So most of the time a character being created is given a number of AP and works within that. So if I have 40 AP and I want -8 DM, I can look at the chart and see that it costs me 16 of my 40AP. That's easy.

But suppose I am constructing a character the reverse way: I have 40 AP of stuff already and want to add -8 DM to it, how much is it? It can't be 16 AP--that puts the character total to 56 AP and then the cost is 22 AP.

What's the math?

-Marco

Well, say the TAP cost is T(S), where S is your total APs. Now, let's call your original APs 40. You don't need 40 + T(40). You get that. Let's name the new quantity, the new total score, Q. So, Q = 40 + T(Q). You get that, yes? So, solving for Q we get Q + T(Q) = 40. Now, is T an invertible function. That is, do we know T', where T'(T(S)) = S. If so, try T'(Q + T(Q)) = T'(40). If T' is simple, that will reduce down. If not, there is no closed form algebraic solution, and you'll have to build a chart.

ReplyDeleteWe have a pretty good estimation formula for most cases (see post following) which fits this formula so, yes.

ReplyDelete-Marco

Actually, you may not even need to compute T'. If T is simple enough, Q + T(Q) can be simplified in terms of Q. Then you win!

ReplyDelete