Hmm...50 natural crit rating? I don't know, I'll reuse the example above of 300 average base damage.
Over the course of 10 hits:
Assuming you encounter no crit shield:
Sidewinder = 300*2*5 + 300*1.4*5 = 5100
Paper = 300*1.68*10 = 5040
Sidewinder is still on top, but not by much. Nevermind the benefits of Critical attacks never missing without PD or Crit Shield (monster luck). In case you're curious, if you use a normal Katar [2], Paper x2 is better than a Sidewinder + Paper around 80 total critical rating, and a 2x Hydra versus Hydra + sidewinder, the latter always wins out, even at 100 crit.
Puppy Hat is 1% unless you have 77 Base AGI, then it's a 3% proc chance.
Ok, 2-2, but no expanded classes yet.
Puppy Hat would be better than the Hairbrush (9 -> 18, versus 6 -> 12, even though it's a proc chance and not a fixed rate, 77 Base AGI is a decent minimum for any Auto-attack build of Assassin, and 3% is a relatively high % value). Versus Alice Doll? Wow...that's a rough calculation, since I'd have to factor an actual build and damage output, that's a lot of maths to work out, but it is pretty universal, and it would affect damage output per hit. In a natural crit build, or one where you have a gloria priest, Alice Doll would be preferable. For a sonic blow build, Alice Doll is far and away preferable, though I forget what types of cards affect Grimtooth damage. So I'd say Alice Doll is more universal in application.