Passedix is a game of chance played with three fair dice. Players bet whether the sum...
Passedix is a game of chance played with three fair dice. Players bet whether the sum of the faces shown on the dice will be above or below ten. During the late sixteenth century, the astronomer and mathematician Galileo Galilei was asked by the Grand Duke of Tuscany to explain why “the chance of throwing a 9 with three fair dice was less than that of throwing a 10.” (Interstat, Jan. 2004) The grand duke believed that the chance should be the same because “there are an equal number of partitions of the numbers 9 and 10.” Find the flaw in the Grand Duke’s reasoning and answer the question posed to Galileo. Hint: What the Grand Duke was saying is: There are six ways to get a 9: 1+2+6; 1+3+5; 1+4+4; 2+2+5; 2+3+4; 3+3+3. There are also six ways to get a 10: 1+3+6; 1+4+5; 2+2+6; 2+3+5; 2+4+4; 3+3+4.
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Passedix is a game of chance played with three fair dice.
Players bet whether the sum...
the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum...
the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7. Similarly, the player can bet $1 that...
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting...
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, using method one, the player can bet $2.00 that the sum will be under 7, that is, 2, 3, 4, 5, or 6. For this bet, the player wins $2.00 if the result is under 7 and loses $2.00 if the outcome equals or is greater than 7. Similarly, using...
. In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the...
. In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or 6. For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than 7. Similarly, the player can bet...
9. In the casino dice game Craps, players make wagers on a sequence of rolls of...
9. In the casino dice game Craps, players make wagers on a sequence of rolls of a pair of dice. A sequence of rolls starts with the "shooter" making an initial roll of two dice called the "come-out” roll. If the sum of the dice on the initial roll is 7 or 11 then a player with a bet on the Pass Line wins. If the initial roll results in a sum of 2, 3, or 12 ("craps") then a...
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll...
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll one six-sided dice. What is the chance that you roll a 4? (If you rolled two dice, rolling a 4 means the sum of the dice is 4) O 1 2 3 36 1 2 1 6 + + 1 4 36 1 6 2 2 1 36 + -10 2 . 4 36 + 4 6 2 2
Example Consider the following dice game. A pair of standard ( fair ) dice are repeatedly...
Example Consider the following dice game. A pair of standard ( fair ) dice are repeatedly rolled. If a ’ 7 ’ comes up before an ’ 11 ’ , then the player wins, otherwise the player loses. Let W be the event that the player wins. Find P(W). To say the dice are fair is equivalent to assuming that Laplace’s rule holds and the 36 possible outcomes for a throw of the dice are equally likely. For convenience, an...
A dice game is played with two distinct 12 sided dice. It costs $3 to roll...
A dice game is played with two distinct 12 sided dice. It costs $3 to roll the pair of dice one time. The payout scheme is as follows 1. Sum of 13 pays $10 Sum of 11 or 15 pays $6 Sum of 7, 9, 17, or 19 pays $3 Any other roll doesn't pay. What is the expected gain/loss after playing the game one time? A "fair" game is one in which the expected gain/loss after playing once is...
In the Going to Boston Dice game, your computer throws three 6-sided dice. On the first throw, th...
in
c++, using this template, try to make it simple.
In the Going to Boston Dice game, your computer throws three 6-sided dice. On the first throw, the h or more of the dice show the highest number, only one is kept). The remain dice is put aside. The final dice is then rolled and the total of all three dice is the computer's score. You have $100 allowance. You wil gain or lose the difference between the computer's throw...
provide your analysis of the game and the bet size by including the odds against a...
provide your analysis of the game and the bet size by including the odds against a player winning one of the prizes, and the house edge. Make sure to include some tables/charts to communicate the calculations involved. Determine the size of the bet that fits the criterion described The Eight is Enough Casino and Resort is developing a new game unique for our casino. We would like this game to use the traditional gaming devices of craps (two dice), roulette...
provide your analysis of the game and the bet size by including the odds against a...
provide your analysis of the game and the bet size by including the odds against a player winning one of the prizes, and the house edge. Make sure to include some tables/charts to communicate the calculations involved. Determine the size of the bet that fits the criterion described The Eight is Enough Casino and Resort is developing a new game unique for our casino. We would like this game to use the traditional gaming devices of craps (two dice), roulette...
9. In the casino dice game Craps, players make wagers on a sequence of rolls of a pair of dice. A sequence of rolls starts with the "shooter" making an initial roll of two dice called the "come-out” roll. If the sum of the dice on the initial roll is 7 or 11 then a player with a bet on the Pass Line wins. If the initial roll results in a sum of 2, 3, or 12 ("craps") then a...
You flip a fair coin. On heads, you roll two six-sided dice. On tails, you roll one six-sided dice. What is the chance that you roll a 4? (If you rolled two dice, rolling a 4 means the sum of the dice is 4) O 1 2 3 36 1 2 1 6 + + 1 4 36 1 6 2 2 1 36 + -10 2 . 4 36 + 4 6 2 2
A dice game is played with two distinct 12 sided dice. It costs $3 to roll the pair of dice one time. The payout scheme is as follows 1. Sum of 13 pays $10 Sum of 11 or 15 pays $6 Sum of 7, 9, 17, or 19 pays $3 Any other roll doesn't pay. What is the expected gain/loss after playing the game one time? A "fair" game is one in which the expected gain/loss after playing once is...
in
c++, using this template, try to make it simple.
In the Going to Boston Dice game, your computer throws three 6-sided dice. On the first throw, the h or more of the dice show the highest number, only one is kept). The remain dice is put aside. The final dice is then rolled and the total of all three dice is the computer's score. You have $100 allowance. You wil gain or lose the difference between the computer's throw...
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