Help a noobie understand critical hits

[Turhan's Bey Company]

Originally Posted by Colonel__Klink

The gaussian distribution comment is fascinating! I'm not quite sure I understand how it's a bell curve? The dice are physical, 3 dice with possible values 1-18.

You roll three six-sided dice and take the sum. Each die has a value from 1 to 6. That gives you a range of possible values from 3 to 18. But there are 216 possible combinations of individual die results which produce sums within that range, and the probability of those sums is not evenly distributed. Consider the possible results of rolling one red die, a green one, and a blue one:

R G B Sum
1 1 1 3
2 1 1 4
1 2 1 4
1 1 2 4

...and so on for a total of 216 possible combinations. Out of all of those combinations, only one gets you a total of 3 and only three get you a total of 4. That's about a 0.5% chance of getting a 3 and a 1.5% chance of getting 3 or 4. This page works through all possible combinations of results, and you can see that totals of 3s and 4s (and 17s and 18s) are sparse on the ground while 9s, 10s, and 11s are significantly more likely. The distribution of probabilities ends up being a bell-shaped curve.


Anyway, if you're using a weapon doing 1d against an opponent with DR7, your best option is probably running away and getting a better weapon. Critical hits can penetrate, but they're unlikely. Depending on exactly what armor your opponent is wearing, you may be able to target eye slits or other gaps in armor, or you can switch to non-lethal weapons like nets or stun grenades to debilitate your enemy rather than killing them, or you can use guile and stealth to avoid them, all of which are options which GURPS supports.