Disregarding enemy's armor, of course.

10% additional chance to crit TIMES 100% additional damage from crit EQUALS 10% additional damage equivalent.

assuming 200% crit damage, additional crit chance is equal to that much additonal damage. AKA, 30% increased crit chance would be 30% increased damage

However, playing someone like tryndamere, where you better have more than 200% crit damage, this number will be increased

The basic formula is "Critical Chance %" multiplied by "Bonus Critical Damage".

"Bonus Critical Damage" is what ever your critical damage is minus 100%. The standard is 200% Critical Damage (which equals 100% Bonus Damage). Some items raise this factor, like an Infinity Edge which gives you a total of 250% Critical Damage or 150% Bonus Critical Damage.

Though its really not that simple, it's 10% chance per attack to do 200% damage.

It doesn't average at 10% this is somewhat stating the obvious, I've crit 3 times in a row out of 5 attacks with 2% crit chance. Also I haven't crit once in 5 attacks with 85% crit chance

So basically...
On any AD character that is not an AD caster and relies on autoattacking regardless, like e.g. Xin Zhao this should be more superior than armor pen - The tradeoff with the current masteries for the point where crit chance becomes better than armor pen is 40sh armor which is...well, nothing.
Ranged carries, any AD character lovin' crit to be more precise.
Now, why won't people use it 0_o?
Afraid of RNG or what?

the formula for average damage would be:

(Crit chance)*(Damage)*(Crit modifier) + (Chance to hit - Crit chance)*(Damage)

Chance to hit is always 100%. Crit modifier in this case is 2.

So a character with 150 damage and 15% crit would have a total average damage of:

(0.15)(150)(2)+(1-0.15)(150) = 172.5

You can see that it is a 15% increase from that. What if we have an IE giving us 250% crits?

(0.15)(150)(2.5)+(1-0.15)(150) = 183.75

15% Crit has not increased our damage by 22.5% rather than 15%, which is, of course, a 50% increase over 15%.

So at 50% Crit chance, for example, on trynd with an IE. You can expect a 75% increase in average damage.

Note that Trynd doesn't actually HAVE any "crit damage boost" anymore. So the only sources of it are the mastery in offense, runes (a terrible idea), and the Infinities Edge.

yes, but since you should have >90% crit chance with full rage while playing trynd, you better have those +crit damage things, so it's kinda dumb to say otherwise. if you dont get IE on tryndamere, you should stop playing league.

please don't listen to this, this is one of the most retarded things ive ever herd.

from wiki: In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set.

this means that though you can get 3 crits in a row with only 1% crit chance, it is EXTREMELY unlikely (<0.0001% chance), and the number of crits you have WILL average to about 10%, because that's what crit chance is: the chance of getting a crit anyone hit, aka the AVERAGE % of your attacks that will crit.

also, to OP: armor doesnt change the effectiveness of crit since it is also a percentage adjustment applied to the damage you do.

Random Number Generators are pretty much all seeded on time, they take the current millisecond, and put a function to it so that it becomes a number between 0 and 1. Then it checks if that number is within a range set by your crit chance. It's not a perfect solution, and riot is trying to make it so that people don't chain crits at 5%.