As we all know, calculating and tracking XP can be a real hassle (based on the specific HPs of the exact number of monsters killed, plus the exact amount of treasure, and the exact worth of magic items, divided into the number of "worthy" PCs, etc...). For those who want to skip all the paper work, here is the ultimate easy button:
Tally the Number of Completed Adventures. You are ready to level up when you have survived a number of adventures (at your current level) equal to your current level.
Complete one adventure - level up to 2nd
Complete two more adventures - level up to 3rd
Complete three more adventures - level up to 4th
It sounds pretty simplistic, but in reality, it captures the holistic concept of "gaining experience", without getting bogged down in the many controversies of how to quantify it. It also removes certain perverse "in-game incentives", like having to needlessly slaughter everything in sight, or rifle through every orc pocket for stray gold pieces, or make sure that every last bit of treasure gets carried out of the dungeon, etc.
Treasure is as an indirect measure of experience in the GP = XP equation, so let's just dispense with it altogether. Especially in a dawn of civ campaign, where coin money is not going to be widespread, it is unfair to punish players for the lack of coinage.
The Inherent Subjectivity of XP
The only variable in my formulation is how to define "an adventure". Well, naturally, that is subjective. But think about it: the amount of treasure given to players is COMPLETELY UP TO THE DM, meaning it is TOTALLY SUBJECTIVE too. The number of monsters available to be killed is also completely subjective, too.
So, what is an adventure? Hard to define precisely, but... we know when we see it! A quest completed... A mystery solved... A treasure gained... An enemy defeated... A territory cleared... Many things would qualify, and they'd all be dependent on the context of the particular campaign. Heck, even "A Significant Delve Survived" might qualify, even if no "boss monster" was defeated and no "monte haul" gained.
For a thief, maybe "penetrating a labyrinth, pinpointing the lair, mapping a path, surveying the defenses, and returning to report" would be a huge undertaking and constitute a completed adventure. Avoiding as much combat as possible, and taking not a copper, the adventure might still be a huge challenge, taking all of the PC's skill, and fulfill the very definition of a successful adventure resulting in much experience gained (even though it counted for nothing under traditional metrics)!
In the end, even with all the bookkeeping of the traditional sort, the level-up decision still based on the DMs subjective opinion! As Gygax makes clear in his opening paragraph on Gaining Experience Levels (1e DMG, p.86):
The gaining of sufficient experience points is necessary to indicate that a character is eligible to gain a level of experience, but the actual award is a matter for you, the DM, to decide.
So, what I am saying is, leveling up based on "the number of significant adventures completed" is no less subjective than "the number of XP gained". Since the whole thing is based on DM subjective decisions anyway, let's just dispense with all the unnecessary paperwork.
Real-time Measurements of Level Advancement
It's not like this is a formula for out-of-control advancement. Let's say you, like many of us, enjoy a once-a-week gaming session.
--After a month (4 sessions), your PCs would be 3rd level.
--After two months (8 sessions), your PCs would be 4th level.
--After three months (12 sessions), your PCs would be 5th level.
--After six months (24 sessions), your PCs would be 7th level.
--After a full year of play (52 sessions), your PCs would be 10th level.
Sounds about right to me.
If your 11 year old son takes up the game with his friends one summer, by all means, teach him to calculate and count XP. It can be very gratifying and a fun part of the game, I remember enjoying it when I was that age.
But if you are like me now, gaming over a table late at night... with loud music on... imbibing copious libations... being generally absurd... well, for me, dropping the detailed accounting requirements is a nice plus.