think about it this way.

Convert the number to binary format.

1010 -> (010 - 10 ) -> 10

If a number at any given point of time is a power of 2, then it will be of the form

10000(xtimes)

Then, remove the right most 0 from the binary representation of the number

else

remove the left most 1 and also remove any left most 0s till you find a 1.

Example:-

1010

this is not a power of 2 ( why? ), so this number gets reduced to 010 = 10 ( 2 in decimal )

10

this is a power of 2.

so, I remove the right most 0 and the game ends.