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The Wonder Wheel
Team S
$175
$155

$155

2

5

$35

8

3

$35
6

$250
$155

$175

4

7

1
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)=-8.125
μx=-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

14/50

155

18/50

250

6/50

35

12/50

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

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Game s

  • 3. 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!
  • 4. 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)=-8.125 μx=-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.
  • 5. Experimental Expected Value and Standard Deviation X (aka money made) P(X) 175 14/50 155 18/50 250 6/50 35 12/50 Expected Value: μx= 25(14/50)+5(18/50)+100(6/50)115(12/50)=-6.8 μx= -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.
  • 6. 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.