A street hustler offers you the following game: Each play you roll 2 dice. Each play...
You play a game in which you roll a number n of dice. You win if you roll at least one 6, but no 1s or 2s; and, otherwise, you lose. What is the optimal number of dice to roll in this situation? Choose the best answer. A) 1 B) 2 C) 3 D) 4
You are on a TV show. You have been asked to either play a dice game or accept a $50 bill. The dice game works like this: You roll four dice. For each dice; if you roll a 1, 2, or 3, you win $60. If you roll a 4 or 5, you lose $30. If you roll a 6, you lose $70. Determine expected value of the dice game? Do you play the game, or take the money? Explain...
. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6 and you win if some number appears 3 or more times. For example, if you roll: (3,3,5,4,6,6) then you lose. If you roll (4,1,3,6,4,4) then you win. What is the probability that you win this game?
You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this: • If you roll a 1, 2, or 3, you win $45. • If you roll a 4 or 5, you lose $20. • If you roll a 6 you lose $70. Should you play the game? Use expected values and decision theory to justify your answer. Yes, you should play...
I propose to you a game. You roll 2 dice. If the sum of the numbers showing is either 6, or 7, or 8, I win. If it is 2, 3, 4, 5, 9, 10, 11, 12, you win. Since you have lots more possible winning combinations than I do, the rules are that you pay me $2.00 when I win and I pay you $1.00 when you win. If we play this game 30 times, how much do you...
You are playing a gambling game with a 12-sided die. If you roll an odd number, then you lose $6. If you roll an even number, then you win that amount in dollars (i.e., you roll a 2, you win $2, etc). What is the Expected average winnings/losings of this game? x = die roll P(x) Payoff(x) P(x)*Payoff(x) 1 2 3 4 5 6 7 8 9 10 11 12 E =
Consider the following game: You roll six 6-sided dice dı,..., de and you win if some number appears 3 or more times. For example, if you roll: (3,3,5,4,6, 6) then you lose. If you roll (4,1,3,6,4,4) then you win 1. What is the probability that you win this game? Hint: The answer is 119/324
You roll a dice. If the number is even you lose that amount of money, if it is odd you win that amount. Let W be your winnings after one turn, what is EW?
In a dice game, you roll a fair die three times, independently. If you don’t roll any sixes, you lose 1 dollar. If you roll a six exactly once, you win one dollar. If you roll a six exactly twice, you win two dollars. If you roll a six all three times, you win k dollars. (A) Let k = 3. What is the expected value of the amount you would win by playing this game (rounded to the nearest...
2. You play a game of rolling a dice at Casino. There are 6 possible outcomes: 1, 2, 3, 4, 5, 6. Each particular number has equal chance to occur. If the number 62' or '5' appear, you win. Write a program as script file to estimate the probabilities of winning using Monte Carlo simulation when you play the game 100, 1000, 10000 times. [10]