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\$\begingroup\$ "Finding the probability distribution of the total point-buy equivalent value is computationally feasible using the right algorithm" I'm not so sure it is, because this system routinely produces characters with ability scores both much higher and much lower than 5e's point buy system allows. \$\endgroup\$ –
There is a tool listed in the equipment section of the PHB called Cook's Utensils, and the rules for tools state: A tool helps you to do something you couldn't otherwise do, such as craft or repair an item, forge a document, or pick a lock. Your race, class, background, or feats give you proficiency with certain tools.
In 5e terms, instead of rolling some dice for strength, then dexterity, then constitution etc, you instead roll dice for which attribute gets a +1 bonus. If two players have the same number of dice, then their attribute total comes to the same value.
6. My friend recently told me a flaw called Chicken infested which could be used for extremely broken things as well as outright silly things. One of the examples he gave was that since drawing a component from your spell pouch was a free action and dropping something was a free action as well you could draw things and drop them till you draw ...
Abyssal Chicken (Baldur's Gate: Descent into Avernus, p. 96, under "Spawning Trees"): With your permission, a character who casts the find familiar spell can henceforth choose to conjure an abyssal chicken instead of a raven. Additional options listed in a section preceding all monster entries in an adventure:
section (page 41) explains how the characters can reopen a closed tavern located in Trollskull Alley. Since the building is already there, the cost for maintenance is 1000 gp, plus 250 gp paid upfront for the guild licenses and contracts. There's additional details involved, like the guilds you have to talk to (Brewers Guild, Fellowship of ...
Here's the relevant ability from Xanathar's guide to Everything: Prepare Meals.As part of a short rest, you can prepare a tasty meal that helps your companions regain their strength.
Your question looks at the D&D 5E ability check system a little bit backwards. The mechanic is in fact called ability checks, not skill checks or tool checks, and it's intended to be used looking at the ability first, and then figuring out whether proficiency in a skill or tool might apply.
CR 5-7: 15 AC. CR 8-9: 16 AC. CR 10-12: 17 AC. CR 13-16: 18 AC. CR 17+: 19 AC. According to the guidelines, the ultimate CR of a creature is the average of their offensive and defensive CRs. However, the DMG encourages additional tweaking and adjustments to individual monsters beyond the listed guidelines:
\$\begingroup\$ @Theik He has the wolf on a rope at the moment and he is feeding it regularly. The wolf was originally chained up, so I don't see an issue with the shackling of the animal.