Help a noobie understand critical hits

[Colonel__Klink]

Hey folks! I have been hard at work designing my first setting in GURPS, I have spent years playing other systems and always wanted to play GURPS but I came across a hurdle studying the "combat lite" section of the basic set.

It describes that a critical hit is scored on a 3-4, but can be augmented to 3-5 with an effective skill of 15 and a 3-6 with an effective skill of 16. that's a pretty big range! 40% of the possible dice range (3-18) is a possible critical hit! That's pretty cool but also insanely powerful for what seems to be pretty easy to achieve, a sixteen skill.

So that makes me wonder, is that 16 effective skill their skill on the character sheet or the effective skill AFTER modifiers such as distance, character speed, cover ect?

How does this effect armor?

*That* question is really why I logged in. How do you allow a chance of victory if the character is using a 1d6 weapon and the enemy has an armor with a DR of 7? Is it entirely critical hits?

Thanks again for any help with these questions ya folk wanna provide :).

[mlangsdorf]

The 3-18 range isn't linear. It's a gaussian distribution, and the chance of rolling a 6 or less is around 1 in 11. See Basic p 171.

The 16 or less is final effective skill, after dealing with size, speed, and range, footing, injuries, lighting, or whatever. So it can be difficult to achieve in practice.

In practice, the big advantage of a critical hit is that the target doesn't get to defend. Around 50% of the rolled results of a critical hit have no other meaningful effect. I've seen plenty of critical hits get absorbed by armor.

If you're using a 1d weapon against a target with DR 7, only a fraction of your critical hits are going to penetrate. Find some other way of dealing with your foe: grapple them, attack their armor chinks, use an All-Out (Strong) attack to get extra damage, shove them off a cliff, or run away/surrender. Not all combat challenges are beatable and not all of them can be defeated by the simple tactic of hitting things with light weapons.

The one adventure I remember when the PCs were street toughs doing around 1d+2 damage per hit and we ran into a gang enforcer in full plate, we turned tail and ran. The enforcer had a sword and could cut through our armor on any hit while we have to co-ordinate and get lucky to grab him and get some injury through his armor. But that's what the GM wanted and why he placed a gang enforcer in full plate there.

[Colonel__Klink]

Originally Posted by mlangsdorf

The 3-18 range isn't linear. It's a gaussian distribution, and the chance of rolling a 6 or less is around 1 in 11. See Basic p 171.

The 16 or less is final effective skill, after dealing with size, speed, and range, footing, injuries, lighting, or whatever. So it can be difficult to achieve in practice.

In practice, the big advantage of a critical hit is that the target doesn't get to defend. Around 50% of the rolled results of a critical hit have no other meaningful effect. I've seen plenty of critical hits get absorbed by armor.

If you're using a 1d weapon against a target with DR 7, only a fraction of your critical hits are going to penetrate. Find some other way of dealing with your foe: grapple them, attack their armor chinks, use an All-Out (Strong) attack to get extra damage, shove them off a cliff, or run away/surrender. Not all combat challenges are beatable and not all of them can be defeated by the simple tactic of hitting things with light weapons.

The one adventure I remember when the PCs were street toughs doing around 1d+2 damage per hit and we ran into a gang enforcer in full plate, we turned tail and ran. The enforcer had a sword and could cut through our armor on any hit while we have to co-ordinate and get lucky to grab him and get some injury through his armor. But that's what the GM wanted and why he placed a gang enforcer in full plate there.

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. Because there are three dice and the minimum pip each one can display is a one and the maximum pip they can display is an 18. The physical dice do not change even as the modifiers for rolls do. addeed: but I see your right. Since the critical threat range depends not just on player skill but the modifiers to the skill. So the threat range is not 40% but up to 40% situationally.

Looking at the page mentioned (probability of success) I think you were referring to the bell curve of success rolls after modifiers take effect. I was thinking of it differently. With 15 possible dice outcomes up to 40% can be critical hit and 13% (a roll of 17 or 18) critical failure. It's kind of funny because I was REALLY thinking about this while imagining damage models.

1d6-2 is not the same as a 1d4. It's the equivalent of a 1d4 RIGGED to roll a 1 50% of the time! On that d6 if the player rolls 1-3 the outcome is 1. Keeping that in mind you can design weapons in game that say... won't penetrate a piece of armor at all 50% of the time. You can do 2d6 - 6 which sounds zany but it's not. That means there's a 50% chance of 1 damage then a mere 16% chance of all other outcomes allowing a maximum of 6 damage rather than a maximum of 4 damage like 1d6-2 would grant. It's been on my mind a lot as I'm not sure if I like the game's damage rules for modern weapons. The idea that with a hunting rifle ONE hit will send a vampire character (vampire the masquerade rules I've been working with that book to help build my setting, ) straight into a topor coma straight out of the gate is... that's not good gameplay to me. It's a bit silly tbh.

I'll take your suggestions about combat encounters to heart and reaaaaaaalllly think about what I'm putting in front of them. It sounds like critical hits are not always the option to score a wounding hit. Maybe rolling for "shoot him in the face." (I'm doing a campaign in a tl9 punk setting so there's going to be a lot of gunpowder with an occasional laser. yes cyborgs AND vampires! )

[dcarson]

There aren't 15 possible dice outcomes, there are 216. The total only has 15 results but they are not even. There is only 1 way to get a 3. There are 27 ways to roll 10. So you get a 10, 27 times as often.

[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.

[Donny Brook]

How many Hit Points (HP) do the vampires have? What is the Damage Resistance (DR) of any armor they have? And what is their typical Health (HT) score?

[Curmudgeon]

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. Because there are three dice and the minimum pip each one can display is a one and the maximum pip they can display is an 18. The physical dice do not change even as the modifiers for rolls do. addeed: but I see your right. Since the critical threat range depends not just on player skill but the modifiers to the skill. So the threat range is not 40% but up to 40% situationally.

Looking at the page mentioned (probability of success) I think you were referring to the bell curve of success rolls after modifiers take effect. I was thinking of it differently. With 15 possible dice outcomes up to 40% can be critical hit and 13% (a roll of 17 or 18) critical failure. It's kind of funny because I was REALLY thinking about this while imagining damage models.

<snip>

Just in case you're still confused about the bell curve for three dice, I'll take a crack at explaining it.

We have three dice, each of which has six faces, numbered 1 through 6, and we are interested in the sum appearing on those three dice. The possible sums vary from a low of 3 (each die shows a 1) to a high of 18 (each die shows a 6). The range of possible sums is 3 to 18, or 16 possible sums.

The problem, as it were, is that the sums do not have an equal probability of occurring. To make this clearer, suppose that we can identify which number appears on which die. For our purposes, we will designate one die as being red, one die as being yellow and one die as being blue (all with white pips).
All the die rolls are independent, i.e., what number appears on the red die has no effect on what number appears on either the yellow die or the blue die. We can now enumerate all the possible sums that appear on the three dice. Imagine that wr have rolled 1 on the red die and 1 on the yellow die, we can still roll any of the numbers 1 through 6 on the blue die, meaning that there are 6 possible sums when the red die is 1 and the yellow die is 1. Now assume that the red die is still 1 but the yellow die is 2. The blue die can now show any value of 1 through 6 for another 6 possibilities. We can do this for the yellow die being 3, 4, 5 and 6 as well. Each case gives us six possible outcomes for a total of 36 possible sums when the red die is 1 and we have run the yellow die and the blue die through all of their possible outcomes. If we rotate the red die to 2 we hve another 36 possible outcomes for the sum that appears on the yellow die and the blue die. This again holds true for each of the other values the red die might show, giving 36 possible sums for each value on the red die. Summing them together, there are 216 distinct and different ways to get our sum which still is confined to a range of 3 to 18.

It is the weight of the different possible outcomes that gives us our bell curve. Of the 216 different rolls we can get on our three dice, only one, red=1, yellow=1, blue=1 will give us a sum of 3 and only one (red=6, yellow=6, blue=6) will give us a sum of 18. However, to get a sum of four, we need two dice to show 1s and one die to show a 2. Whether it is the red, yellow or blue die that shows the 2 is immaterial, any of those possibilities will give us a sum of 4. Likewise for 17, where we need two dice to show a 6 and one die to show a 5.

Turning these 216 different possibilities into percentages, gives us roughly:
Chance of rolling a 3 is 1/216 or a little less than 0.5%. Chance of rolling a 4, 3/216, or slightly less than 1.5%. Chance of rolling a 5, 6/216, or slightly less than 3%, and so on, until we get to chance of rolling an 18, 1/216 or slightly less than 0.5%.

However, we aren't actually interested in rolling the exact number but in rolling a number or less, making the percentage chance, the sum of the the chance of rolling that number plus the chance of rolling each number that is less than that, which is why the table doesn't quite look like a bell curve. The rolls for an exact number do form a bell curve when plotted.

For a number or less, the progression is 3- = chance of rolling exactly 3 , less than 0.5%.
4- = Chance of rolling a 3, less than 0.5% and chance of rolling a , less than 1.5%, totaling less than 2%.
5- = chance of rolling a 5, 10/216, slightly less than 5% and chance of rolling a 3 or 4, which we just calculated was slightly less than 2%, for a total of slightly less than 7%.
6- = chance of rolling a 6, 15/216, slightly less than 7.5%, and the chance of rolling a 3, 4 or 5, which we just calculated was slightly less than 7%, for a total of slightly less than 14.5%

So, if you can manage an effective skill of 16-, you will critically hit about 14.5% of the time, not 40% of the time.

I hope this helps clarify the matter for you.

[whswhs]

Originally Posted by Curmudgeon

For a number or less, the progression is 3- = chance of rolling exactly 3 , less than 0.5%.
4- = Chance of rolling a 3, less than 0.5% and chance of rolling a , less than 1.5%, totaling less than 2%.
5- = chance of rolling a 5, 10/216, slightly less than 5% and chance of rolling a 3 or 4, which we just calculated was slightly less than 2%, for a total of slightly less than 7%.
6- = chance of rolling a 6, 15/216, slightly less than 7.5%, and the chance of rolling a 3, 4 or 5, which we just calculated was slightly less than 7%, for a total of slightly less than 14.5%

So, if you can manage an effective skill of 16-, you will critically hit about 14.5% of the time, not 40% of the time.

Actually, there's one way to roll a 3, three ways to roll a 4, six ways to roll a 5, and ten ways to roll a 6. So the chance of rolling 3 1/216, a 4 or less is 4/216, a 5 or less is 10/216, and a six or less is 20/216, or just under 10% in that last case.

[Colonel__Klink]

Originally Posted by Turhan's Bey Company

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.

The best way to approach a rabbit hole is to leap straight down it. Really fascinating to think about the probabilities now as that explained it muuuuuch better than pp 171 did. I had simplified too much apparently! But in that insight there's a new bit of information. It seems to me... adding dice will skew possible results to the median and away from the extremes won't it? So while 2d6-6 will skew results to 1 due to changing results of 1-6 into ones, there's more combinations in those dice that can result in a 7 than a 2 which means that the results aren't quite skewed "50% rolls will result in a 1."

And yes, it seems if someone's that armored and your weapon is that outclassed then per game rules it seems that guile or sheer skill at shooting his eyeballs are the options. TBH, that's not frustrating it's simply illuminating on how I should plan encounters and set up scenarios to prepare characters to approach them appropriately.

Originally Posted by Donny Brook

How many Hit Points (HP) do the vampires have? What is the Damage Resistance (DR) of any armor they have? And what is their typical Health (HT) score?

In gurps the typical character has a range of 10-13 HP. Even vampires from the vampire the masquerade book.

Per the rules in the book being a vampire (with all the associated disadvantages) costs 55 points. A vampire CAN have a discipline (a spell) that can be fueled by blood or fatigue points. One option is fortitude which for the cost of TEN FATIGUE at MAXIMIUM LEVEL will grant a paltry ten damage resistance. It will cost 2 fatigue to have 1 damage resistance which is well.. useless.

So farmer John shoots him with a 7.62 bolt action rifle from the equipment section from the basic set. This does 7d PI damage. On my first roll it was 26 damage. On my second roll it was 24 damage. On my third simulated roll it was again 26 damage. So lets say it's 26 damage. Lets say the character has 13 hp.

Without having literally max level fortitude and spending all of his fatigue he will be at -13 HP. He then makes a roll to stay conscious against his HT of 14 correct? I rolled 5 times and succeeded every time just to see. He then has to make the same roll to not immediately be "killed" (vampries don't die per the rules the same as other characters.) Same HT roll correct? He succeeds.

If he uses all of his blood points (generation 13 vampire is the basic one, 10 blood poitns) over 5 rounds he will be at -3 HP. He still didn't make it and literally will not survive without blood. He will fall into topor. A vampire coma lasting hours to years depending on the character's condition an lose 1 attribute point. He's lucky most people just die.

If he literally uses max level fortitude for 10 damage resistance he will be at -3 , suffer all the defensive penalties (his dodge is HALVED because he lost more than 2/3rds his hp), have to spend two full rounds healing to not be in danger and is likely to just flat out die anyway.

He MIGHT be able to get some more blood while succeeding in that stay awake roll but here's the catch.... He's lost more than 2/3rds of his HP so all of his defenses are halved per the game rules. He's a sitting duck.

Farmer john shot dracula jr ONCE with the remington he keeps in his truck rifle rack and it's game over.

And no dracula jr is not going to plausibly in the story (edited: i had said realistically originally but I'm not interested in "realistically" I'm interested in a good game.) be strolling around everywhere wearing gear that makes him look like he's invading fallujah. This all is why I'm sitting there re-writing all the weapons with new damage models. As bad as farmer john's remington is it doesn't even compare to a ar-15 (5d 3 shots per turn) or a m16 (5d 12-15 shots per turn.)

[mburr0003]

Originally Posted by Colonel__Klink

How do you allow a chance of victory if the character is using a 1d6 weapon and the enemy has an armor with a DR of 7?

If you're the GM you do not throw heavily armored foes at lightly armed PCs, unless you want them to run away, surrender, TPK, or get very creative in taking the foe down.

If I had to face a heavily armored foe who I couldn't just outmaneuver (heavy armor usually means slower), I'd hope my skill was high enough to suck up the penalties of chinks, eye shots, or hitting lighter armored areas. Or hoping that as a group we could swarm and grapple them into submission or to line up a careful stab/coup d'grace into the eye slots.

Originally Posted by Colonel__Klink

The idea that with a hunting rifle ONE hit will send a vampire character (vampire the masquerade rules I've been working with that book to help build my setting, ) straight into a topor coma straight out of the gate is... that's not good gameplay to me. It's a bit silly tbh.

That's also a vamp with no Fortitude, average HT, not wearing armor, and just chilling out waiting to get tagged by a sniper.

Even in White Wolf's VtM that's what happens in that situation, dumb weak vamp gets snipered, dumb weak vamp goes down.