Leveling Up
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First, in theory human characters could advance to almost unlimited level in every class except druids assassins, and monks. So the game doesn't end at 20th level. This means that there's a possibility to set up kingdoms, fortresses, create magic items, create spells, and advance the game in some interesting directions. Now, for reasons we'll talk about in a minute it isn't practical to have 100th level characters (for example).
Let's start with restrictions. In 1E there are level restrictions for different character races. Elves, dwarves, half elves, halflings, gnomes, and half orcs can only advance to certain levels in the classes they are allowed to participate in. The only exception is thief, where tall but half orcs can be unlimited (they can be unlimited as assassins). This is because they can be so much longer lived than humans in AD&D that it would unbalance the campaign if they could become unlimited level in everything. So this is a pretty huge change for people playing IE for the first time.
Another big change is that leveling up isn't automatic. You have to pay for it and study/train/pray for it. The Dungeon Master's Guide gives some guidelines but basically the higher the level you want to achieve, the more it costs and the more time it takes. A good rule of thumb is 1000-2000 gold pieces/level advanced to and 2 weeks/level advanced to. So if we're advancing to 10th level it might cost 10,000-20,000 gold pieces and take 20 weeks! This is a built in limitation to keep characters from getting too far in terms of their levels.
This is also a great reason for treasure and magic items, they have to be sold to pay for the next level!
Why is all of this a limitation? Simple, characters get older in 1E (even non humans). Old age has an impact on abilities. Eventually characters become too old to function! If a character was advancing to 100th level it might cost 100,000-200,000 gold pieces and take almost four years to study/train for it.
Now, DM's can certainly modify all of this, but it's a great way to maintain balance in a campaign.
Another thought, and this can be controversial. Characters can't increase by multiple levels at one time. The DMG is very specific about this (and it's in capital letters on page 86). When a character reaches enough experience to level up, they stop earning experience until they have completed the process to level up at which point they can continue earning experience.
So, character a needs 4501 experience to level up to level three. They earn 6000 experience in their adventure, so they're close to level four right? No, they actually only earned 4501 and have to train/pay/study to reach level three and then they can start earning experience beyond 4501.

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