Calculating Average Value of Damage w/ 30% Crit Chance

[benorin]

How do I calculate the average value of some damage values where there is say a 30% chance of critical hit and on a crit 150% damage is done? I run into this problem often, if I had to guess I'd say it's likely related to the binomial distribution because there's either a crit or not, fixed probability of success, and presumably a fixed number of trials. I should mention that what value a crit does 150% of is based on a fixed number $\theta D$ where $\theta\in\left\{ .88, 1.12\right\}$ is a random number but please try not to use that fact in the calulation if at all possible I'd like it in general terms please. Thanks!

 

[Dale]

It is the expected value of the damage roll times 0.3*1.5+0.7*1.0

 

[benorin]

So 0.3 from the crit rate, 1.5 from the 150% dmg, I'm assuming the 0.7=1-0.3 and 1.0 for normal or 100% dmg, correct?

 

[Dale]

So 0.3 from the crit rate, 1.5 from the 150% dmg, I'm assuming the 0.7=1-0.3 and 1.0 for normal or 100% dmg, correct?

Yes, it is a weighted average.