Grouped count table of 1000 simulated values of d=p1-p2:

d = p1 - p2	Count	Probability
(-1, -.9)
(-.9, -.8)
(-.8, -.7)
(-.7, -.6)
(-.6, -.5)
(-.5, -.4)
(-.4, -.3)
(-.3, -.2)
(-.2, -.1)
(-.1, 0)
(0, .1)
(.1, .2)
(.2, .3)
(.3, .4)
(.4, .5)
(.5, .6)
(.6, .7)
(.7, .8)
(.8, .9)
(.9, 1)