Luck in general:
Luck is a parameter that cannot be increased by training. The only way to increase luck is to wear +luck equipment or, on Underworld realms, buy tattoos. Some races also have bonus luck.
1) Increases the chance for successful ambush providing +1% bonus to Reputation for every point of luck. For example if you have 10 luck and 100 Reputation you'll 110 Reputation when determining the chance of success. This effect is added after buildings bonuses, arcana and items. This effect does NOT increase your hp.
2) Increases the chance for successful quest. Every 5 lucks adds +3/+2/+1 % respectively.
3) Increases the chance to loot a preffixed/suffixed item.
4) Increases the chance to find more items in a quest. For example in 5th zone you can find either one or no items so the more luck, the more chance to find at least one.
5) Increases the chance to find a better quality item on Necropolis type realms.
6) The difference in luck between player during combat increases the critical strike chance::
Chance for critical hit = (Luck A - Luck B)/5 * 1%
(where A and B are player) Do not forget that critical strike chance is capped at 85%
7) The difference in luck during combat modifies minimum and maximum chance to hit. For every 5 points of difference in luck the chance to hit is increased for the person with more luck. The player with more luck gains bonus to chance to hit while the player with less luck receives penalty equal to the bonus of the first player.
Example: Player A has 20 luck, Player B has 10 luck. The modifier will be equal to 2, because the difference between luck is 10 (10 / 5 = 2). So, player A will have +2% to a maximum chance to hit and player B will have -2% to the minimum chance to hit.
Chance to hit = (Luck A - Luck B)/5 * 1%
8) Increases the chance to find legendary items on Pilgrimages in Act II
Luck does NOT influence:
1) Finding stones
2) Quality of prefixes and suffixes.
3) Quality of items on Underworld type realms.
4) Quantity of items found on caravans.
5) Items looted during expeditions.
6) Chance for a successful upgrade in Well of Souls.