Question 1184637
<pre>
Here are the 36 dice rolls with 2 dice:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
 
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
 
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 
 
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 
 
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
 
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Here are the positive differences of those above:

  0     1     2     3     4     5
  1     0     1     2     3     4
  2     1     0     1     2     3
  3     2     1     0     1     2
  4     3     2     1     0     1
  5     4     3     2     1     0

$X        P(X)           E(X) 
------------------------------
$0        6/36              0
$1       10/36           10/36
$2        8/36           16/36 
$3        6/36           18/36
$4        4/36           16/36
$5        2/36            2/36
------------------------------
     total expectation = 62/36 = 31/18 = $1.72222... 
                         
No. it isn't fair, because the expected value of the
game is $1.72222... minus $5.00 = -$3.27777...

So you expect to average losing about $3.28 per game
if you played the game many times.

Edwin</pre>