Turning probabilities

Just for fun, what is the chance of a 1st level cleric turning 4 zombies over the course of 2 rounds? 

Looking at a few different D&Ds:

Holmes: 25.4% 
1e: 30%
Moldvay/LL: 24.1%
"Black Book:" 20.2%

I'm throwing in the book from the 1991 boxed set (black box), the 15th version of basic (as per Acaeum).  At boardgamegeek the reviewer says it, "walks the line between rpg and board game but I think it really does fall on the board game side of the fence."  I disagree.  Acaeum states, "it is meant to be a primer for the D&D Rules Cyclopedia."  I do not own the Rules Cyclopedia and I don't know off hand if the turning rules there agree with the "black book."

In Holmes and AD&D multiple attempts are not allowed and so the "2 rounds" part doesn't matter, and the above is just the chance of turning 4 zombies in these versions.  Moldvay, as mentioned in this post -- and this jibes with my experience -- is typically interpreted as putting no restrictions on the number of attempts.  In the black book (1991), however, “once a cleric fails an attempt to turn undead, all his other attempts during the same battle also fail.”

Since the turning is "spread out" over 2 rounds in Moldvay and the "black book," here are the probabilities of turning all four zombies on the 1st try (1st round) in these versions:

Moldvay chance of turning all in 1st round: 11.6%
"Black book" chance of turning all in 1st round: 16.2%

The reason this is such a big difference is because of rounding the number of hit dice turned.  In Moldvay, round down: "he rolls agains to see how many monsters he turns.  The result of 9 means that 4 ghouls (a total of 8 hit dice worth) are turned away (extra hit dice have no effect)."  In the "black book" on the other hand, round up: the DM "divides the number rolled by the number of Hit Dice each monster has (round leftovers up).  The result is how many undead monsters the cleric turned."  In Holmes and 1e, the roll is not for the number of hit dice turned but the number of undead and so rounding is not an issue.

Some more clerical comparisons (some of the same ground covered in this post - most everything discussed in D&D has been discussed before):

Holmes:
A spell at first level? No

Number of undead turned: 2d6 (number of undead, not the number of hit dice)

Number of attempts: “When a cleric confronts one or more of the undead, consult the following table.”  Once per confrontation, no further attempts. 

1e:

A spell at first level? Yes. In fact, they’ll usually start with more than one, based on wisdom bonus. For example, with a wisdom score of 14, a 1st level cleric starts with the ability to memorize 3 spells. With higher wisdom, they’ll have more.

Number of undead turned: 1-12 usually (or 7-12 or 1-2, depending on type; this is the number of undead, not the number of HD)

Number of attempts: Basically one. “Failure to score the number shown, or greater, means the turning was unsuccessful. No further attempt by the cleric can be made with respect to the particular undead, and they may proceed to attack or otherwise operate unconstrained” and “this function may be attempted only once by each cleric.” There is an exceptional case, when “multiple forms of creatures subject to turning are involved.” Part of the beautifully baroque 1e AD&D.

Moldvay:

A spell at first level? No

Number of undead turned: 2d6 hit dice

Number of attempts: Interpret as unrestricted 

“The Black Book” of the 1991 boxed set (and “The Classic Dungeons & Dragons” of the 1994 boxed set):

A spell at first level? No.

Number of undead turned: 2d6 hit dice

Number of attempts: One each round until failed.

Labyrinth Lord:

A spell at first level? Yes.

Number of undead turned: As Moldvay.

Number of attempts: As Moldvay.

I'm personally happy with any of them.  My favorite is Holmes (probably 'cause that's what I started with), but with a spell at first level a la AD&D/LL.

It's not really possible to directly compare with the others but…

Pathfinder Beginner Box:

1st level cleric…

• Either heal the living OR damage undead: 3 + charisma modifier times per day (so 4 or more likely)
• Cast detect magic, read magic, light, and stabilize “over and over again as much as you want, up to once per round.”
• One more spell (or two more if wisdom is 13 or more – most likely it is because ability score generation is 4d6 drop lowest, arrange to taste).

Trying to relate it to the others...

A spell at first level? Yes.  Basically about 10, 4 of which can be cast ad infinitum.

Number of undead “turned” (actually damaged): all in 30 foot radius

Number of attempts: About 4 or 5 per day depending on charisma