Question

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 (ball and wheel), and cards (standard deck). In order to promote the casino as much as possible, we have the winning combination to use the number 8 as much as possible. Also, our marketing strategy for the grand opening of the casino will include a strong connection to this newest, wildest game downtown. We have developed two options that we would like you to examine for us. For the game, we would like to have four outcomes: player (1) lost initial bet, (2) paid grand prize, (3) paid $1,000, and (4) paid $100. For our opening day, we would like to have the game consist of a grand prize of $1,000,000 with a house edge within the $5—$10 range and the initial bet to be between $10 and $100. For our regular operations, we would like to have a grand prize of $10,000 and payouts of $1,000 and $100 with a house edge within the $2.00—$5.00 range and the initial bet to be between $5 and $20.

Option 2: Player wins:  Grand prize if sum of two dice is 8, spin a 8 on the roulette wheel, and draw two 8s.  $1000 if the player gets two out of three of the Grand prize outcomes.  $100 if the player gets one out of the three of the Grand prize outcomes

Prize	Outcome	Probability in fraction	Probability in decimal
1,000,000
1,000
100
Bet
Total House edge

Answer 1

Observe that the probability of getting 8 from the two dice roll is 5/36, the probability of getting 8 from the roulette wheel is 1/38,

the probability of getting two 8s from the cards is 2/52 = 1/26.

Hence the distribution of probability is given below:

Prize	Outcome	Probability in decimal
1,000,000	3	0.0183
1,000	2	0
100	1	0
Bet	0	0.9817
Total House edge