gmalivuk wrote: King Author wrote:
So do the Triangular Numbers, which I just recently learned about, but those ones you have to manually add together
What do you mean by this? Can't you just check the total XP against the triangular numbers like you would the Fibonacci numbers? Spreadsheets I've made for D&D 3 and 3.5 characters basically did just that, since those editions required 1000n points to move from level n to level n+1.
Yes, technically I could treat the Triangular XP like Fibonacci XP (yikes, I think I just broached the nerdiness density limit), but they scale differently so they need to be treated differently; every couple of iterations in the sequence, the Fibonacci numbers add an order of magnitude, whereas the Triangular numbers stay the same number of digits for long stretches. Like, Fibonacci 50 is 12,586,269,025. Triangle 50 is 1275. Fibonacci 100 is up to 354,224,848,179,261,915,075 which is ridiculously higher than Fibonacci 50. In contrast, Triangle 100 is 5050; not even quadruple Triangle 50.
So if the characters in the game in question have a cumulative XP stat, Fibonacci works better because each next number in the sequence is just the next milestone for your constantly-accumulating XP. And more importantly, the rate at which the Fibonacci numbers scale is perfectly suited to something like cumulative XP progression; assuming that higher and higher-level monsters/whatever give you progressively higher amounts of XP, you'll never level up too fast or too slow.
With the Triangular numbers, however, because each number in the sequence is so close to the number before and after it, if you had cumulative XP, you'd level up ridiculously fast. Take Fib 50 and Tri 50 again -- to get from Fib 50 to Fib 51 you need to gain 7,778,742,049 additional XP. To get from Fib 51 to Fib 52, you need an additional 12,586,269,025 XP -- a significant increase from the last level-to-level amount. By contrast, to get from Tri 50 to Tri 51 you need, obviously, 51 additional XP. To get from 51 to 52, you need an additional 52; the "XP to Next Level" using Triangular numbers is always only one more than you needed last time, a very linear, very shallowly-increasing amount. When using Fibonacci numbers, on the other hand, the "XP to Next Level" starts jumping up by larger leaps and bounds the higher level you get.
So what I was saying was, if you want to use Triangular numbers (which I highly recommend for tabletop RPGs where humans are dealing with the numbers -- Fibonacci is better for computer and videogames where the electronic brain is doing all the maths), it's a good idea to zero-out XP after every level up. Such that, going back to the earlier example, to get from Level 50 to Level 51 you'd need 1,326 XP (rather than 51). To get from 51 to 52, you'd need an additional 1,378 (rather than 52). And again, every time you level up, your XP is reset to zero and you have a new goal to shoot for, rather than your XP just being a running total of all XP you've ever obtained.
By the way -- what's it say that you can google "first 1000 fibonacci numbers" and get a first-page hit, while googling "first 1000 triangular numbers" doesn't get you what you're looking for?
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