[Technical Grappling] Faster Grip ST calculation for Extra Arms (and efficiency)

[vicky_molokh]

Greetings, all!

Looking at my crazy idea of seeing how TG handles a cephalopod, I realised what a slow, slow process the calculation of Grip ST is. (Figure number of limbs used in a given grapple [including which ones of them can be legally paired!], add, square, multiply, take a square root.) That seems tedious for something in the middle of a combat.

Instead, there's a shorthand way to do it without checking through the BL table.

Assuming we start with a two-armed creature, and that 'Base Grip ST' is the Grip ST of a two-armed grapple, adding more arms has the following effects:

• Adding two (paired) arms is equivalent to +40% BGST.
• Adding four (paired) arms is equivalent to +70% BGST.
• Adding six (paired) arms is equivalent to +100% BGST.
• Adding eight (paired) arms is equivalent to +120% BGST.
• Adding ten (paired) arms is equivalent to +145% BGST.
• Adding one (unpaired) arm is equivalent to adding +10% BGST.
• Adding two (unpaired) arms is +20% BGST.
• Adding three (unpaired) arms is +30% BGST.
• Adding four (unpaired) arms is +40% BGST, like two paired ones.

How did I arrive at those numbers?

Spoiler:  

Adding six paired arms results in quadrupling BL. We know that each time ST doubles, BL quadruples, since BL is quadratic.
Adding two paired arms doubles BL. Doubling BL is roughly equivalent to increasing ST by 40.1421%. Simply put, Sqrt(2) = 1.41421...
Adding four paired arms multiplies BL by 3, and sqrt(3) = 1.73...

For unpaired, things get slightly more fiddly. An unpaired arm adds ¼ Base BL, since ½ST=¼BL. So yeah, calculate square roots once, then see the ST value.

Conclusions:
Based on TG rules, Extra Arms have diminishing returns for purposes of Grip ST / Control Points. The +2 per extra arm to all rolls to Grapple, Break Free, and to prevent an opponent's attempt to Break Free, OTOH, is still a very, very cool thing. The flat +2 ST to Choking being replaced with a percentile-and-diminishing bonus to Grip ST means that the whether Extra Arms are a point-efficient investment for boosting Choking will depend enormously on the number of arms and the base ST of the character.

Somewhat subtly, having Stretching and increasing your limb SM by 1 seems like the cheapest way of attaining +1 DX and +15% Trained ST from p. 9, as opposed to buying the Long enhancement to do the same (since you don't really need +swing for grappling except in rare cases).

Comments? Additions?
Thanks in advance!