Iliana Casino Slot Games
One major project that we completed for Chemistry was the casino project. Out project team completed this project for exhibition which was so much fun. We were instructed to create our own casino game but it could not be a card game. This project was all about probability and with cards it would have taken too long to figure out the probability. The habit of mind that I used most in this project was connection, because it required that I relate the math concept of probability to the bigger picture of real life gambling. Prior to actually starting to work on the project we did a great deal of preparation with homework and labs about probability to refresh our memory. Next we brainstormed ideas for games which we submitted and Mr. Fozi helped us choose the best ones. To do this we had to use prior knowledge of casino games with dice and slots, then adapt them to create our own game. Over time we developed a game proposal which included the objectives, rules, and construction plans. Sage is the best at probability so she did much of the math, I created the rules and wrote most of the game proposal. Jason constructed the station we designed. Exhibition night was
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fun and the games were all great. It allowed us to connect our math project to the larger school community. I think the visitors enjoyed the games and the entire experience, because it appeared as if they were having fun on the night of the exhibition. The final product turned out very well and was an excellent chance to link math to real life.By Iliana Arias Carrillo
Jason Porter
Sage Morretti
Table of Contents
I. Rules and Regulations
a. Detailed Rules
b. Simplified Rules
II. Probability Analysis
a. Method
b. Table of possibilities
c. Tree Diagram
d. Probability Calculations
III. Construction Notes
a. Drawing of Game Board
b. Drawing of Booth
Detailed Rules
There are 3 dice in this game. The Player rolls the first dice and that dice has to be a number less than the second roll of the next dice. So the Player has rolled two dice total by now. The 3rd dice will be rolled depending on what the last roll was if the first was smaller than the second you can roll the third. The third dice has to either between the number of the first and second dice rolled, or either of the two numbers rolled, and lastly it can be the sum of the two dice that were rolled. If any of the three things listed happens you win if nothing happens you lose. Another way to win is the have three of a kind, when you get this you win $5. When your third roll is in between the other two rolls win $1. When you third rolls is the sum of of the first two rolls you get $2. When your third dice is either one of the first rolled dice you get $3.
Simplified rules
1st roll has to be a small number or smaller than the second roll
2nd roll has to be bigger than the first roll
3rd roll has to either the sum of both dice rolled before or in between or one of the numbers rolled before.
You win $5 when you get three of a kind
$3 for two of a kind
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$2 for your third dice is the sum of the other two
$1 If you third dice is in between
Probability Analysis
Math explanation:
The reason I got these numbers in each row where based on probability, which is the number of times it can happen out of the number of sides in this case it's a dice with 6 sides. ex. If you want to roll a one the probability of that would be 1/6 because there is only one 1 and one 6.
1st | 2nd | 3rd | Outcome | Probability | Prize |
1 (1/6) | 1 (1/6) | 1 (1/6) | Win (matching 3) | 1//216 | $5.00 |
1 (1/6) | 1 (1/6) | 2 (1/6) | Win (sum) | 1//216 | $2.00 |
1 (1/6) | 1 (1/6) | 3,4,5,6 (4/6) | Lose | 4//216 | $0.00 |
1 (1/6) | 2 (1/6) | 1,2 (2/6) | Win (matches 2) | 2//216 | $3.00 |
1 (1/6) | 2 (1/6) | 3 (1/6) | Win (sum) | 1//216 | $2.00 |
1 (1/6) | 2 (1/6) | 4,5,6 (3/6) | Lose | 3//216 | $0.00 |
1 (1/6) | 3 (1/6) | 1,3 (2/6) | Win (matches 2) | 2//216 | $3.00 |
1 (1/6) | 3 (1/6) | 2 (1/6) | Win (between) | 1//216 | $1.00 |
1 (1/6) | 3 (1/6) | 4 (1/6) | Win (sum) | 1//216 | $2 .00 |
1 (1/6) | 3 (1/6) | 5,6 (2/6) | Lose | 2//216 | $0.00 |
1 (1/6) | 4 (1/6) | 1,4 (2/6) | Win (matching 2) | 2//216 | $3.00 |
1 (1/6) | 4 (1/6) | 2,3 (2/6) | Win (between) | 2//216 | $1.00 |
1 (1/6) | 4 (1/6) | 5 (1/6) | Win (sum) | 1//216 | $2.00 |
1 (1/6) | 4 (1/6) | 6 (1/6) | Lose | 1//216 | $0.00 |
1 (1/6) | 5 (1/6) | 1,5 (2/6) | Win (matching 2) | 2//216 | $3.00 |
1 (1/6) | 5 (1/6) | 2,3,4 (3/6) | Win (between) | 3//216 | $1.00 |
1 (1/6) | 5 (1/6) | 6 (1/6) | Win (sum) | 1//216 | $2.00 |
1 (1/6) | 6 (1/6) | 1,6 (2/6) | Win (matching 2) | 2//216 | $3.00 |
1 (1/6) | 6 (1/6) | 2,3,4,5 (4/6) | Win (between) | 4//216 | $1.00 |
2 (1/6) | 1 (1/6) | Game ends (6/6) | Lose | 6//216 | $0.00 |
2 (1/6) | 2 (1/6) | 2 (1/6) | Win (matching 3) | 1//216 | $5.00 |
2 (1/6) | 2 (1/6) | 1,3,5,6 (4/6) | Lose | 4//216 | $0.00 |
2 (1/6) | 2 (1/6) | 4 (1/6) | Win (sum) | 1//216 | $2.00 |
2 (1/6) | 3 (1/6) | 2,3 (2/6) | Win (matching 2) | 2//216 | $3.00 |
2 (1/6) | 3 (1/6) | 5 (1/6) | Win (sum) | 1//216 | $2.00 |
2 (1/6) | 3 (1/6) | 1,4,6 (3/6) | Lose | 3//216 | $0.00 |
2 (1/6) | 4 (1/6) | 1,5 (2/6) | Lose | 2//216 | $0.00 |
2 (1/6) | 4 (1/6) | 2,4 (2/6) | Win (matching 2) | 2//216 | $3.00 |
2 (1/6) | 4 (1/6) | 3 (1/6) | Win (between) | 1//216 | $1.00 |
2 (1/6) | 4 (1/6) | 6 (1/6) | Win (sum) | 1//216 | $2.00 |
2 (1/6) | 5 (1/6) | 1,6 (2/6) | Lose | 2//216 | $0.00 |
2 (1/6) | 5 (1/6) | 2,5 (2/6) | Win (matching 2) | 2//216 | $3.00 |
2 (1/6) | 5 (1/6) | 3,4 (2/6) | Win (between) | 2//216 | $1.00 |
2 (1/6) | 6 (1/6) | 1 (1/6) | Lose | 1//216 | $0.00 |
2 (1/6) | 6 (1/6) | 2,6 (2/6) | Win (matching 2) | 2//216 | $3.00 |
2 (1/6) | 6 (1/6) | 3,4,5 (3/6) | Win (between) | 3//216 | $1.00 |
3 (1/6) | 1 (1/6) | Game ends (6/6) | Lose | 6//216 | $0.00 |
3 (1/6) | 2 (1/6) | Game ends (6/6) | Lose | 6//216 | $0.00 |
3 (1/6) | 3 (1/6) | 3 (1/6) | Win (matching 3) | 1//216 | $5.00 |
3 (1/6) | 4 (1/6) | 3,4 (2/6) | Win (matching 2) | 2//216 | $3.00 |
3 (1/6) | 4 (1/6) | 5,6 (2/6) | Lose | 2//216 | $0.00 |
3 (1/6) | 5 (1/6) | 1,2,6 (3/6) | Lose | 3//216 | $0.00 |
3 (1/6) | 5 (1/6) | 3,5 (2/6) | Win (matching 2) | 2//216 | $3.00 |
3 (1/6) | 5 (1/6) | 4 (1/6) | Win (between) | 1//216 | $1.00 |
3 (1/6) | 6 (1/6) | 4,5 (2/6) | Win (between) | 2//216 | $1.00 |
3 (1/6) | 6 (1/6) | 3,6 (2/6) | Win (matching 2) | 2//216 | $3.00 |
3 (1/6) | 6 (1/6) | 1,2 (2/6) | Lose | 2//216 | $0.00 |
4 (1/6) | 1,2,3 (3/6) | Game ends (6/6) | Lose | 18//216 | $0.00 |
4 (1/6) | 4 (1/6) | 4 (1/6) | Win (matching 3) | 1//216 | $5.00 |
4 (1/6) | 5 (1/6) | 4,5 (2/6) | Win (matching 2) | 2//216 | $3.00 |
4 (1/6) | 5 (1/6) | 1,2,3 (3/6) | Lose | 3//216 | $0.00 |
4 (1/6) | 5 (1/6) | 6 (1/6) | Lose | 1//216 | $0.00 |
4 (1/6) | 6 (1/6) | 1,2,3 (3/6) | Lose | 3//216 | $0.00 |
4 (1/6) | 6(1/6) | 4,6 (2/6) | Win (matching 2) | 2//216 | $3.00 |
4 (1/6) | 6(1/6) | 5 (1/6) | Win (between) | 1//216 | $1.00 |
5 (1/6) | 1,2,3,4 (4/6) | Game ends (6/6) | Lose | 24//216 | $0.00 |
5 (1/6) | 5(1/6) | 5 (1/6) | Win (matching 3) | 1//216 | $5.00 |
5 (1/6) | 6 (1/6) | 1,2,3,4 (4/6) | Lose | 4//216 | $0.00 |
5 (1/6) | 6(1/6) | 5,6 (2,6) | Win (matching 2) | 2//216 | $3.00 |
6 (1/6) | 6 (1,6) | 6 (1/6) | Win (matching 3) | 1//216 | $5.00 |
6 (1/6) | 1,2,3,4,5 (5/6) | GAME ENDS! (6/6) | Lose | 30//216 | $0.00 |
Prize | Probability | Expectation Value |
$5.00 | 6//216 | 5//36 = 0.14 |
$3.00 | 15//216 | 5//24 = 0.20 |
$2.00 | 8//216 | 2//27 = 0.07 |
$1.00 | 10//216 | 5//108 = 0.05 |
$0.00 | 21//216 | $0.00 |
Our Expectation Value turned out to be 101//216 = $0.47
The Game cost $1 to play so $1-$0.47 = $0.53
Our profit is $0.53
Construction Notes
Materials:
-a lot of wood
-lights
-red carpet
-blue felt
-2 pairs of fuzzy dice
-4 microphone stand
-paint
Plan:
We are going to have a whole bunch
of wood. We will be using both
plywood and long rectangular blocks
of wood. We will use the plywood to
make the top and sides of the table.
We will use the long rectangles for the
legs of the table. The box that the table
will stand on will be a rectangle made
out of plywood but it will be supported
by many wooden triangles because they
are very strong. we will make the stairs
leading up to the top will be made the
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same way. We will cover the base with
carpet to make it look very nice. We
are going to connect the wood together
by using both glue and nails.