Analyzing Probability: Games Fair Project Write Up and Reflection Theme: Jelly Belly - Jelly Bean Company Banujan Gathieswaran MDM4U, Mrs. Barring Green Apple Alternative School Assessment of Learning Evaluation June 2017 Introduction Description of The Game The game that I designed is called Beanify. The theme of my game is Jelly Belly, which is a jelly bean company. I chose this as my theme because I know that students would be attracted to the game if I gave away free candy. Another reason why I chose this as my theme is because I wanted to make the poster board and respective, applicable materials very colorful. Colorful and bright colors have the tendency to stand out and attract people's attention. This was very effective because it did prove to draw the students' attention in the classroom. Outline of The Rules There are three different stages to the game, with a $20 and $30 prize. In the first stage, the player selects a ball from a bag which includes ten different coloured balls. If he or she selects any ball other than a green, blue or orange ball, they move on to the next stage. In the second stage, the player spins a wheel which includes ten different flavours of jelly beans. If he or she lands on any flavour but cream soda, orange, blue raspberry, or chocolate, they can either take home $20 or lose the $20 and continue to the third stage in attempt to win $30. In the last stage, there are different jelly bean cards covered with cups and the player must select a pink jelly bean card in order to win the $30. I made the probability of winning the first two stages high. The probability of winning the first stage is 7/10 and the probability of winning the second stage is 6/10. This allows the players to continue on to stage 3 because they'll think they have a great chance of winning the last stage as well since they've won the first two stages. The probability of winning the third stage is 2/10 which is fairly low but this allows the house to make a profit. Fee Structure and Results To play this game, it costed $10 of theoretical money. I chose this price, in a real casino setting, it would be a competitive cost to charge. Even in the classroom setting, and the other games in the classroom setting. This is somewhat of an innovation of the game called \"Bean Boozled\". The $10 fee to play this counts towards the revenue the winners make. Because there are 3 stages in my game, there are a lot of different probabilities, and it would be a hassle to list all the probabilities available. What I will be doing is going through some of the common probabilities and list the outcome of them, followed by a reflection. Probability of winning the game, in any given case: 7/10 x 6/10 x 2/10 = 21/250 = 8.4%. Although the odds might seem low, the first two stages are really high, which makes up for the really low 3rd stage. In our class there was a 8.4% Scenarios Red ball Chocolate Calculation 1/10 x 1/10 Probability 1/100 Percentage 1% Purple Ball Cherry Red Bean 1/10 x 1/10 x 1/10 1/1000 0.1% Yellow Ball Watermelon Pink Bean Green Ball 1/10 x 1/10 x 2/10 1/500 0.2% 1/10 1/10 1% Red Ball Root Beer 1/10 x 1/10 x 3/10 Yellow Bean 3/1000 0.3% Yellow Ball Lime Yellow Bean 1/10 x 1/10 x 3/10 3/1000 0.3% Black Ball Orange Pink Bean 1/10 x 1/10 x 2/10 1/500 0.2% chance every player would win, which are obviously against the odds because we had two winner; Trinatae and Jaskaran. Below are some calculations and probabilities of some possible scenarios. The probability of winning is 8.4%. However, the probability of winning with a really specific set is very low. I will be analyzing those Probabilities. Calculations As you can see, many different scenarios were drawn out. The probability of getting these scenarios is almost uncertain, the more less stages we include, the greater the probability is because there are that many less option. However, once you add everything up, there's is an 8.4% chance of being victorious. Discrepancies I expected that more people would want to move on to stage 3 rather than keeping the $20 which they've won from stage 2. Since winning the first two stages is very easy, I thought that people would want to move on to stage 3 but some people (Mrs. Barring and Vishav) did not want to move on. If the prize money of stage 2 was lower than $20, people would've wanted to move on and take a risk for a higher prize money but since the prize money for stage 2 and 3 were very close to each other, people were satisfied with their $20. Also, if I made the probability of the player winning in stage 3 a little higher, players would want to move on and play stage 3 since the chances of them winning are higher. I think these differences occurred because when people came to play our game again they knew stage 3 was difficult to win so they did not attempt to play stage 3 and instead kept the $20 which they've won from stage 2. This was biggest loophole in the design of our game. Insights and Reflections Though my game I was able to make a profit and attract many customers, to improve I could've made a few minor changes. Firstly, I could've increased the final prize money in attempt to draw a greater crowd. Since our competitors offered larger prizes, individuals opted to play their game rather than return to ours. Secondly, I could've made our game more interactive, with customers being able to interact or move around more in the game, there would've been a greater chance of them coming back. Lastly, I could have altered our prize money in stage 2 by decreasing it. Many players did not want to move on to stage 3 because they were satisfied with the money they made from winning stage 3. If those players moved onto stage 3 instead of taking $20 home and continuing the game, the house would've made more money. Conclusion I believe that Beanify did a good job at attracting people to come play the game. I used bright colours on my poster board to draw people's attention. Since many teenagers love candy, I thought that making our game related to it will make the game more interesting, and have more involvement, everyone was interacting as expected for jelly beans. Everyone loves freebies, especially if it is candy, hence why I decided to give everyone who played the game free jelly beans which excited the class The data that was collected from the game helped me conclude that my game was fortunately successful. Like I expected, my game made a substantial profit. I thought that making the probability of the player losing almost half the probability of the player winning will make the player want to return and play our game again and also will motivate them to win. It also made the game somewhat fair. Rating before game started = 2.5 Rating after game ended = 4.0 The Reflection Did this project help you understand the probability any better? This unit was definitely easier than the previous unit for me, so I understood it quite well from the beginning. This assessment did help me understand probability better as it taught me the reallife applications of probability distributions, expected value, experimental probability, and how it can affect consumers' purchasing decisions at casino settings. This assignment also helped me distinguish the difference between experimental and theoretical probability, and how to identify and quantify the effect of its differences. Explain why your theoretical probability and your experimental probability may not have matched up. It is first important to distinguish the difference between theoretical and experimental probability. Theoretical probability is what is expected to happen, but it isn't always what actually happens. Whereas, experimental probability when the experiment or trial is run and executed. Nevertheless, the probability is still calculated the same way, \"using the same number of possible ways an outcome can occur divided by the total number of outcomes\" (softschools.com). As more trials are conducted, the experimental probability generally gets closer to the theoretical probability (softschools.com), which is one of the major reasons that these two probabilities may have not matched up. The game was only run about three times, given the time limit we had. Relevance What have you learned about \"Fair Games\"? To begin with, as I understand there are two types of mathematical games: fair and unfair. Fair games would be games where all players have exactly the same chance of winning, and that the outcome of the game is not affected by the order of players taking turns (math.stackexchange.com). To elaborate What is your opinion about Las Vegas and the gaming industry? Do you think it's fair to have establishments designed for people to lose money? What is your opinion on the lottery? Would you advise your grandmother to play? What do you think about gaming casinos