If a paper a glass half full of water, then the glass is flipped, paper doesn't fall, y??

i know when it’s full that the pressure of water acting on the paper is less than that of air from the other side..

but when the glass is half full, air and water pressure act on the paper from inside the glass which makes that pressure > that of air yet it doesn’t fall..

i got two answers but i’m not usre:
1 – about water cooling air inside glass so it has low pressure (but i tried it with hot water and worked)
2 – about the size of glass: http://www.newton.dep.anl.gov/askasci/ph…

i don’t know if they’re right, can any1 tell me and give me more details??