assuming you have 50% critical strike chance.
you hit an enemy twice. at least one of the hits is a crit. assuming a 50% crit chance. what is the probablility both hits are crits?
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Assuming exactly a 50% chance of a crit per hit:
- 25% chance neither hit crits
- 50% chance one hit crits
- 25% chance both hits crit
Having said that crits in LoL are pseudo random, with some increase or decrease to the chance of a crit applied if you're critting significantly less or more than expected. Purpose of that is to mitigate against extremely lucky or unlucky streaks, without making crit behavior easily predictable.
Honestly? No offense, but that is really simple math.
Can we just remove critical hit chance and replace it by something that doesn't rely on luck mechanisms? What happened with Ashe was good, now same thing needs to happen for every other ADC (an example would be to make Caitlyn's Headshot passive damage scale with crit chance very highly so that her Headshot actually feels like one), and critical hits be removed from all other champions.
I'm saying this as someone who enjoys building Trinity Force on many champions, but it's stupid to win a fight just because that 10% just decided to randomly happen on a full E Hecarim charge combined with Sheen proc and deal absurd amounts of damage.
I believe the OP is simply trying to catch people up by asking the question in this certain way.
Common sense would lead you to answer 1/2 as you'd take the crit for granted, then ask what the chance is to crit on the other attack, which is 50%.
However, if you parse all the cases out, the answer is 1/3. At a 50% crit chance, there are 4 possible outcomes all with equal probability: XX, XO, OX, OO, with X being a crit and O being a non-crit. Throw out OO, because we're assuming one of the hits is a crit, and we're left with 3 equally-probable outcomes. Of those, only 1 has both attacks critting, hence 1/3.
that is sooo not how probability works...and i guess the unability of too many people to understand the basic concepts of probability is the only reason this unnecessary RNG is still in the game.
Fun and useful math note: the odds of something with probability X% happening at least once in Y tries is equal to 100% minus the probability of it never happening. In other words, the odds of something happening at least once are equal to 100% minus the odds of it never happening. This makes sense; if it must either happen or not happen, then you can capture the entire universe of probabilities with those two probability values.
So, for example, let's say you roll five d10s and you want to know the odds of getting at least one result above an 8. The odds of rolling a 9 or 10 are 20% for each roll. The odds of rolling something else are 80% for each roll. So the odds of rolling a 9 or 10 on at least one die are equal to 100% minus the odds of rolling an 8 or below five times:
100% - (80%)^5
= 100% - 33%
= 67%.
I didn't learn this until my sophomore year of high school. I thought it was pretty eye-opening as to the nature of probability; one of those things that's really obvious once you learn it, but is actually quite enlightening. It's somewhat related to the equally important concept of independent events. Critting on one attack doesn't make it any more or less likely that you'll crit on the other.
https://www.youtube.com/watch?v=NbInZ5oJ0bc
…except in League, where Riot actually coded the crit mechanic to make probability work the way people think it does before they study probability. Not that this was a dumb decision; it's just kind of funny that within League probability works the way laypersons think it does. ("I just got three heads in a row; odds are definitely tilting toward tails now.")
you hit an enemy twice. at least one of the hits is a crit. assuming a 50% crit chance. what is the probablility both hits are crits?
If you assume one hit is a crit (which would be because of something like old Ashe passive) then theres a 50/50 split of 1 or 2 crits
If you don't then theres a 25/50/25 split of 0/1/2 as mentioned elsewhere in the thread assuming a true random generation
However due to league's pseudo-random generation the spread may end up being slightly more likely to land one crit than expected. Although I don't know the actual numbers and this is probably far to big of a swing an easy way to imagine this would be a 24/52/24 split.
you hit an enemy twice. at least one of the hits is a crit. assuming a 50% crit chance. what is the probablility both hits are crits?
If you are playing Ashe, only the second hit will be a critical as long as the enemy is still slowed from the first hit. If you wait too long, neither will be crits.