What are the gambling games in the “Black Box” edition of Basic D&D?

I have a vague memory of my father teaching me about dice probabilities from a “mini-game” within the Black box set, at the beginning of being in jail in the salt mines. The other prisoners, is willing to gamble with me, but we use different combinations of dice to see who will roll the higher number. From what I can remember it was from the Escape from Zanzer Tem’s dungeon adventure.

I’m looking to find what exactly those combinations of dice were, and what the rules of the gambling game were.

Nearest neighbors analysis in Red Black Trees

I use a Red Black Tree where each nodes contains a symbol sequence, e.g. top node BB, left child AB, right child CB.

Given a symbol sequence from the tree, is there an efficient way to retrieve n nearest neighbors or all neighbors within a distance radius?

Could I recursively search the children and parent nodes and keep adding each visited node until I have n of them or in the radius case the encountered node is outside the radius?

I know the efficient way for neighborhood queries is e.g. a KD Tree, but I am looking for a data structure that will allow me to insert new sequences without having to rebuild the whole tree each time.

Does Evards Black Tentacles affect the 5 foot cubes above its area?

So I’m playing in a tomb of annihilation game and there were some succubi that we were fighting. We had information ahead of time that a lot of them were grouped up together talking to someone and so I decided it would be a good time to whip out my new spell Evard’s Black Tentacles. Now the problem is that the Dm said that the creatures are flying creatures and are unaffected.

My problem is this, when the spell designates that the 20 foot square area is the area of the spell, does that actually mean hostile enemies have to be physically touching the ground or does the spell reasonably affect the 5 foot cubes that the 20 foot square has above them.

How to roll for avoiding damage when using Black Hack 1e with optional rule “Original armor”?

The Black Hack 1e has an optional rule called "Original Armour". It reads like this:

Original armor

The traditional concept of ascending AC bonuses can still be used with The Black Hack. Attacks are still made by rolling below attributes (such as STR and DEX) however the AC bonus of the target is added to the roll.

For example in ascending AC systems Leather typically adds +2 to a base of 10 (giving you AC12) – with TBH you would roll an attribute test to see if you hit or are able to avoid taking damage, and add +2 to the dice roll. The quick way to read AC from existing resources is just use the last number as a bonus.

But to avoid taking damage in this edition of the The Black Hack one also has to roll under a stat. In which case it makes no sense, in my opinion, to add +2 to the dice roll. Rather, it makes sense to add +2 to the target number. Is my interpretation correct?

For reference, the Black Hack 1e SRD is here. And the optional rules, including the one in question, are here.

Hardwiring the output in quantum black box separation

In this paper, while using a diagonalization argument in Section $ 5$ , the authors write:

Fix some enumeration over all $ poly(n)$ -size quantum verifiers $ M_{1}, M_{2},…$ which we can do because the number of such machines is countably infinite (by the Solovay-Kitaev theorem [15]). Some of these verifiers may try to decide a language by trivially “hardwiring” its outputs; for example, by returning 1 independent of the input. We start by fixing a unary language $ L$ such that no machine $ M_{i}$ hardwires the language. We can always do this because there are more languages than $ poly(n)$ -sized machines.

Maybe I am missing something very basic, but:

  1. Why do we care if some of the verifiers have the output hardwired?
  2. How can we find an $ L$ , like in the description? Why will this $ L$ even be decidable? I know there are more languages than there are Turing machines; but those extra languages aren’t decidable.

Is a young black dragon enough of a challenge alone for group of five level-5 characters?

I have a 5-member party in D&D 5e (ranger, fighter, sorcerer, rogue and bard) who are all level 5. They will soon be meeting with the “big bad”, a young black dragon, in his lair which contains pools of acid. They would most likely be fully rested before the fight.

I know the CR is 7, but I was wondering whether it would prove to be a satisfying battle, in the sense that they may come close to defeat and might be able to beat the odds.

Is this fight well-balanced? Would it be challenging?

If not, should I add some hatchlings or small mobs to adjust the action economy appropriately?

Do Black Tentacles “protect” you from ranged attacks as creatures grappling you do?

If you are trying to shoot some creature, and your target is grappling, rules say: "roll randomly to see which grappling combatant you strike".

Does Black Tentacles spell’s effect count as a combatant? Or should you just roll high enough attack to strike a creature, grappled by Tentacles, as there is no actual target other then the creature you are aiming at?