Game p
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Transcript of Game p
CARD SUITS WHEEL
TEAM P
THE WHEEL
• 8 SPACES
• 2 HEART SPACES
• 3 SPADE SPACES
• 2 DIAMOND SPACES
• 1 CLUB SPACE
HOW TO PLAY
• PAY $20 TO PLAY
• LAND ON A HEART- WIN NOTHING
• LAND ON A DIAMOND- WIN $25
• LAND ON A SPADE- WIN $21
• LAND ON A CLUB- WIN $40
EXPECTED VALUE AND STANDARD DEVIATION (THEORETICAL)
• EXPECTED VALUE-
[0*(2/8)]+[25*(2/8)]+[21*(3/8)]+[40*(1/8)]= $19.13
• STANDARD DEVIATION-
[(0-19.13)^2 *(2/8)]+[(25-19.13)^2 *(2/8)]+[(21-19.13)^2 *(3/8)]+[(40-19.13)^2
*(1/8)]= $155.0594
= $12.48
EXPECTED VALUE AND STANDARD DEVIATION (SIMULATION)
• SIMULATED THROUGH RANDINT ON CALCULATOR, 1 AND 2 ARE HEART, 3 AND 4 ARE DIAMOND, 5 6 AND 7 ARE SPADE, 8 IS CLUB
• DONE 50 TIMES
• RESULTS: 4, 2, 5, 3, 7, 5, 8, 8, 3, 5, 2, 5, 4, 7, 7, 3, 8, 6, 4, 7, 8, 6, 4, 3, 6, 2, 6, 5, 4, 1, 6, 1, 3, 6, 1, 2, 4, 1, 8, 1, 7, 6, 5, 7, 8, 5, 2, 8, 7, 8
• HEARTS- 10/50
• DIAMONDS-11/50
• SPADES- 21/50
• CLUBS- 8/50
EXPECTED VALUE AND STANDARD DEVIATION (SIMULATION) CONT….
• AVERAGE VALUE-
[0*(10/50)]+[25*(11/50)]+[21*(21/50)]+[40*(8/50)]= $20.72
• STANDARD DEVIATION-[(20-20.72)^2 *(10/50)]+[(25-20.72)^2 *(11/50)]+[(21-20.72)^2 *(21/50)]+[40-20.72)^2 *(8/50)]= $63.64
== $7.98
COMPARING RESULTS
• WHEN I DID MY THEORETICAL OUTCOME AND THE SIMULATION I FOUND THAT THE EXPECTED VALUE WAS HIGHER THAN THE THEORETICAL. THIS MEANS THAT ON AVERAGE INSTEAD OF THE HOUSE MAKING $.87 FOR EVERY TIME SOMEONE PLAYS THE GAME, THEY ARE GIVING AWAY $.72 TO EVERYONE THAT PLAYS. IN ORDER TO IMPROVE THE GAME WOULD PLAY WITH THE AMOUNT OF MONEY NEEDED TO PLAY AND AMOUNT AWARDED IN ORDER TO GIVE THE HOUSE A GREATER ADVANTAGE.