Starting The Mathematics of Old School D&D

Much ink has been spilt on how old school Dungeons and Dragons favors clever players who act cautiously in the face of terrible danger.  But what actually constitutes playing cleverly?  What course of action is, in fact, wise?  What is an effective precaution?  Cleverness can consist of acting imaginatively and thinking "out of the box." While that kind of thinking often leads to entertaining gaming sessions, a lot of D&D is also about learning to play the odds effectively.   A more modest sort of cleverness is about making good decisions to improve one's probability of survival in a hostile and constantly evolving environment.  Both players and dungeon masters must learn to make decisions in the face of uncertainty, simply by virtue of the randomness inherent in the game's rules. 

This isn't to say I'm intending to blog on power-gaming or meta-gaming.  That's because creating over-powered characters in old school D&D is fairly difficult.  They're created randomly by one of several processes.  Rather, I intend to focus on rational decision making and planning for dungeon masters and players.  I'm also curious about the implications some house rules have on the outcome of combat.  I want to steer away from questions that may involve thinking too much about "realism" through the lens of physics.  As far as I'm concerned, talking about "realism" in a fantasy game is a waste of time.  What does realism mean in an imaginary world where unicorns and pixies frolic, anyhow?  I'm more concerned purely with what the rules entail and any insights thinking about things mathematically might provide for the sake of an improved afternoon of play.

I'll try to present charts, graphs and equations to explain my thinking.  If I'm feeling ambitious, I may even present the results of the odd Monte Carlo model.  If I'm wrong, feel free to call me out on it.  My hope is that this doesn't turn into me pedantically droning on about stochastic processes and turns into an interesting discussion of rational decision making, tactics, techniques and the interesting mathematical problems presented by old school roleplaying games in general, and D&D specifically.  Hopefully the end result will be a practical advice that will contribute to better dungeons, better dungeon masters, and smarter players.