The expected column is just the mathematical probability of the result:
+-------+-------------------------+--------------------+-------------+
| Value | Possibilities | # of possibilities | Probability |
+-------+-------------------------+--------------------+-------------+
| 2 | 1+1 | 1 | 1/36=2.78% |
| 3 | 1+2,2+1 | 2 | 2/36=5.56% |
| 4 | 1+2,2+2,2+1 | 3 | 3/36=8.33% |
| 5 | 1+4,2+3,3+2,4+1 | 4 | 4/36=11.11% |
| 6 | 1+5,2+4,3+3,4+2,5+1 | 5 | 5/36=13.89% |
| 7 | 1+6,2+5,3+4,4+3,5+2,6+1 | 6 | 6/36=16.67% |
| 8 | 2+6,3+5,4+4,5+3,6+2 | 5 | 5/36=13.89% |
| 9 | 3+6,4+5,5+4,6+3 | 4 | 4/36=11.11% |
| 10 | 4+6,5+5,6+4 | 3 | 3/36=8.33% |
| 11 | 5+6,6+5 | 2 | 2/36=5.56% |
| 12 | 6+6 | 1 | 1/36=2.78% |
+-------+-------------------------+--------------------+-------------+
You don't have to compute it, just print it in order to compare with the actual statistical results:
double expected_Array[11] = {1/.36, 2/.36, 3/.36, 4/.36, 5/.36, 6/.36, 5/.36, 4/.36, 3/.36, 2/.36, 1/.36};
...
show_Data_Results_line((counter+2), total_Array[counter], expected_Array[counter], actual_Array[counter]);