How do "% chance on critical strike to apply condition" effects stack in Guild Wars 2?

Solution 1:

Bleeds

Bleed effects stack with intensity, meaning the more stacks you have the more damage it does every time it 'ticks'. The duration of each bleed is individually tracked; You can apply a 20 second bleed and then three 5 second bleeds all running at once, and you'll have 4 stacks for that 5 second period, and it will fall back to 1 stack after that until the long stack runs out.

Superior Sigil of Earth

The Superior Sigil of Earth has a 60% chance on critical to 'proc' and apply a bleed stack for 5 seconds. It has a 2 second internal cooldown, which means it can only proc once every 2 seconds. It has a chance to proc on every attack or ability you use.

Ignoring other bleed producing sources, assuming you crit 100% of the time, and you get lucky and proc every crit, you'll have a maximum of 5 stacks of bleeding on your target from auto attacks with this Sigil. Factoring in your ability use will push the number up, but in practice you'll need a very high crit rate to consistently see around 5 stacks.

Dual Wielding

Dual Wielding rules for sigil stacking are complex. For sigils that proc effects, they stack multiplicatively, they share the same internal cooldown, and they can trigger the effect with the same chance no matter what hand is attacking.

If you're dual wielding pistols with a superior sigil of earth, with a 60% proc rate, you have a 1-(1-.6)*(1-.6) = .84 = 84% chance to proc the sigil on each critical strike.

Sharpshooter

Sharpshooter has a 30% chance on critical to proc and apply a bleed stack for 3 seconds. Like all traits of this nature, it can proc independently of your sigils.

If you have a Superior Sigil of Earth and Sharpshooter, its possible to proc two stacks of bleed (one 3 second stack and one 5 second stack) on a critical strike, if you get lucky.

With a high crit rate, you can expect to see around 8-10 stacks with both sharpshooter and two Sigils of Earth.

Solution 2:

Bleeding stacks intensity, so with Sharpshooter and a Superior Sigil of Earth, it's door number 3 (30% chance AND 60% chance, potentially two stacks if both trigger on the same crit).

If wielding two weapons with the same sigil, you'll have another ANDed chance to have its effect trigger on a critical hit, but you need to remember that the two weapons share the same cooldown (in this case, 2 seconds). So, if either of them triggers on a critical, it's another 2 seconds before either of them can trigger again.

I'll leave the detailed calculations of how the percentages work to others, suffice it to say that it can get tricky (see this talk page).