60 Minutes of Thoughts: The Minimal Megadungeon

 I started imagining a dungeon based on the connecting branches of our christmas tree, which is a story I won't go into now. It got quite big, which made me wonder when it starts to qualify as a megadungeon? I know various people have expressed various opinions online and in some of the game's earlier editions, but this is the method that makes most sense to me for defining a megadungeon.

Note, this doesn't factor in features that make a good megadungeon, things like multiple factions, entrances and exits, etc.

A megadungeon is one with enough encounters to take you at least from the game's starting level to the level at which your characters have a scope of power and concern beyond dungeon-crawling. Ideally, this can be reverse-engineered to a number of rooms to have that many encounters.

(N.B. this standard probably means that games which don't provide a clear method for making dungeons, don't provide any way to level up/gain game-changing power through dungeon exploration, or at least give some ratio of rooms:encounters, can't have megadungeons. I think I'm OK with this for my definition - such a game evidently isn't very concerned with dungeons, so making a campaign of one would be an odd choice.)

So for example, in bog-standard 5e (because that's what I have the books for on-hand, and because I find interrogating its undercooked default outcomes is often funny or interesting):

• Level 11 is the level at which characters are considered 'masters of the realm', potentially determining 'the fate of a nation or even the world'. They might choose to keep on crawling but the game isn't expecting it (not that it's expecting them to be megadungeoning as a default anyway, but that's besides the point here).
• According to this post on reddit, you'd expect 266 'easy', 133 'medium', 88 'hard' or 60 'deadly' encounters to reach level 11 from 1. 
• According to 5e's dungeon-building appendix, about 50% of all rooms should contain a monster encounter of some sort. (Given that XP for traps and other challenges is optional, we'll ignore it here). 
• The highest incidence of random encounters the game suggests is an 18+ on d20 rolled every 4 hours, for the most dangerous areas. The dungeon probably counts as this. If we assume the PCs are resting in safe places (since we're looking for a minimum size of space, we set harsh conditions) and are taking the 8-hour adventuring days the game expects before resting or retreating, that's two 15% chances per day.
• There's no random dungeon encounter table, so if we assume that - as a megadungeon - PCs sometimes stumble into level-inappropriate encounters and sometimes into trivial ones. Let's assume an average of a 'hard' encounter. 
• An adventuring day is expected to be 6-8 medium-hard encounters. Let's assume 6 if the PCs are being careful and slow, and since the encounters are hard. If these take 8 hours and thus trigger 2 random encounter checks, then on average there's a 25.5% chance that one encounter will be a random one rather than a room one and a 2.25% chance that two will. The mean number of random encounters per day will be 0.3. (Thanks, AnyDice)
• So the party clears 5.7 encounters per day. 5e's dungeon-building appendix doesn't include the possibility of non-random encounters in corridors (lol) so that's 5.7 rooms. 95% of the party's encounters take place in rooms. Keeping to our assumption that they're all hard, the party will need to clear 83.6 encounter-rooms to reach level 11.
• If 50% of rooms contain encounters, and assuming rooms never refill except for random encounters (5e provides no other guidance on this), the minimum number of rooms to class as a megadungeon is 167.2; let's say 168 in the name of harshness.
• It'll take 14.667 (say 15) days to do this. Stupidly fast, but that's just how this edition goes if played by its own default assumptions. If we assume that for each week mostly in the dungeon the PCs spend a week in town buying gear and taking downtime activities (possibly a bit high for 5e without Gritty Resting, which would entirely change the maths of this bit), and that in this time some of the rooms DO refill, we can lower the number of rooms a bit thanks to these two refill opportunities.  
• A refill rate equal to the random encounter rate of 15%, for example, reduces the number of rooms needed by (non-random encounters in wks 1 and 2*0.15), so 5.7*14=79.8, 79.8*0.15, 11.97, reducing the required 167.2 rooms to 155.23, call it 156. Not a huge difference. A higher refill rate equal to the initial chances of an encounter in a room being something other than a presumably-stationary 'dominant inhabitant', of 35%, reduces the number of rooms needed in the same way by 27.93, to 139.27, call it 140. 
• As such, I think we can fairly say that the bare minimum rooms to count as a megadungeon for 5e purposes are 140 with a high rate of refilling or a lot of very dangerous encounters, and you're in a grey area until you're at 168. 
• By this standard, alas, my christmas tree dungeon with its 70-some rooms is definitely not a megadungeon. Yet.
• But in other games it might be. Need to check some treasure tables and creature incidence rates in older editions...

Maybe if I do the same for the other side and connect them? I'm thinking this map is inversed-vertical, so more things on each layer might help anyway... (this is highly unlikely to come to anything please do not get too excited.)