Examples of mathematics algorithms that apply to game development

I am designing a RPG game like final fantasy.

I have the programming part done but what I lack i开发者_如何学Gos the maths. I am ok at maths but I am having trouble incorporating the players stas into mu sums.

How can I make an action timer that is based on the players speed? How can I use attack and defence so that it is not always exactly the same damage? How can I add randomness into the equations?

Can anyone point me to some resources that I can read to learn this sort of stuff.

EDIT: Clarification Of what I am looking for

for the damage I have (player attack x move strength) / enemy defence.

This works and scales well but i got a look at the algorithms from final fantasy 4 a while a got and this sum alone was over 15 steps. mine has only 2.

I am looking for real game examples if possible but would settle for papers or books that have sections that explain how they get these complex sums and why they don't use simple ones.

I eventually intent to implement but am looking for more academic knowledge at the moment.

Not knowing Final fantasy at all, here are some thoughts.

• Attack/Defence could either be a 'chance to hit/block' or 'damage done/mitigated' (or, possibly, a blend of both). If you decide to go for 'damage done/mitigated', you'll probably want to do one of:
  • Generate a random number in a suitable range, added/subtracted from the base attack/defence value.
  • Generate a number in the range 0-1, multiplied by the attack/defence
  • Generate a number (with a Gaussian or Poisson distribution and a suitable standard deviation) in the range 0-2 (or so, to account for the occasional crit), multiplied by the attack/defence

For attack timers, decide what "double speed" and "triple speed" should do for the number of attacks in a given time. That should give you a decent lead for how to implement it. I can, off-hand, think of three methods.

• Use N/speed as a base for the timer (that means double/triple speed gives 2/3 times the number of attacks in a given interval).
• Use Basetime - Speed as the timer (requires a cap on speed, may not be an issue, most probably has an unintuitive relation between speed stat and timer, not much difference at low levels, a lot of difference at high levels).
• Use Basetime - Sqrt(Speed) as the timer.

I doubt you'll find academic work on this. Determining formulae for damage, say, is heuristic. People just make stuff up based on their experience with various functions and then tweak the result based on gameplay.

It's important to have a good feel for what the function looks like when plotted on a graph. The best advice I can give for this is to study a course on sketching graphs of functions. A Google search on "sketching functions" will get you started.

Take a look at printed role playing games like Dungeons & Dragons and how they handle these issues. They are the inspiration for computer RPGs. I don't know of academic work

Some thoughts: you don't have to have an actual "formula". It can be rules like "roll a 20 sided die, weapon does 2 points of damage if the roll is <12 and 3 points of damage if the roll is >=12".

You might want to simplify continuous variables down to small ranges of integers for testing. That way you can calculate out tables with all the possible permutations and see if the results look reasonable. Once you have something good, you can interpolate the formulas for continuous inputs.

Another key issue is play balance. There aren't necessarily formulas for telling you whether your game mechanics are balanced, you have to test.