Carnival Games: How to Play, What to Win, and More

Description of the Game 

Name of the game: Wheel of Numbers 

Props: Spinning wheel marked evenly with the numbers 1-8, and with a pointer at the top. 

Aim: 

The wheel will be spun around to land the pointer on a particular number; the higher the number, the higher their chances of winning. Each contestant will be given two chances to spin the wheel and the number the pointer lands on is recorded and summed for the two spins. 

Winning 

There will be three categories of winners based on the sum total of the two spins: 

10-12 – Good competitors. The prize for this category is a Hamburger yoyo. 

13-14 – Almost winners. The prize for this category is Jumbo sunglasses. 

15-16 – Ultimate Winners. The prize for winners is a stuffed star with the words ‘You are a Winner’ embroidered on the top. 

Probability of winning the game 

To win a prize in the game, the contestant needs a total of at between 10-12 in the two spins to be labelled a ‘Good competitor’, 13-14 to be an ‘Almost Winner’, and 15-16 to be the ‘Ultimate Winner’. 

Since the wheel is numbered 1-8, the probability of getting any number on the wheel is 1/8. 

To get 10-12, one needs either (2+8), (3+7), (3+8), (4+6), (4+7), (4+8), (5+5), (5+6), or (5+7) in the two spins i.e. any of these 9 combinations. Probability of getting one such combination is 1/8*1/8 = 1/64. Therefore, the probability of getting either of the 9 combinations is 1/64*9 = 9/64 

To get 13-14, one needs either a (5+8), (6+7), (6+8), or (7+7). 

Probability of getting any of these 4 combinations is 1/64 * 4 = 4/64 or 1/16 

To get 15-16, one needs (7+8) or (8+8) 

Probability of getting (7+8) =1/64; (8+8) = 1/64. Therefore, probability of getting at 15-16 in the game is 1/64 + 1/64 = 2/64 or 1/32. 

Therefore, the overall probability of winning anything in the game is 9/64 + 1/16 + 1/32 = ¼ or 25%. 

Expected Profit 

The cost of spinning wheel for the two rounds will be 2$. 

The costs of the hamburger yoyos, the jumbo sunglasses and the stuffed star are 44cents, 91 cents and 77cents respectively. This means that for each turn played the game stands to make a minimum of 1.09$ and a maximum of 2$. 

A score of below 9 will yield a profit of 2$, a ‘good competitor’ score will yield 1.56$, an ‘almost winner’ will yield 1.09$, while an ‘ultimate winner’ will yield a profit of 1.23$. 

Table of data from game 

Picture 1: Screenshot of Table showing data from 50 contestants who took part in the game. 

Experimental probability of winning the game 

Out of the 50 contestants who took part in the experimental part of the game: 

10 won hamburger yoyos i.e. a probability of 10/50 or a 20% chance of winning a yoyo 

7 won sunglasses i.e. a probability of 7/50 or a 14% chance of winning sunglasses 

6 won stuffed star i.e. a probability of 6/50 or a 12% chance of winning a star 

27 won nothing i.e. a probability of 27/50 or 2/5 or a 54% chance of winning nothing. 

Game justification 

Games of chance are usually loved by many people because of the equal probability of anyone winning the game despite of their age or skill. The ‘Wheel of Numbers’ offers this to contestants with all of them having an equal chance at winning something in the game 

The game is also easy to understand and play for all age groups in addition to raking in a good profit with an investment of $15.39 yielding a profit of $84.61. It is for these reasons that the game should be selected for the Texas State Fair.