Do all NY hunters have a doe tag so they can make the choice to which you referred?
Bow or mz gets an either/or tag. If you get both bow and mz, its 1 antlerless and 1 either/or.
Regular season (gun) gets a buck only and can draw up to 2 doe tags - lottery based on wmu's. About 40 % of the wmu's are low or no chance for the dmp's. Even in the high probability dmu's, you can not draw. With AR, there is a very good chance a regular season hunter good go several seasons not seeing a deer to legally shoot - unless they want to travel or take up archery/mz. Regular season hunters (no bow or mz) represent well over 50% of the big game licenses sold.