Chris is playing a dice game at a casino. The game is played by rolling a single six-sided dice. If an even number shows up, the player wins 10 times whatever shows up (for example, if 4 shows up, then he wins 4 x10 = $40). If an odd number shows up, the player loses $25.
a. (3 pts) What values does X take on?
|
X |
P(x) |
a.
b.
c.
(4 pts) Write out the probability distribution of X in the given table.
(4 pts) Calculate the expected value and of the game.
(4 pts) Is this a good game for Chris to play? Give your mathematical reasoning.
Chris is playing a dice game at a casino. The game is played by rolling a...
2. "Craps" is a game played by rolling two fair dice. To play one round of this game, the player rolls the dice and the outcome is determined by the following rules: If the total number of dots is 7 or 11 (a "natural"), then the player wins. If the total number of dots is 2, 3, or 12 C'craps"), then the player loses. If the total number of dots is 4, 5, 6,8,9, or 10, then this number is...
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...
Suppose a casino has a game where a fair six-sided die is rolled. If an odd number is rolled, the player loses $2. If a six is rolled, the player wins $20. Otherwise, the player loses $1. If a player played this game 1000 times, how much money should he expect to gain (or lose)? Show work.
Bob and Doug are playing the following game. Bob starts by rolling two fair dice; if the sum of his dice is six, then he wins the game. If not, then Doug rolls the dice, and if the sum of his rolls is seven, then he wins the game. If neither player wins the game during the first round, then they repeat the process (with Bob going first) until someone wins a round. What is the probability that Bob wins...
The dice game craps is played as follows. The player throws two dice and if the sum is seven or eleven, the player wins. If the sum is two, three, or twelve the player loses. If the sum is anything else, the player continues throwing until either that same number is thrown again (in which case the player wins) or the player throws seven (in which case the player loses). Calculate the probability the player wins within 0.01 (hint -...
In the game of Lucky Sevens, the player rolls a pair of dice. If the dots add up to 7, the player wins $4; otherwise, the player loses $1. Suppose that, to entice the gullible, a casino tells players that there are many ways to win: (1, 6), (2, 5), and soon. A little mathematical analysis reveals that there are not enough ways to win to make the game worthwhile; however, because many people's eyes glaze over at the first...
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...
using python
[6] Craps is a dice-based game played in many casinos. Like blackjack, a player plays against the house. The game starts with the player throwing a pair of standard, six-sided dice. If the player rolls a total of 7 or 11, the player wins. If the player rolls a total of 2,3, or 12, the player loses. For all other roll values, the player will repeatedly roll the pair of dice until either she rolls the initial value...
A dice game is played as follows: The "buy-in" to play a round costs $4. Then a fair 6-sided die is rolled and the player receives an equal number of dollars as the number shown on the die (i.e. 1 earns $1, 2 earns $2, etc.). What is the player's expected profit from playing one round of the game? -$0.25 $0.25 O-$1.00 -$0.50 Page 4 of 34 Dronnie Dace Next Pare
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]