance Var(X). ii. What is the conditional probability that player A rolls , given that...
Two player Dice game In C++ The game of ancient game of horse, not the basketball version, is a two player game in which the first player to reach a score of 100 wins. Players take alternating turns. On each player’s turn he/she rolls a six-sided dice. After each roll: a. If the player rolls a 3-6 then he/she can either Roll again or Hold. If the player holds then the player gets all of the points summed up during...
The Dice game of "Pig" can be played with the following rules. 1. Roll two six-sided dice. Add the face values together. 2. Choose whether to roll the dice again or pass the dice to your opponent. 3. If you pass, then you get to bank any points earned on your turn. Those points become permanent. If you roll again, then add your result to your previous score, but you run the risk of losing all points earned since your...
Problem 5. A lopsided six-sided die is rolled repeatedly, with each roll being independent. The probabil- ity of rolling the value i is Pi, i = 1, … ,6. Let Xn denote the number of distinct values that appear in n rolls. (a) Find E|X, and E21 (b) What is the probability that in the n rolls of the dice, for n 2 3, a 1, 2, and 3 are each rolled at least once?
In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The standard deviation of the number of times she will be audited is?
Complete each problem separately and perform in python. 1. Create a script that will roll five dice and print out their values. Allow the user to roll the dice three times. Prompt them to hit enter to roll. Ex: Hit enter to roll 1,4,3,6,6 Hit enter to roll 3,5,1,2,1 Hit enter to roll 4,3,4,2,6 2. Write a script that will roll five dice (just one time). The user's score will be the sum of the values on the dice. Print...
Please show work :) Will upvote/rate! 3. Discrete Random Variables You have a biased die, where the probability that a number n appears on the die when it is rolled is defined as a random variable X such that Р(X %3D п) — с:п Here c is a positive real number. Now answer the questions below: (a) Find the value of c (b) What is the expected value of the random variable X? (c) Find how close a number you...
java thank you! Pig is a traditional dice jeopardy game. Players take turns, starting with a randomly-chosen player. On their turn a player rolls a single 6-sided die 1 or more times. After each roll, the player has a choice: hold Stop rolling and add the total of al numbers rolled this turn to their score, or roll Roll the die again. If the player rolls a 1, their turn ends and they score 0 for the turn. Points scored...
Requirements: 1. You are not allowed to use global variables. 2. Must declare the following two constants public static final int POINTS = 30; public static final int FORFEIT_POINTS = 20; 3. You can implement your own solution but you are required to break down the problem into smaller pieces. 4. You must provide the output for two rounds of game minimum. 5. Since we are using the Random number generator your output will not be exactly like mine. However,...