Workbench crate

A workbench crate is a storage container in the Fallout: New Vegas add-on Honest Hearts that is always located next to a Workbench. The random loot of this container is the only source of additional skill books in Honest Hearts.

Locations
The information in parantheses describes the fastest way of reaching a specific crate, optimizing the time between resetting and checking the content.





Contents
Entering a cave containing a workbench crate for the first time permanently sets its content, which is irreversible without loading a save game prior to entering the specific cave. To ensure you receive a skill book from each workbench crate, save directly in front of the entrances to the caves listed above. Reload your save game if you didn't get the desired skill book(s).

Each crate contains random loot created by two checks against a random loot table. Each check results in one of 25 different items or item sets, which mostly include Crafting ingredients and drained Energy Weapons ammunition, but also skill books. This sets the chance for any single item set to 1/25 = 4% (see the specific chances for any contained item below).

Most importantly, each of the two checks has a 4% chance (c1) of creating a and a 4% chance (c2) of creating any two of: Otherwise, it has a 100%-2*4%=92% chance (c0) of anything else as follows:
 * Big Book of Science (BB)
 * Big Book of Science
 * Chinese Army: Special Ops Training Manual
 * D.C. Journal of Internal Medicine
 * Dean's Electronics
 * Lying, Congressional Style
 * Tales of a Junktown Jerky Vendor
 * Tumblers Today

Chances for a variable amount of drained ammunition (if not said otherwise, every unit of drained ammunition has a 25% chance to not appear at all):
 * 4%: 12 checks of 11 Drained flamer fuel tank or 15 Drained microfusion cell or 20 Drained small energy cell
 * 6% $$= 4\%*25\%+4\%*50\%+4\%*75\%$$: 1 check of 8 Drained flamer fuel tank or 11 Drained microfusion cell or 15 Drained small energy cell
 * 4%: 2 checks of 6 Drained flamer fuel tank or 8 Drained microfusion cell or 11 Drained small energy cell
 * 6% $$= 4\%*25\%+4\%*50\%+4\%*75\%$$: 1 check of 6 Drained flamer fuel tank or 8 Drained microfusion cell or 11 Drained small energy cell
 * 4%: 5 Drained flamer fuel tank
 * 4%: 5 Drained electron charge pack
 * 3% $$= 4\%*75\%$$: 1 Drained microfusion cell
 * 4%: 5 Drained small energy cell
 * 2% $$= 4\%*50\%$$: 1 Drained small energy cell (50% chance to create nothing)

Chances for all other items:
 * 4%: 1 Healing powder
 * 4%: 2 Sacred datura root
 * 8%: 1 Knife (25 or 35% weapon condition)
 * 4%: 1 Wonderglue
 * 12%: 1 Leather belt
 * 4%: 7 Fission batteries
 * 0.8% $$= 4\%*20\%$$: 1 Fission battery (80% chance to create nothing)

From this information (and BB standing for Big Book of Science, c0 for a check resulting in no skill books, c1 for a single skill book (which can only be a BB) and c2 for any two of the seven listed skill books) you can derive the chances for:
 * Nothing whatsoever from a single check (neglecting the very unlikely indirect chances of no single unit of ammunition in the first four cases, instead adding a straight 0.01%):
 * $$2*4\%*(25\% + 50\% + 75\%) + 3*4\%*(25\%)^{5} + 4\%*25\% + 4\%*50\% + 4\%*80\% + 0.01\% = 18.22\%$$


 * Empty crate (nothing whatsoever from both checks):
 * $$(2*4\%*(25\% +50\% + 75\%) + 3*4\%*(25\%)^{5} + 4\%*25\% + 4\%*50\% + 4\%*80\% + 0.01\%)^{2} = 3.33\%$$


 * No skill books:
 * $$92\%*92\% = 84.64\%$$
 * c0 and c0


 * Two or more skill books:
 * $$92\%*4\% + 4\% + 4\%*4\% = 7.84\%$$
 * c0 and c2 OR c2 and anything OR c1 and c1 (two BBs)


 * Four skill books:
 * $$4\%*4\% = 0.16\%$$
 * c2 and c2


 * One or more copies of BB (if you receive only one book, it will inevitably be a BB):
 * $$4\% + 4\%*(\frac{1}{7} + \frac{6}{7*7} + 4\% + 4\%*(\frac{1}{7} + \frac{6}{7*7})) + 92\%*(4\% + 4\%*(\frac{1}{7} + \frac{6}{7*7})) = 9.92\%$$
 * c1 and anything OR c2 with at least one BB and anything or c2 with no BBs and c2 with two BBs OR c0 and at least one BB


 * One or more copies of a specific skill book other than BB along with any other skill book:
 * $$4\%*(\frac{1}{7} + \frac{6}{7*7} + 4\%*(\frac{1}{7} + \frac{6}{7*7})) + (92\% + 4\%)*4\%*(\frac{1}{7} + \frac{6}{7*7}) = 2.12\%$$
 * c2 with one or more copies of the desired book and anything or c2 with no copy of the desired book and c2 with one or more copies of the desired book OR (c0 or c1) and c2 with one or more copies of the desired book


 * Two or more copies of BB:
 * $$4\%*(4\% + 4\%*(\frac{1}{7} + \frac{6}{7*7})) + 4\%*(\frac{1}{7*7} + \frac{6}{7*7}*(4\% + 4\%*(\frac{1}{7} + \frac{6}{7*7}))) + 92\%*4\%*\frac{1}{7*7} = 0.38\%$$
 * c1 and (c1 or c2 with at least one BB) OR c2 with two BBs and anything or c2 with one BB and (c1 or c2 with at least one BB) OR c0 and c2 with two BBs


 * Two or more copies of a specific skill book other than BB:
 * $$4\%*(\frac{1}{7*7} + \frac{6}{7*7}*4\%*(\frac{1}{7} + \frac{6}{7*7})) + 92\%*4\%*\frac{1}{7*7} = 0.16\%$$
 * c2 with two same books and anything or (c2 with one book and c2 with at least one of the same book) OR c0 and c2 with two same books


 * Four specific skill books or copies:
 * $$\frac{4\%}{7*7}*\frac{4\%}{7*7} = 0.00001\%$$
 * c2 twice in a row with any specific books

Therefore, even though it is possible, it is not recommended to hope for two copies of a specific skill book to appear in a workbench crate. And unless you are a psychotic perfectionist, it may be very unhealthy to hope for a combination of four specific skill books or even four copies of the same book.