Who is More Fightey? D&D Monsters or AD&D Monsters

Continuing my thinking about morale in the two different systems...

Figure 1: A creature with a morale score of '7' has an almost 60% chance of failing a morale check compared to AD&D's base morale of 50%. 

Since D&D Morale rules mandate the use of 2d6 instead of d% as in AD&D, comparing the two systems requires looking at the distribution of outcomes.  If a relatively cowardly monster in D&D has a morale score of 7 then I would argue that the weakest D&D monsters are slightly less aggressive than in AD&D where their base morale score is 50%.  That's assuming the morale rules are applied under similar circumstances and left unmodified.  The modifiers are where things get complicated, though.

2d6 Versus 1d12 and Clerics Turning Undead

A discussion of clerics turning undead got me thinking about how likely they would be successful given multiple attempts.  To turn undead, you roll 2d6 and compare the result to the target.  I wanted to see how likely one was to succeed against varying hit-dice of baddies, and what the cumulative probability would be if there was no limit on the number of attempts. That in turn got me thinking about why we use 2d6 instead of 1d12 and what the impact would be. 

The d12 is probably the least loved die.  People tend to use 2d6 instead.  But should they? 

The answer is, of course, it depends on what you want to do.  The reason is that the results are distributed differently. 

Figure 1:  1d12 results are uniformly distributed while 2d6 follow a peaked distribution favoring moderate outcomes.

Using 2d6 tends to force more moderate outcomes at the expense of more extreme outcomes.  Using 1d12, since the results are uniformly distributed if the die is fair, will result in more extremes.

Figure 2:  2d6 makes exceeding higher targets less likely while lower targets are easier.

Using 2d6 makes clerics more powerful against lesser undead with lower target numbers to turn, but less powerful against more powerful undead with higher targets.  Using 1d12 makes them more powerful against powerful undead and less powerful against easier undead.  It's an interesting result, I think.