Hi I'm Tom! Would you even know that you had no memory? Hi I'm Tom! Would it be like a cutoff from a certain...Hi I'm Tom!
Seriously though, if you had no memory at all, then everyday you would wake up like a newborn child, unable to do anything or have any idea about what is going on around you.
If say, when I wake up I only remember things from before a given point, a la 50 First Dates, then that would be weird, it might be doable but one day you're going to wake up and see "1 Year after Michael Jacksons death" on the tv and think what the hell he was alive yesterday.
The best thing to do for me at any rate, would be to just "stop playing" as you put it.