The Wonder Wheel

Team S

$175 2

$175 7

$155 4

$155 8

$35 6

$250 1

$35 3

$155 5

Description of Game

• Pay $150 to play this very fun game• Spin the Wonder Wheel • Whatever amount of money that you land on,

is the amount of money that you win!• The other numbers on each wedge do not

have anything to do with the money you will win

• Don’t forget to have fun!

Theoretical Expected Value and Standard Deviation

X=price on wheel-price you have to pay• Expected Value:μx=5(3/8)+25(1/4)+100(1/8)-115(1/4)=-8.125μx=-8.125

This means that on average, the players can expect to lose $8.13 each time they play and the casino makes an average of $8.13 each time someone plays.

X=price on wheel-price you have to pay• Standard Deviation:σX

2= (3/8)(5+8.13)2+(1/4)(25+8.13)2+(1/8)(100+8.13)2+ (1/4)(-115+8.13)2

σX 2=1223.0933

σX= 34.97

The money that the players win or lose varies on average $34.97.

Experimental Expected Value and Standard Deviation

X (aka money made)

P(X)

175 14/50155 18/50250 6/5035 12/50

Expected Value:μx=25(14/50)+5(18/50)+100(6/50)-115(12/50)=-6.8μx= -6.8

This means that on average, the players can expect to lose $6.80 each time they play and the casino makes an average of $6.80 each time someone plays.

Standard Deviation:σX

2 = ((14/50)(25+6.8))2+((18/50)(5+6.8))2+((6/50)(100+6.8))2+((12/50)(-115+6.8))2 =30.14

σX 2 =30.14

The money that the players win or lose varies on average $30.14.

Conclusion

• This game could be very successful if it was put into a casino. It is very attractive to players because of the large amounts of money they can win. Also, as both the theoretical and experimental data shows, there is a house advantage in the game. This game could be improved by having a lower standard deviation. This would lower the variations of game winning numbers.