I think you would better understand Back off algorithm after I provide some more clarity.
The range from which a number can be selected lies between $0$ to $2^{n-1}$.
When the collision number is 1, then the range is between $0$ to $2^{1-1}$ = $0$ to $2^{0}$ = $0$ to $1$. So now A and B can choose a number between this range.
Subsequently if collision occurs again, say A and B both chose $0$ then this time collision number would be $1$. So now number would be between $0$ to $2^{2-1}$ = $0$ to $2^{1}$ = $0$ to $2$
and process goes so on..
So, as you can see there is nothing as re-initialization of particular number, only range is re-initialized.