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# AP Statistics Carnival Game Project

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## Tim Hayduk

on 7 December 2012

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#### Transcript of AP Statistics Carnival Game Project

AP Stat
Carnival Game Project Emma Farrell, Bryan Campbell, Cheyenne Tavana, and Tim Hayduk Spinner Roulette Players start off with \$10 in Monopoly money, and choose whether they'd like to bet on red or black.
If the spinner lands on the color they chose, they double their money, and if not, they lose the game.
A player can spin up to three times, each time playing for "double or nothing".
Twizzlers are "bought" with the money won, each Twizzler cost \$20. Probabilities Theoretical:
Winning first spin: 5/11=45.5%
Winning first and second spin: 25/121=20.7%
Winning all three spins: 125/1331=9.4% Expenses, Revenue, and Profit If we were to have this game in a real carnival and have 500 people play it:
Expenses: Cost of the materials to build the game were around \$10, and cost of the prizes are about \$0.50 each and we'd expect to give away 250 Twizzlers, so total expense is about \$135.00.
Revenue: We would charge \$1.00 per person.
Profit: Each person is expected to win and cash out \$0.5474, on average. Net profit for each person, on average, is -\$0.4526. If 500 people played our game, we would take in roughly (\$0.4526*500) - \$135.00 = \$81.30 net profit Observed:
Winning first spin: 50/100=50%
Winning second spin: 20/100=20%
Winning third spin: 12/100=12% Sweet Probability The player first flips a coin to see if they are able to play. If they get tails, they get to spin the wheel, if they get heads they lose.
The player then spins the wheel. If it lands on gold, they win a Twizzler. If it lands on any color but gold, they must again flip a coin, and if they get tails, they win a Twizzler, if they get heads they lose. Probabilities Theoretical:
First coin toss: 1/2=50%
Wheel spin(winning color): 1/6=16.7%
Second coin toss: 1/2=50% Observed:
First coin toss: 54/100=54%
Wheel spin(winning color): 9/46=19.5%
Second coin toss: 21/37=54.1% Expenses, Revenue, and Profit If we were to have this game in a real carnival and have 500 people play it:
Expenses: Cost of the materials to build the game were around \$25, and cost of the prizes are about \$1.25 each and we'd expect to have enough with about 200 Prizes, so total expense is about \$275.00.
Revenue: We would charge \$1.00 per person.
Profit: Each person is expected to win (assuming prizes are worth \$1.25 each) \$0.3625, on average. Net profit for each person, on average, is -\$0.6375 If 500 people were to play this game we would gain a net profit of (\$0.6375*500)-\$275= \$43.75 Difference between theoretical and empirical probabilities:
(Theoretical v. empirical)Winning first spin: 5/11-5/10=-4.5%
(T v. E) Winning first and second spin: 25/121-2/10=-0.66%
(T v. W)Winning all three spins: 125/1331-12/100= -2.6% Learning Experiences Though our game was both entertaining and interesting, it was not as popular as other games. That may be due to the fact that Sweet Probability involves consequences....but this is simply a theory. Why a Carnival Would Be Interested In Our Game In the future, either we eliminate the funny, be it less popular consequences, or we raise the stakes, offering more than a giant chocolate bar in return. A carnival game is a game of chance or skill. Our games, “Spinner Roulette” and “Sweet Probability” would be perfect for any carnival because they involve gambling, the risk of chance, and multiple ways to win.

Carnival games are usually operated on a "pay per play" basis and most games offer a small prize to the winner. A random outcome gives all players the chance of winning a prize.

In our game “Spinner Roulette”, continued play is encouraged for a chance to double or win nothing in round two. Most people cannot resist this urge. The more you play, the more you can win. It’s all about being risky.

In our other game “Sweet Probability” there is a 50/50 chance to even play the game. Neither game involves a high amount of skill and they both work well in small spaces. Our games would be the perfect fit in a carnival setting. We did however choose a successful initial 50/50 probability with a coin toss, determining whether they could even play or not, racking in the revenue with a 50 percent chance of them walking away gaining nothing. Learning Experiences This game was very popular, and tended to be a cyclical game, meaning that those who played could not stop playing. They came back time and time again, continuing to bet more and more, turning down the option to take their lesser winnings. We played with the minds of our players much like casinos do, drawing them in with the chance of winning increasingly higher stakes. This was our biggest revenue game, and to make the profits even higher, we could begin the game much like we did with the Sweet Probability game, with a coin toss initiation to increase the chance of payment without playment. In this way, we could further the profit success of this game. Difference between theoretical and empirical probabilities:
(Theoretical v. empirical)Winning first spin: 1/2-54/100=-4%
(T v. E) Winning first and second spin: 1/6-9/46= -2.8%
(T v. W)Winning all three spins: 1/2-21/57= -4.1%
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