Creating a Dice Game in a Casino: An Analysis

In summary, the dice game has a probability of 15/36 for Ann to win, 6/36 for Bob to win, and 15/36 for the game to not have a winner. Additionally, if the game is played indefinitely, Ann wins on the first roll, Bob wins on the second roll, and the game ends in a draw for the third and final roll.
  • #1
kirman
2
0
Hello everyone,

I want to ask questions about my task. Below are the description. Thank you in advance.

Kind regards,
Kirman.


The aim of this task is to create a dice game in a casino and model this using
probability. It is important to examine how best to run the game from both the
perspective of a player and the casino. In doing so analyse the game to consider the
optimal payments by the player and payouts by the casino.

1. Consider a game with two players, Ann and Bob. Ann has a red die and Bob a white die. They roll their dice and note the number on the upper face. Ann wins if her score is higher than Bob’s (note that Bob wins if the scores are the same). If both players roll their dice once each what is the probability that Ann will win the game?

2. Now consider the same game where Ann can roll her die a second time and will note the higher score of the two rolls but Bob rolls only once. In this case what is the probability that Ann will win?

3. Investigate the game when both players can roll their dice twice, and also when both players can roll their dice more than twice, but not necessarily the same number of times. Consider the game in a casino where the player has a red die and the bank has a white die. Find a model for a game so that the casino makes a reasonable profit in the case where the player rolls the red die once and the bank rolls the white die once. (When creating your model you will need to consider how much a player must pay to play a game and how much the bank will pay out if the player wins. Do this from the perspective of both the player and the casino and consider carefully the criteria for whether the game can be considered worthwhile for both the player and the casino.)

4. Now consider other models for the game including cases such as where the player or the bank rolls their dice multiple times, or where multiple players are involved in the game.
 
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  • #2
This looks like homwork and no effort is shown. I am moving this to the "precalculus homework" section. kirman, if you do not show some effort by tomorrow, I will delete it.
 
  • #3
Hi HallsofIvy,

Sorry for my late reply. Below, are my answer:

The Dice Game
Table of rolling the two dice

A = event where Ann is winning
B = event where Bob is winning
L = event neither Ann and Bob is winning
P(A)=15/36, P(B)=6/36, P(L)=15/36

(point number one) Case where Ann is winning has probability of P(A)=15/36
(point number two) Case where Ann rolling for the second time is only happened when both Ann and Bob didn’t win the first roll. The probability is:
P(L)∙P(A)=15/36∙15/36
(point number three)
Case where both player can roll two times. There are two situations:
Ann is winning: P(L)∙P(A)=15/36∙15/36
Bob is winning: P(L)∙P(A)=15/36∙6/36
Case where they can roll to infinity
And Ann finally win the game
Winning the 1st roll = 15/36
Winning on the 2nd roll =15/36∙15/36
Winning on the 3rd roll =15/36∙15/36∙15/36

Sum of all (using geometric progression)
S=t_1/(1-r)
S=(15/36)/(1-15/36)
S=15/21
And Bob win the game
Winning the 1st roll = 6/36
Winning on the 2nd roll =15/36∙6/36
Winning on the 3rd roll =15/36∙15/36∙6/36

Sum of all (using geometric progression)
S=t_1/(1-r)
S=(6/36)/(1-15/36)
S=6/21
(point number four) In a casino, whenever a player wants to roll the die, he/she have to pay the bet. In this case, the situations where neither the player or bank are winning add favor to the bank’s side.
A = event where player is winning. P(A)=15/36
A’ = event where bank is winning. P(A')=21/36
P is pay out, the amount of the bank pays if the player win. B is betting value, the amount of money the player has to pay each time she/he wants to play.
Now, let’s calculate for a fair game (the expectancy is zero)
E=P(A)∙P-P(A')∙B
0= 15/36∙P-21/36∙B, thus we have the ratio
P=21/15 B
Case where they can roll to infinity
And the player finally win the game
Winning the 1st roll = 15/36
Winning on the 2nd roll =21/36∙15/36
Winning on the 3rd roll =21/36∙21/36∙15/36

Sum of all (using geometric progression)
S=t_1/(1-r)
S=(15/36)/(1-21/36)
S=15/15
This can't be right since the calculated probability is 1.
And Bank win the game
Winning the 1st roll = 21/36
Winning on the 2nd roll =15/36∙21/36
Winning on the 3rd roll =15/36∙15/36∙21/36

Sum of all (using geometric progression)
S=t_1/(1-r)
S=(21/36)/(1-15/36)
S=21/21
This can't be right since the calculated probability is 1.
 

FAQ: Creating a Dice Game in a Casino: An Analysis

1. How do you determine the odds of winning in a dice game at a casino?

The odds of winning in a dice game at a casino are determined by the number of possible outcomes and the probability of each outcome occurring. In a standard six-sided dice, there are six possible outcomes with equal probability, giving each number a 1/6 chance of being rolled. However, in a casino, the odds may be adjusted by using loaded dice or adding more dice to the game.

2. What is the house edge in a dice game at a casino?

The house edge in a dice game at a casino refers to the percentage of each bet that the casino keeps as profit. In most dice games, the house edge is around 1-2%, meaning that for every $100 bet, the casino will keep $1-2 as profit. This is how casinos make money and stay in business.

3. How do casinos ensure fair play in dice games?

Casinos use various methods to ensure fair play in dice games. One way is by regularly inspecting and calibrating the dice to make sure they are balanced and not loaded. Casinos also employ trained dealers to handle the dice and ensure fairness in the game. Additionally, most casinos have surveillance systems in place to monitor the gameplay and detect any cheating or foul play.

4. What strategies can players use to increase their chances of winning in a dice game?

While there is no foolproof strategy for winning in a dice game, players can increase their chances by understanding the odds and making smart bets. For example, the "pass line" bet in craps has a lower house edge compared to other bets, making it a more favorable option. Players should also set a budget and stick to it, as well as avoid betting strategies that claim to guarantee wins.

5. Are there any differences between creating a dice game for a physical casino versus an online casino?

While the basic principles of creating a dice game are the same, there are some differences between physical and online casinos. Online casinos may use random number generators to simulate dice rolls, while physical casinos use actual dice. Additionally, the rules and odds may vary slightly between the two, and online casinos may offer different types of dice games than what is typically found in physical casinos.

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