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I believe the perk books are equal chance, I'm not positive on that but some one please correct me if I'm wrong as I'd like to know myself.
That said, assuming equal drop chance, there are 133 perk books in the game (19 sets times 7). Thus you are sort of asking how many perk books do I need to collect in game in order to have collected all 133 books that have an equal chance of dropping. Luckily there is an exact match to this situation and it is called the Coupon Collectors Problem.
https://en.wikipedia.org/wiki/Coupon_collector%27s_problem
I won't pretend to understand these concepts, but it looks like you have to get into Sterling Numbers of the Second Kind and some really advanced mathematics.
https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind
I found this calculator for this situation and ran 20 examples at 133 perk books to see how many books your group would need to find in order to get every perk book.
https://demonstrations.wolfram.com/CouponCollectorProblem/
I think this should be a pretty fair number for you to consider as again, I'm pretty sure you are focusing on one of, if not the last book of the 133 and thus you are unintentionally focusing on one of, if not the last book in the 133 set you need.
In any case, the results of the 20 runs were 842, 449, 733, 601, 798, 719, 970, 632, 821, 579, 671, 964, 1048, 1458, 942, 473, 581, 846, 944 & 587. Based on this on average your group seems to need to find about 783 perk books to get every one of the 133 books.
I would say that if you think you've found more than 783 perk books (seems unlikely to me on day 25) then you might be having slightly bad RNG luck. If you your group is approaching the 1,458 perk books (the highest in my 20 run sample) then the RNG gods are probably hating you.
I do realize that you have 4 people playing, but I think you actually have to focus on how many perk books you've found as a group, and not how many people are playing. As a multiplayer situation with 4 people likely does not increase your chances by 4x, if you consider that some players might focus on farming, cooking or base building and not be actively collecting books. Also, if multiple people are doing the same quests at the same times, then you have to consider that there are still only so many places in that quests POI where a perk book can spawn/drop and all 4 of you are sharing those same spawn drops, so the amount of perk books you collect during shared quest is likely the same as if 1 player was playing.
That said you can argue you can complete more quests quicker as with 4 people you will complete the quests faster, but that will be a small speed increase, and wont be 4x as fast. In fact, in my experience playing multiplayer with people I know actually tends to slow down a lot of our game play as you divvy up books and other loot figuring out who needs what and you get side tracked having side conversations unrelated to the game as your character stands about in the zombie wasteland when he could be looting etc.
Yep, it's absolutely just RNG.
OP - unless you are playing a self-imposed "no traders" game keep checking the traders whenever they refresh.
If you want to find Lucky Looter books put a point or two in the Lucky Looter perk. When you get the full set the loot bonus drops to 0. With one or two points into the related perk I've never taken more than a few days to find all 7 in a set.
For example:
Deadeye - Sniper perk book
Spear Master - Spear Hunter perk book
Salvage Ops - Wasteland Treasures book
Lucy Looter - Lucky Looter perk book
Gunslinger - Magnum Enforcer and Pistol Pete perk books
Archery - Ranger's Guide to Archery
Miner 69'r - The Art of Mining
Hidden Strike - Urban Combat
and so on.
I mean, there still are bugs in the game. Yucca smoothie gives cold resistance not heat resistance, for example. Pretty sure that's an error.
It is mentioned in the game.
Apologies, you're right. Sleep deprivation; Was thinking of the 1st advanced survival challenge, but that specifically mentions shotgun weekly, not shotgun messiah.
Perk points in Lucky Looter is suppose to increase the chance of finding each of the books until all are read by using the tag "LuckyProb".
Volume 3 is missing the tag, so the outcome is that the book is EXTREMELY rare unless I respec with no lucky looter skill.
Lucky Looter 2-7 all extend Lucky Looter 1, meaning they inherit the values from that item, which does have the tags, unless overridden with new values. Unless Lucky Looter 3 specifically has some tags to override that inherited value it should still work.