Examples of integers which increase in both directions simultaneously

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

The original statement

2n and 2n+1

Statistically, there are more possibilities to have the amount of the cheque increased when the integer value is 0 or any positive number by a margin of 6 to 5, so take the cheque that has not been turned over.

However, as stated earlier, if the first cheque is a worthwhile value take it and sight unseen burn the second cheque.