Instead of 53% attack it should be 48% attack. Gotta subtract the initial 10.
Using OP Stats:
Willpower: 106
Cunning: 126
Base Crit: 5%
Base Crit Damage: 40%
Attack% = (106-10)/2 = 48% = 0.48
Crit% = (126-10)/2 + 5 = 63% = 0.63
NonCrit% = 1.0 - 0.63 = 0.37
CritDamageBonus% = 40% = 0.4 + 1.0(Hakkon) = 1.4
[(1 + Attack%) * (1 + Crit Damage Bonus%) * (Crit Chance%)] + [(1 + Attack%) * (1 - Crit Chance%)]
Attack Ring:
[(1.58)*(2.4)*(0.63)] + [(1.58)*(0.37)] = 2.38896 + 0.5846 = 2.97356
Crit Damage Ring:
[(1.48)*(2.6)*(0.63)] + [(1.48)*(0.37)] = 2.42424 + 0.5476 = 2.97184
Crit Chance Ring:
[(1.48)*(2.4)*(0.73)] + [(1.48)*(0.27)] = 2.59296 + 0.3996 = 2.99256
Keep in mind there are multiple passives and abilities that work to increase effective critical chance. Deathblow and Terrifying Fury come to mind for the Reaver. OP would be best served using the critical damage ring, IMO.
Quick takeaway: If you have low cunning/critical chance, but have a Hakkon weapon...you want to boost critical chance as much as possible.
Example 1: 10/10/10
Base: 1.07
Attack Ring: 1.177
Crit Damage Ring: 1.08
Critical Chance Ring: 1.21
Example 2: 30/30/30
Base: 1.331
Attack Ring: 1.452
Crit Damage Ring: 1.364
Critical Chance Ring: 1.485
Example 3: 70/70/70
Base: 1.937
Attack Ring: 2.086
Crit Damage Ring: 2.028
Critical Chance Ring: 2.119
Example 4: 100/100/100
Base: 2.465
Attack Ring: 2.635
Crit Damage Ring: 2.610
Critical Chance Ring: 2.668
Example 5: 130/130/130 (Critical Damage leapfrogs attack and is very close to Critical Chance)
Base: 3.056
Attack Ring: 3.247
Crit Damage Ring: 3.264
Critical Chance Ring: 3.28
Like Kmeeg pointed out. Once you get to 70% critical chance, you should CERTAINLY prioritize Critical Damage. I would do it much sooner than that though(50ish). Game-play varies when you add in all the things I mentioned before the examples.
For those curious, attack prevails in most circumstances when Hakkon's are not the weapon being used. I only say this because I doubt there are TOO MANY who have super high cunning/willpower but don't have the Hakkons. (snakebitten players ignored)
if you wish to calculate for yourself, just use this formula:
[(1 + Attack%) * (1 + Crit Damage Bonus%) * (Crit Chance%)] + [(1 + Attack%) * (1 - Crit Chance%)]