Question

The Perfect 10 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 ten 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 $50. 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 $1.50—$3.50 range and the initial bet to be between $5 and $10.
Option 1:
Player wins:
? Grand prize if sum of two dice is 10, spin a 10 on the roulette wheel, and draw two 10s.
? $1000 if sum of two dice is greater than 10, spin is less than 10, and draw two 10s.
? $100 if sum of two dice is less than 10, spin is greater than 10, and draw two face cards.
Option 2:
Player wins:
? Grand prize if sum of two dice is 10, spin a 10 on the roulette wheel, and draw two 10s.
? $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.

Fill the below sheet.

Opening Night

Prize ($)	Outcome	Probability (fraction)	Probability (decimal)
1,000,000
1,000
100
Bet:
Total House Edge

Regular Operations

Prize ($)	Outcome	Probability (fraction)	Probability (decimal)
10,000
1,000
100
Bet:
Total House Edge

Answer 1

1.

Prize	outcome	probability in fraction	probability in decimal
1000000	Sum on two dice=10,spin 10 on roulette wheel and two 10 cards	(3/36)x(1/37)x(6/1326)= 18/1766232	0.000010191
1000	sum>10,spin<10 and 2 ten cards	(3/36)x(10/37)x(6/1326)=180/1766232	0.0001019
100	sum <10, spin>10 and 2 face cards	(32/36)x(26/37)x(66/1326)=54912/1766232	0.03109
Bet
Total house edge	13.4019

2.

prize	outcome	probability in fraction	probability in decimal
10000	sum=10,spin 10 and 2 tens	(3/36)x(1/37)x(6/1326)=18/1766232	0.00001019
1000	two out of 3 grand prize outcomes	4806/1766232	0.0027210
100	one out of three grand prize outcomes	193248/1766232	0.1094
Bet
Total house edge	13.76