Comparing HD-based cleave mechanics to d20 combat

While not having a session, I've been tinkering with python and excel to crunch some numbers on a cleave mechanic. The proposed mechanic is:

When fighting opponents whose HDs are 1 or less, roll your HD in d6s. Any 5s or 6s rolled will destroy one creature.

I wrote a python script to simulate fighting a goblin (AC 6, HD 1-1) after inputting your THAC0. You can also adjust the damage you do, by default you do 1-6 damage. I found the average number of rounds it takes you to slay a goblin over 100,000 trials at each THAC0 breakpoint, up to HD 9 (THAC0 14). I call this number "GPR" or "Goblins Per Round," e.g. at a THAC0 of 19 it takes you an average of about 4 rounds to slay a goblin, so your GPR is .25 (you slay 1/4th of a goblin every round). I call this d20 combat or ACS (for Alternative Combat System as per LBB)

 Your GPR with the D6 system will be 1/3 of your HD, since you roll a 5 or 6 (a goblin slain) 1/3 of the time (i.e. on a 5 or 6). I call this cleave.

To find out how much more effective cleave is than d20, I divide cleave's GPR by d20's GPR. So if you slay 3 goblins per round using cleave at HD 9, and only slay an average of about one goblin every 2 rounds, cleave is 3/.41 = 7.32 times more effective. This makes sense: at level 9, with a normal sword dealing d6 damage (an average of 3.5 damage every hit), you're killing a goblin in an average of 2.44 hits (sometimes you miss, sometimes you hit but don't quite kill it in one hit), whereas chucking 9 dice per round, you can expect about 3 of each to be either a 5 or a 6, thereby killing 3 goblins every round!

Remember, under normal (btb) combat rules, even if you had 100% chance to hit and did 1,000,000 damage every hit, you'd still max out at one goblin per round, since you can only make one attack per round.

But how do magic weapons change the calculations? I fiddled with excel and got the following:

 (click to enlarge)

As you can see, the more enchanted your weapon is, the smaller the gap between the efficacy of slogging through goblin-by-goblin under normal d20 combat and cutting swathes through the bastards using the cleave mechanic. This stands to reason: a magic weapon won't give you more HD, but it will help you hit harder and hit more often.

As it stands, I'm comfortable using it in this stage. Cleave speeds up combat versus hordes of small enemies.

But what about the odd case where a level 1 fighter with no magic weapon is better off "cleaving" versus a single opponent using his (i.e. the fighter's) one hit die, re-rolling every round and trying to hit that 5 or 6? Remember, using d20, the fighter can only slay a goblin about every 4 rounds, while using his HD, he can slay it in about 3. Isn't it odd to encourage this ostensibly mass-combat system in one-on-one combat?

Fantastically, there's something of a built-in solution: cleave-based combat is binary: either the goblin is dead or it is unharmed. In a party, the fighter will want to help his team by doing damage to the goblin, hoping that this makes it easier for another player to finish it off. (Tangentially related but kind of funny: if you're level 1 and you have a +2 weapon or better, you're always worse off trying to "cleave" a single opponent!)

I'll have to further test how this works when you are mounted (in my system, this gives you a +2 to-hit) or using a longsword (d8 damage instead of d6), but as it stands I'm confident to introduce it to my games. Perhaps being mounted will extend the range that counts as a hit, or will allow you to add 1 to any one die rolled? Maybe every +3 to your damage roll adds 1 to any one die rolled? There are many angles to consider this from, but I will have to sleep on it.