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...
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
A street hustler offers you the following game: Each play you roll 2 dice. Each play costs $1 If you roll an even number you win that amount If you roll an odd number you lose that amount in addition to the $1. 1) Calculate the probabilities P(X 1+X 2-3) 2) write the reward function, rie), where s -X + X, in the following form r(e)-a 3) What is the expected reward? Should you take up the bet?
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...
. 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?
Dice game rules: you win $21 if you roll a 1 or a 2, you win $13 if you roll a 3,4,5 or 6. What should you pay to make this a fair game?
1 point) Three brothers play a game with a pair of fair (six-sided) dice. Scott will win if the sum of the dice is 3, Dave will win if 9, and Jim if 11 They will roll the die until a winner is declared Part (c) Realizing this, theoretically, is a game that could go on forever..the three brothers decide that if no winner has been decided in three rolls or "turns" Scott will be deemed the winner. Let Y...
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...
Here is a version of the game of crap. First, you roll two well-balanced, six-sided dice; let x be the sum of the dice of the first roll. If x = 7, or x = 11 you win, otherwise you keep rolling until either you get x again, in which case you also win, or until you get a sum of 7 or 11 in which case you lose. Write a function that takes no input, and simulate the game...
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...