FrankTrollman wrote:You're asking for a solution to the equation:
And while there are fixed integer solutions to that, there are no solutions that work for multiple values of X (other than trivial bullshit like "N = 0").
Wolframalpha says the solution is ...
Y = (1 - 2^(1/N))X
For positive X and N. Which, yes they are. That does indeed work, I even checked.
Obviously you'd want that built into the XP table, but it's not that hard. I mean, you're right that it's not an
integer solution, but you can obviously stay within half a level of power at all times, which is probably better than your power margins on single class characters in the first place outside anything like 4e (or also in 4e as written).
In more general terms, for Z(X-Y)^N = X^N the solution is
Y = (1 - Z^(1/N))X
In case they don't add everything. Now, if things add very differently, you need to balance for the best way to add them and the rest become trap options, but that's matter of either pointing out the traps (with suggested or enforced dual-class options that just fucking work), or making sure none of your classes overlap too much in the first place and everyone just has to get a reasonable package if they do that.
At a design level, you can just fucking compare the dual class options to the single class options as you go, and note how many levels behind they should roughly be to not be stupidly weak or strong. And yes, that's a problem with 40 classes because 40^2 is not something you can check, but if you have some sort of decent option for being more than one class in your game most of those vanish anyway, a lot of them are effectively just a dual-class in one.
The way they built things for the 3.5 PClass factory which let your multiclass characters work at all, that would suggest (given N ~= 1.4) a Z of 1.4 or so for 3e, a second class being worth a bit under half the first, so you're 3-4 levels behind at higher level as a dual-class, which might've been too harsh really, but obviously, duh, it works.
The sort of XP table that has you fall behind appropriately in two classes is also pretty easy to construct, though it could make the awarding of XP slightly more complicated to fit it nicely, it wouldn't be any worse than 3e and would at least have a purpose.
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There are indeed issues around "you must be this tall to ride" powers, but as 3e showed, you don't even need powers or monsters like that in the game (DR 5/+1 3e instead of +1 required to hit from AD&D), and if you want to sandbox at all it's probably better not to. Things should generally have workarounds that make it harder for slightly low level folks, rather than suddenly impossible, and then don't build powers into the game which ignore that difficulty.
Hell, I bet there's even a solution for 4e, no matter how you stacked the powers. Every power is effectively somewhat better than the at-will stuff, and the daily powers are somewhat better than the encounter powers, and the reduction in damage for losing out on the level bonus is entirely predictable. I just don't care enough about 4e to figure it out.
PC, SJW, anti-fascist, not being a dick, or working on it, he/him.