Alternate Turn Undead Mechanics

I got a great question from commentator Nathan Jennings the other day (in the "Best Combat Algorithm" thread; link). Definitely not something I'd considered before, so it intrigued me. He wrote:

Question (perhaps worthy of a blog post?): I know you don't like clerics. But, for the sake of a nice reader like me, can you imagine how the turn-undead mechanic could be cleaned up?

Let's look quickly at the Turn Undead table in OD&D Vol-1:

Notice that the places where the results are numerical are very narrow; just 3 cells long/wide. These values can be modeled with a table-free mechanic of rolling 2d6 + 2 × (Cleric level − Undead hit dice), needing a total of 9+ for success. (In some printings of OD&D skeletons are shown as 1/2 HD [treat as 0], with zombies 1 HD, then ghouls 2 HD, etc., adding 1 for each type.) If we extrapolate this, then the "T" values in the table effectively get replaced by 5's and 3's, easy but not automatic success, and when the roll is automatic then you get "D" results.

If I used clerics in my games, then I might consider taking out the unnecessary multiplier of "2" throughout this formula, and simply roll 1d6 + Clr level − Undead HD. Success, as usual for 1d6 rolls, is 2-in-6; that is, a total of 5+ indicates success. Impossible results are "N" and automatic results give the "D".

But here, let me meta-turn Clerics themselves: I get "D" and the problem disappears. :-)

I love questions like that; thanks, Nathan!