Instead.

Unfortunately for both a player and the casino it never happens that both make profit in a single game. Due to simple logic, if one lost, another made profit. However in terms of a multiple number of games being played it can be close to making the game worthwhile for both a player and the casino however to make it 100% is impossible due to the simple fact that casino is a profit-oriented organization and the rules will be set in a such manner that House will always win in a long run.

Casinos are the organizations that will almost never allow a player to end up winning a large sum, leaving casino with negative cash flow for the day, after a series of games played. Regular customers of such places know this fact very well however it doesn’t stop them from going in again and again losing. There are a lot of possible reasons for that. Perhaps a Casino has a good strategy in terms of complementing its customer such as offering free drinks and little snacks as a potential player walks in through the doors. Another reason could be due to the human avarice that is developed in some people more than in others, people want to make money by putting little effort as possible and therefore they go back to the casino with the hope that it is their lucky day. Ardor is another really significant reason for people going into Casino, as soon as they have any money. Ardor leads to playing non-stop until they lose all their money and sometimes even to the extreme part of it when a player eventually becomes a debtor of a Casino.

Logically thinking, the probability of the player winning or losing in the game doesn’t change in case other people join the game at the table since they throw a die each at a time however it does change for the Casino since the chance of losing money increases accordingly with the number of people participating in the game. Since the probability of losing or winning by a player is not affected by the number of people playing at the table, I can come up with a general formula for calculating the probability of Bob winning and then by simple algebraic manipulations for Ann winning.

To extend the investigation and to examine the dice game further I will consider a rule for the game that allows a player to roll a die more than once and hence this will allow me to conclude whether it is going to work in casino’s or player’s favor. However the rule won’t be applicable for the casino (only allowed to roll once) due to the issues that may arise regarding unethical implications where players may feel in a big disadvantage if casino will roll a die more than once, which in essence lower the chance of players to win. Also due to the fact that as the number of times a player rolls a die increases the time it takes for one game to be over gets longer, I am not going to consider more than 4 rolls by a player. It is important since there is high possibility that people who wait for their turn to play, for long time, will perceive the game negativity and therefore will turn away from the dice game, which in essence decreases the volume of customers playing the game, and the profit respectively.

As it was calculated earlier, the probability of a player, rolling a die twice, winning is . And the formula for the percentage profit margin where Y(fair game)

As it was considered before, the Casino decided to have profit margin of 20% with the cost of $5 for a player to play Y(unfair game) will be found by substituting the values into the equation:

$6.912 the payout value to a player if the one wins.

Throwing thrice’s probability of a player winning is

Y(fair game)

the payout value to a player if the one wins.

Rolling a die four times, will result in probability of a player winning:

Y(fair game)

the payout value to a player if the one wins.

Number of throws by a player	The payout value to a player if the one wins($)
1	9.5
2	7
3	6
4	5.5

There is no distinct or any special pattern spotted in the payout value that a player gets. However it is easily recognizable that as the number of throws by a player increases the payout value to a player if the one wins is less with each extra throw. Therefore the suggestion to the shareholders of “The Glorius” is to have the dice game only with an option of a player to be able to roll a die no more than once. This is due to the fact that when a player rolls once, the chance of him losing is much greater compared to instances when a player has an option of multiple throws of a die. Further more in order to have it worthwhile for both a player and the Casino in terms of the profit, a player has to play minimum of 3 games in a row. This is due to the risk Casino faces if a player plays once only i.e if a player has the higher number on the face of the dice he wins and Casino loses since there is only one way ticket for the payout.

Theoretical probability of rolling a die once and getting any number on the face of the die for the Casino was calculated as (16.67%) and it is supported by the simulation below:

The conclusion however is not 100% accurate for the real life case since the probability for Casino rolling any number on the dice by throwing the die once is not according to the dice simulation software that was used by me: