As of January 11, 2020:
Luck in the code has three definitions:
PerkService.GetCreaturePerkLevel (creature, PerkType.Lucky) = Your Lucky Perk Rank
effectiveStats.Luck (Referred to ‘Effective Luck’ below)
_playerItemStats.Luck (Referred to Luck from Items’ below)
According to Zunath these “look like they’re the same thing just named differently. effective stats take into account when a player’s skill is below the required skill level of a perk.” (Bit odd for luck which has no skill or required skill level for the perk). But essentially they should take into account luck bonuses from items, which on that note:
Luck can be increased by items. Enhancements are not capped, but luck granted by mod slots are capped at five per item. However currently only a few things take into consideration luck from items: Blocking Recovery, Expulsion Maneuver, Molecular Reassembler (at /3), Scavenging.
Lucky Perk Chance of doubling healing dealt.
Tranquilliser and Mass Tranquilliser
Lucky Perk chance of doubling duration. You are informed of the occurrence with a message (“Lucky Shot!”)
Increases the chance of recovering health on hit by luck points (Lucky Perk + Effective Luck). (So at perk level 3, you have (50+Luck)% to regain 3hp).
Increases chance of BaB bonus by luck (Lucky Perk + Effective Luck).
The duration of healing its is calculated as:
30 seconds + Medicine rank x 0.4 seconds + Perk duration bonus (Healing kit expert x 6 and Lucky Perk x 2) (Capping at 94 seconds, as it doesn’t seem to include medicine bonuses from items) .
If you have immediate improvement, there is also a Lucky Perk/2 chance of the immediate health regained being doubled (So capping at 3%).
Works the same as heal kits but with the relevant perks (Healing Kit Expert and Immediate Force Pack).
There’s a Lucky Perk chance that the duration is doubled. You even get a message (“Lucky Force Push!”) informing you that this has occurred.
There’s a Lucky Perk Chance that the points recovered are doubled. You even get a message (“Lucky Force Body!”) informing you that this has occurred.
There’s a Lucky Perk Chance that the duration is doubled. There is a message (“Lucky Force Speed!”) Informing you that this has occurred.
That’s all I can find currently. It look’s like Drain Life, Force breach, Force Lightning, and Force Heal have had their luck effects removed.
Scavenging is calculated like this: Each area has a set ‘level’ if your scavenging level is more than 8 points below this level, you can’t scavenge. Otherwise the DC to scavenge is DC 6 + (Area level - scavenging level) (Min 4). There’s a (Lucky + Effective Luck /2) chance this DC or later DCs are affected, I believe reduced by 1 point.
Smelting is calculated by the Ore Level - Harvesting Level = ‘Delta’. If delta is more than 2, that’s your ingot count (max four, min 2). You have Lucky Perk chance to increase this by one. This is calculated separately from the Processing Efficiency perk which can also add an extra ingot. (Potentially giving 6 ingots?)
Using Molecular Reassembler
There is a second roll based on luck to succeed if you fail your first roll, but looks like it’s not your total luck but rather Luck (from lucky perk) + (Luck from items /3) .
So there’s a Lucky Perk Chance that, ‘chance’ is increased anywhere between 1 and your Lucky Perk Rank. Chance seems to affect a lot- I’m not certain on the full extent but does seem to be basically the chance of transferring an items properties to a craft.