The value of any experience curve has to be tested against the game it's rooted in. Hard to comment whether or not it's useful in isolation because an experience curve will be interacting with all the other balancing factors of your game.
Any experience curve would have to be measured against the gained experience planned due to the new level of actions (assuming you will have scenarios where the amount of experience gained changes) either way it sounds like you have a very specific idea how you would like the curve to "look" why not plot it on a graph and use nurbs or splines to build the line you desire and forget about mathematical purity. Just a thought.
I'm with @Nandrew on this - I'd have a hard time deciding on how to balance an experience system up-front mathematically without playing the thing the experience curve was supposed to interact with.
Note that experience might be a balance factor, but it's a much stronger player reinforcement and engagement tool than simply a balance thing. That means that there are a whole number of ways to increase experience gains and losses that you're missing out on by designing an element of your gameplay with no gameplay present: What if you simply had a base amount of experience per enemy that was multiplied by your current combo (or whatever)? Then you'd want a simple increasing experience cap so that players would push themselves to combo better and better as they progressed so that they could keep earning new levels at the same rate.
Experience and other player-earning systems should bolster and reward them for the gameplay decisions they're making, I feel like you've got the cart before the horse on this. Especially if you're trying to decide on something this easily changeable in advance... Play with different solutions, see which feels the best in practice for users.
You can hardly balance when you don't know how the game plays, which items make you kill faster, how long it takes between enemies, how long players actually will take while chatting/waffling/inventory managing/whatever, or if it's fun to kill things or better to just backpedal to gain exp (Skyrim) or if some items make a difference or if etc etc etc.
Mathematics curves don't mean much until the game is built and is playable, I think.
Yeah, on a similar note, I used to spend many moons obsessing over physical accuracy of my games, making sure that all the weights make absolute sense and all the variables are as close to reality as possible. It usually means very little until you playtest with it. Now days I start off with 'close enough to reality' numbers and then it's largely experimentation from there (maybe revisiting the numbers again, but only for brief periods in between experimentation).
Tho I guess this you are experimenting with non-physical things. I'd just implement a parabola or exponential function (root at zero, adjust parameters to more or less where you want it to be) and playtest. You'll probably find that a simple formula tuned out in the wild will work better than one over-engineered in the lab, so to speak... this is my experience with these things, anyway
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Do you have a playable to show?
Note that experience might be a balance factor, but it's a much stronger player reinforcement and engagement tool than simply a balance thing. That means that there are a whole number of ways to increase experience gains and losses that you're missing out on by designing an element of your gameplay with no gameplay present: What if you simply had a base amount of experience per enemy that was multiplied by your current combo (or whatever)? Then you'd want a simple increasing experience cap so that players would push themselves to combo better and better as they progressed so that they could keep earning new levels at the same rate.
Experience and other player-earning systems should bolster and reward them for the gameplay decisions they're making, I feel like you've got the cart before the horse on this. Especially if you're trying to decide on something this easily changeable in advance... Play with different solutions, see which feels the best in practice for users.
You can hardly balance when you don't know how the game plays, which items make you kill faster, how long it takes between enemies, how long players actually will take while chatting/waffling/inventory managing/whatever, or if it's fun to kill things or better to just backpedal to gain exp (Skyrim) or if some items make a difference or if etc etc etc.
Mathematics curves don't mean much until the game is built and is playable, I think.
Tho I guess this you are experimenting with non-physical things. I'd just implement a parabola or exponential function (root at zero, adjust parameters to more or less where you want it to be) and playtest. You'll probably find that a simple formula tuned out in the wild will work better than one over-engineered in the lab, so to speak... this is my experience with these things, anyway