That might be the probability of something, but it’s not related to headshots. You added 2^6/3^6 + 2^7/3^7? The head hit chance for a volley of 7 weapons at .35 and 3 weapons at .18, assuming 95% to hit, is:
Well, there are no 3 weapons with 18%, at least none that I know of. The assumption is 7 weapons (4 pre-HM energy, 3 ballistic), all with at least 35 damage. That means 7 regular weapons fire. The chance you have to compute is the chance that less than 2 hit, which is the chance that 0 hit and the chance that just 1 hit which is 2^6/3/6 + 2^7/3^7, which is roundabout 15%, leaving 85% for a headCAPPING.
Are there any additional rules I don't know of?
Anyway - I didn't mod the Marauder chances because I was so impressed by the guy who managed to single-mech a high-skull mission; I modded it, because when I got my first Marauder (house rule: I keep only one of each mech model), I equipped it with an UAC5, a Snub PPC, 3 ML and an LBX2 (all various plus weapons) + 2 MGs and I think it failed ONCE to destroy a Mech's head when I aimed at it (although the LBX is not the right weapon; an AC/2 would work even better), which simply makes the game silly.
The solution FOR ME is, not to put the Mech away or whatever, but to mod the headshot probability down to something that might be successful, but might also fail (basically what Kereminde says: that you CANNOT rely on it). On the other hand, a Called shot to the head will always hit the head with that array of weapons, and so at least produce an injury. A second called shot to the head will quite probably finish the job.
The thing is, that many missions don't work that way that you can pick targets and shoot them in the head A COUPLE OF TIMES (when you have a very high probability to finish a mech with one shot, the game is way simpler), but instead have priorities (like, hitting every enemy mech in order to avoid them shooting at convoy vehicles or buildings, for example).
In other words, the headcapping probability has to go down to a point where you cannot really RELY on a one shot success and in fact the probability becomes LESS than 50% (this is what Kereminde says is alreadyy the case, but is not).
If you take 20% (for ease of math) and the same mech, you are at 4^6/5^6 + 4^7/5^7 for not headcapping, leaving 53%. At 25% it would be at 69%
Now, this probability WOULD be right, if there were no such things as single weapon hit probability or cover and bulwark and so on. The actual weapon to hit probability is never 100%, and sometimes a weapon may have lower prob like 70%. (If you have a headshot prob of 35%, but the actual weapon to-hit prob is just 50%, for example, due to some pips on the target, then the actual prob goes down). Or there is a damage deduction due to cover/bulwark and so on, so that 2 head hits won't be enough. So the ACTUAL chances to headcap a mech are a lot more situational and generally lower than that theoretical ideal value (for a mech standing in the open, unmoving).
On the other hand, a Called Shot to the head will, if there is a hit (and when you fire with enough things there will always be some kind of hit), there is also an injury, plus the CS will reduce initiative of the Mech by 1(!). In addition, the shots not hitting the head will hit something else - CT, LT, RT, whatever.
The other option is Vigilance, which will give a Mech +1 init plus additional cover and remove all stability damage.
This is also a very powerful option, and the thing is, if you just have a certain probability to decapitate a Mech (and therefore solve a problem terminally), Vigilance is oftentimes a better place to spend morale on - when there is no cover, for example. Or when you have an unsteady mech. Or when you have a mech with partially shorn armor. Or even when you face a lot of enemies.
The bottom line is, that for me, the 23% work. I could change the setup of the Marauder, but the LBX2++ is a pretty fine weapon with nearly no heat, and I don't care. When I use Precision Shot with the Marauder, I still aim to the head, but I do it not because I expect to kill it immediately, which means, I'll be satisfied with the result no matter what, otherwise I don't (or I must be really desperate).
From a gaming perspective, headcapping a mech with a single salvo should be still a delightfully rare thing, not an expected event.