Video Game Math (MMORPG FFXI)

I'm going to heavily simplify everything here, I'd appreciate someone to show me their analysis so that I can adjust it accordingly. I will try and talk about this so that anyone who has ever played a video game can understand - basically just make it straight up math.

Quick glossary:
Weapon skill - "ability" you can do in the game, focus of this question

Alright so there is this weapon skill and I have to figure out whether or not to add 20% critical rate or 20% critical damage, one or the other.

For simplicity, let's assume:

1. That a critical hit on average does 2x the damage of a normal hit.
2. The base critical damage bonus is 80% (So 180% of critical damage is 2x the damage of a normal hit), so in the "critical damage build" a 20% bonus is really just 11% for each hit.
3. Your base critical hit rate is 70%, so in the "critical hit build" you have a 90% crit rate.
4. Accuracy is so high, we will assume that it is 100% (You can never miss).

The problem:

The given weapon skill has three hits (none of which can miss), each of which can critical. What would be better - adding the 20% (11%) damage to each critical or bringing your critical hit rate to 90%.

I'm looking for three different expected values:

1. 70% crit rate, each critical hit does 200%
2. 70% crit rate, each critical hit does 222% (edit mistake)
3. 90% crit rate, each critical hit does 200%

Final statement: I understand this is quite a bit of work, but I also remember that there are a handful of junkies here who might enjoy doing something different. At the very least, I'd like to know how to calculate the expected probabilities to get 0, 1, 2, 3 critical hits without. Thank you for anything you can give me.

Edit: I made a mistake and didn't give you a real way to express expected values. Normal hit = 1, Critical hit = 2 or 2.22. Therefore the total value for the weapon skill will be 3-6.66.

This is what I came up with, please critique:

.7^3+(.7^2)*.3*3+.7*(.3^2)*3+.3^3=1

.343 Full crit
.441 2x crit
.189 1x crit
.027 0x crit

Full crit = 6.66
2x crit = 5.44
1x crit = 4.22
0x crit = 3

Expected value = 5.562

.9^3+(.9^2)*.1*3+.9*(.1^2)*3+.1^3=1

.729 Full crit
.243 2x crit
.027 1x crit
.001 0x crit

Full crit = 6
2x crit = 5
1x crit = 4
0x crit = 3

Expected value = 5.7

2.5% increase

Quote: ahiromu

I'm going to heavily simplify everything here, I'd appreciate someone to show me their analysis so that I can adjust it accordingly. I will try and talk about this so that anyone who has ever played a video game can understand - basically just make it straight up math.

Quick glossary:
Weapon skill - "ability" you can do in the game, focus of this question

Alright so there is this weapon skill and I have to figure out whether or not to add 20% critical rate or 20% critical damage, one or the other.

For simplicity, let's assume:

1. That a critical hit on average does 2x the damage of a normal hit.
2. The base critical damage bonus is 80% (So 180% of critical damage is 2x the damage of a normal hit), so in the "critical damage build" a 20% bonus is really just 11% for each hit.
3. Your base critical hit rate is 70%, so in the "critical hit build" you have a 90% crit rate.
4. Accuracy is so high, we will assume that it is 100% (You can never miss).

The problem:

The given weapon skill has three hits (none of which can miss), each of which can critical. What would be better - adding the 20% (11%) damage to each critical or bringing your critical hit rate to 90%.

I'm looking for three different expected values:

1. 70% crit rate, each critical hit does 200%
2. 70% crit rate, each critical hit does 222% (edit mistake)
3. 90% crit rate, each critical hit does 200%

Final statement: I understand this is quite a bit of work, but I also remember that there are a handful of junkies here who might enjoy doing something different. At the very least, I'd like to know how to calculate the expected probabilities to get 0, 1, 2, 3 critical hits without. Thank you for anything you can give me.

Edit: I made a mistake and didn't give you a real way to express expected values. Normal hit = 1, Critical hit = 2 or 2.22. Therefore the total value for the weapon skill will be 3-6.66.

1 = .7*2+.3 = 1.7
2 = .7*2.22 +.3 = 1.854
3 = .9*2 +.1 = 1.9

Edit. Looks good to me. Mine was per hit.

Oh nice, thank you.

General question, if you add in a 20% chance at missing any of the hits - would that change the comparison at all or just lower all of the values equally? If it's equally, is it by 20%?