warmaster can proc once per skil.. 

warmaster is for those single and 2hit champs, to give them a chance to do some extra dmg warmaster is 60% chance on a skill use.

giantslayer can proc once per hit.

so a 4 hitter like coldheart has 4x30% chance to proc. so it can net out in more dmg.

Derpa666-SPA said:

warmaster can proc once per skil.. 

warmaster is for those single and 2hit champs, to give them a chance to do some extra dmg warmaster is 60% chance on a skill use.

giantslayer can proc once per hit.

so a 4 hitter like coldheart has 4x30% chance to proc. so it can net out in more dmg.

Currently, I have Towering Titan maxed out with artifacts (+16) and masteries. A1 attacks one enemy, A2 attacks 4 times at random (what does that even mean?) recycles in 4 turns and A3 applies buffs (so not really an attack, 5 turns). Equipped with retaliation and cruel artifacts.

Other posts suggest using Warmaster given A1 attacks one enemy. So my question is:

If I use the Retaliation (4) artifacts (generates a counter-attack with 25% probability), would GS be invoked for a counter-attack?

yes.

CA is just A1 used outside of your own turn.

4 attacks at random is exactly that. there will be 4 attacks and each will randomise its own target (apart from 1st attack that always hits your targeted enemy).

all 4 hits can go to single enemy, team of 4 enemies can get hit once each or any combination in the middle ...

lets take 5 turns fight into consideration:

a2 hit 4 times and goes on cooldown

a1

a1

a1

a1

total of 8 hits over 5 turns

WM:

5 chances - 60% each:

Number of successes Probability

0 0.0102400

1 0.0768000

2 0.2304000

3 0.3456

4 0.2592

5 0.0777600

GS:

8 chances: 30% each:

Number of successes Probability

0 0.0576480

1 0.1976503

2 0.2964755

3 0.2541218

4 0.1361367

5 0.0466754

6 0.0100019

7 0.0012247

8 0.0000656

GS have potential to hit 8 times (0.006561%) 

WM have potential to hit 5 times (7,7%)

GS to hit 5 times: 4,66%

most likely scenario:

GS - 2 hits (29,6%), close second: 3 hits (25,4%)

WM - 3 hits (34%), second: 4 hits (25,9%)

answer: go for WM for this champion

Looking at the cumulative probabilities, I agree. For WM, P( 2<= HITS <=4) = 0.84, for GS = 0.69. Even allowing that the CA for the Retaliation Artifact will on average generate an extra hit in 5 five turns, then P( 2<= HITS <=4) = 0.71 for GS.

So, WM would be better for this champion. 

The reason I looked at P( 2<= HITS <=4) was that the binomial distribution average (np) number of hits for WM is 3 and for GS is 2.4. With the extra hit, GS average would be 2.7.

Thanks for the probability analysis.

~ ES