Friday, July 31, 2015

mathematics - Make a fake random distribution?


Sometimes a "real" random event seems unfair and makes players frustrated. For instance a enemy has probability of 20% to cause double damage("critical hit"). Thus he could make 4 critical hits in a row with 1/725 probability. It's not as small as it sounds.


I hope the probability could be adjusted after each hit. If the player just got a critical hit, the probability decreases for the next hit. Otherwise it increases.



Is there a mathematical model for this behaviour?



Answer



You may wish to completely rethink what "critical hits" do in your system and why you're using them. "Well, other RPGs use them!" is not a valid reason. One warning sign of a skewed design is the need to apply more and more special rules.


Any kind of random bonus takes away from direct, tactical player skill and adds to strategic planning (RPG item load-out, prioritizing stats on gear, etc...). Because of this shift of focus you have to decide what your game is about before wantonly applying old standards like criticals and fumbles.


My suggestion is that if you want randomness to take any part in your game then glory in it, let it be random.


But if you really want to add more arbitrary rules you can simply start a countdown when the first critical happens and during that countdown any more criticals are reduced to 50% and then 25% and so on. Each critical, of course, resets the countdown. This gives you two places to tune your arbitrary rules: how long is the countdown and how much reduction is accumulated at each critical. A combination of those two controls lets you clearly avoid the unspoken problem of "what if the boss gets a critical, then normal, then second critical?" that a simple chain check wouldn't fix.


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