What equation would you use to obtain a curve for determining experience points per level in an RPG?

The level curve cannot exist in a vacuum. It matters more the sources of XP and the total to be awarded over the course of the game. You should look at paper RPGs if you are creating a closed system (as opposed to open ended system like you might in a "social" game). In social style, games as a service games we think more in terms of time. I usually make the early levels come in a rush increasing the average level gain over time to 1 level a day until a max of 4 or 5 days per level at higher levels. We usually have no max level, and often levels have less meaning than in traditional RPGs. Excel is your friend.

One of the main variables is the monsters destroyed (if the RPG has this gameplay mechanic of destroying monsters, that's it). Usually that's the single variable for most RPGs. One really common formula goes like this: XPToNextLevel (level) = level * K * xpPerMonster(level) In english: your hero has to destroy K*level monsters to get to the next level. Assuming you're destroying monsters having a level equal to your hero level. Higher level monsters would yield more xp while lower level monsters less (or nothing if their level is too low). A monster would yield more XP if it's more dangerous or in other ways harder to kill. Using this formula leads to a linearly increasing time required to level up.

There are so many factors to consider.What does a level change do, how much does it actually increase the characters ability to cope with the world?What is the level of team members, are any of them around, how should it change comparing that to single player?Can a skilled player win fight even though he is underleveled? (Compare Dark Souls with a turn based RPG like Golden Sun/FF/Dark Souls and similar)How are the skills obtained?When you found an answer to this question, you can determine how a character can reach the next level. Also take a look what a level can be & mean. If a level increases an attribut by a marginal amount you can easily set the cap quite low, if there are only five levels and each changes the power level by a lot the cap would be really high.Some often used systems:Gradual System - Transistor, Paper Mario, Darkest DungeonReach a certain number of exp to get to the next level, often 100. You normally reach a new lvl slightly quicker the longer you play since bosses&mini-bosses give you more stars/percent.Exponential System - 80% of games, like Bloodborne, DS I&II, Bloodbowl and many moreThe experience point needed to reac a new level is exponentially increased - lower level characters can catch up more quickly while the bonus of a level is noticible, but not a game changer.Step System - Most othersSomewhere in the game you find an upgrade which increases the strength of a character, think a weapon in shooters or an item in the Zelda series. These indirect experience is also strengthening your character and improving his strength.

My method may be over simplified, but it works well for me. Let's say I made a var called xprequired = 1000Once XP >= xprequired, I would subtract xprequired from the XP, increase the level by 1, and I generally use xprequired = xprequired * 1.2.What makes it good for me is that it will increase in a compound manner.Here are the XP requirements for levels==========================Level 1 = 1000Level 2 = 1200Level 3 = 1440Level 4 = 1728Level 5 = 2,073.3Etc...If you dislike the fact that it's in strange amounts, you could just round it to the nearest 50 or 100.

This is an interesting question.   When programming a game what mathematical equation would you need to determine experience?  Now we are asking for a predefined value that we can program blindly into an application as the experience based algorithm.  Isn't that pretty much like the common core and holding teachers to a mathematical result.  If I were to create a game, the game would be inspiring both girls and boys to work together and appreciate their natural strengths while avoiding their weaknesses.  There could be any number of ways this might be accomplished.   What if the answer is not mathematical?  What if we are scoring on creative contributions and interaction between two players?  There must be an algorithm or it simply cannot have an award system.  Let me think about this further.