The other tutor has the payout and the income switched, and that's why he came
up with a negative answer. 

We have to find the probabilities of rolling 6 or greater and 5 or less:

Here are all the possible dice rolls with two 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)

I will color the ones red which are 6 or greater,
and the one 5 or less blue:

(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)

Since there are 26 red rolls above and 10 blue rolls, the probability
of rolling 6 or greater is 26/36 or 13/18 and the probability of
rolling 5 or less is 10/36 or 5/18

So we make a probability distribution function:

dice roll     x     p(x)
6 or more     -1    13/18      
5 or less     +3     5/18

E(x) = ∑[x·p(x)] = (-1)(13/18) + 3(5/18) = -13/18 + 15/18 = 2/18 = 1/9

and 1/9 as a decimal is .111···

Edwin