Statistically this benefit is not large, but is not neglegible. My best guess on how to express luck is to use the 'standard error of the mean'. This is the average value of how off can the average of the roll results be from the mean dice roll value after a certain number of rolls. A die rolls a uniform distribution and its standard deviation can be obtained from Wikipedia.
Doing some maths, it is clear that 'luck' dissipates rather fast:
So if you used a deck of a single set, you would have a standard error somewhere under 1.5 damage point depending on the damage dice.
A rapier is a d8 and after 8 rolls the error is of 1 damage point (technically 0.81). So after eight d8 rolls an bad average of 3.5 is common and it means that instead of doing 36 points of damage, one did 28 (12% less). Expressed differently, the distribution of the obtained averages can be calculated (I cheated and used the anydice website for the data so I didn't have to do much math). A d8 on average does 4.5, but you have after 8 rolls got a 23% chance of it being between 4.25 and 4.75 , while a 19% chance between 3.75 and 4.25, 10% between 3.25 and 3.75, which is the last bin within the 1 point of the standard error. Below which the chances are 4%, 1% and lower.
PS. If a royal-free poker deck where used instead of a dice, the suits could be a marker for some interesting dynamic, say the weapon does fire, slashing, acid or blugeoning damage.