Estimating the Average Payoffs of Gambles

Look at the gambles below. Think of each gamble as a container holding exactly 100 tickets. The tickets are all identical, but they have different cash prizes printed on them.

A single ticket will be drawn randomly, and the prize is determined by the value printed on that prize. For example, W2 below is a gamble with 50 tickets to win $100 and 50 tickets to win $0. Half the time, this gamble pays $100 and half the time it pays $0. If it were played many times, what is the average payoff that this gamble would pay?

Please do not make computations, but instead estimate the average payoff to the nearest dollar and type that value in the box provided on each trial. Some people use the term, "arithmetic mean" for this type of average, and other people call it the "expected value" of a gamble. Your job is to estimate this expected or average payoff of a gamble intuitively.

In this first example of W1, it should be easy to see that the average payoff would be exactly $50, because half of the time it pays $100 and half the time it pays $0. Your task is to estimate the average payoff of each gamble. Do not make any any calculations or do any arithmetic with paper and pencil. Your task is to make an estimate of this average intuitively without actually making any calculation.



W1:
   50 tickets to win $100
   50 tickets to win $0
$


W2:
   50 tickets to win $35
   50 tickets to win $25
$


W3:
   70 tickets to win $100
   30 tickets to win $0
$


W4:
   35 tickets to win $100
   10 tickets to win $35
   55 tickets to win $25
$


W5.
   50 tickets to win $45
   50 tickets to win $35

$


W6.
   70 tickets to win $80
   10 tickets to win $50
   20 tickets to win $0

$


W7.
   20 tickets to win $100
   80 tickets to win $0

$


1.
   10 tickets to win $98
   10 tickets to win $2
   80 tickets to win $2
$


2.
   85 tickets to win $96
   05 tickets to win $96
   05 tickets to win $14
   05 tickets to win $12
$


3.
   45 tickets to win $58
   45 tickets to win $56
   10 tickets to win $2
$


4.
   10 tickets to win $100
   45 tickets to win $44
   45 tickets to win $40
$


5.
   05 tickets to win $96
   95 tickets to win $12
$


6.
   85 tickets to win $100
   10 tickets to win $50
   05 tickets to win $50
$


7.
   90 tickets to win $96
   05 tickets to win $14
   05 tickets to win $12
$


8.
   10 tickets to win $98
   80 tickets to win $40
   10 tickets to win $2
$


9.
   50 tickets to win $44
   50 tickets to win $40
$


10.
   05 tickets to win $96
   05 tickets to win $12
   90 tickets to win $3
$


11.
   20 tickets to win $58
   20 tickets to win $56
   60 tickets to win $2
$


12.
   90 tickets to win $96
   05 tickets to win $14
   05 tickets to win $12
$


13.
   10 tickets to win $98
   90 tickets to win $2
$


14.
   80 tickets to win $100
   10 tickets to win $44
   10 tickets to win $40
$


15.
   80 tickets to win $96
   10 tickets to win $44
   10 tickets to win $40
$


16.
   80 tickets to win $98
   10 tickets to win $98
   10 tickets to win $2
$


17.
   85 tickets to win $100
   15 tickets to win $50
$


18.
   48 tickets to win $44
   48 tickets to win $40
   04 tickets to win $2
$


19.
   90 tickets to win $98
   10 tickets to win $2
$


20.
   80 tickets to win $100
   10 tickets to win $96
   10 tickets to win $4

$


21.
   01 tickets to win $100
   20 tickets to win $97
   20 tickets to win $11
   59 tickets to win $4

$


22.
   10 tickets to win $40
   10 tickets to win $40
   80 tickets to win $2

$


23.
   85 tickets to win $96
   05 tickets to win $90
   05 tickets to win $12
   05 tickets to win $12

$


24.
   45 tickets to win $96
   45 tickets to win $4
   10 tickets to win $2

$


25.
   10 tickets to win $100
   45 tickets to win $96
   45 tickets to win $4

$


26.
   10 tickets to win $52
   90 tickets to win $12

$


27.
   85 tickets to win $100
   10 tickets to win $100
   05 tickets to win $7

$


28.
   59 tickets to win $100
   20 tickets to win $97
   20 tickets to win $11
   01 tickets to win $4

$


29.
   25 tickets to win $96
   05 tickets to win $90
   70 tickets to win $12

$


30.
   10 tickets to win $40
   80 tickets to win $40
   10 tickets to win $40

$


31.
   50 tickets to win $96
   50 tickets to win $4

$


32.
   05 tickets to win $52
   05 tickets to win $48
   90 tickets to win $3

$


33.
   20 tickets to win $96
   20 tickets to win $4
   60 tickets to win $2

$


34.
   85 tickets to win $96
   05 tickets to win $90
   10 tickets to win $12

$


35.
   20 tickets to win $40
   80 tickets to win $2

$


36.
   90 tickets to win $96
   10 tickets to win $10

$


37.
   80 tickets to win $98
   10 tickets to win $40
   10 tickets to win $40

$


38.
   95 tickets to win $100
   05 tickets to win $7

$


39.
   48 tickets to win $96
   48 tickets to win $4
   04 tickets to win $2

$


40.
   80 tickets to win $98
   20 tickets to win $40

$


41.
   59 tickets to win $100
   20 tickets to win $49
   20 tickets to win $45
   01 tickets to win $4
$


42:
   80 tickets to win $100
   10 tickets to win $44
   10 tickets to win $40
$


43:
   01 tickets to win $100
   20 tickets to win $49
   20 tickets to win $45
   59 tickets to win $4
$


44.
   80 tickets to win $96
   20 tickets to win $40
$


45.
   70 tickets to win $89
   10 tickets to win $88
   20 tickets to win $11
$


46.
   10 tickets to win $44
   10 tickets to win $40
   80 tickets to win $2
$


47.
   90 tickets to win $96
   10 tickets to win $4

$


48.
   80 tickets to win $90
   10 tickets to win $13
   10 tickets to win $12

$


49.
   10 tickets to win $96
   10 tickets to win $4
   80 tickets to win $2

$


50.
   80 tickets to win $100
   10 tickets to win $96
   10 tickets to win $4

$


51.
   90 tickets to win $100
   05 tickets to win $96
   05 tickets to win $12
$


52.
   95 tickets to win $96
   05 tickets to win $12
$


53.
   90 tickets to win $100
   05 tickets to win $52
   05 tickets to win $48

$


54.
   90 tickets to win $96
   10 tickets to win $48

$



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