oh god the NAP system is so absurd... if you were to have a zero turn warning, then you're just attacked "out of the blue".  A one turn warning, basically says "i'm attacking, you will be hit next turn".  so a 1 turn warning on turn 38 would mean attacks could land on turn 39, just as a zero turn warning on turn 38 meant you were attacked right then...
and a 3-turn warning on turn 38 means attacks can land turn 41.
mind you, I would have preferred to have waited another turn 
 
I guess that means we should just restart the NAP cancellation timer ;p