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Old 02-29-2024, 12:17 PM   #1
Bathawk
 
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Default Is There An "Easy" Formula To Figue KO/Kill Odds?

Hello, I was wondering if there was some way to grade how incapacitating/deadly attacks are. Looking at the Skill "Probability Of Success" table on pg.171, you have a 50% chance of getting a "10" and only 1 in 200 chance of rolling a "3"....and of course that changes as you add or subtract dice.

For example. take a ST: 14 opponent with a baseball bat hitting a target HP/HT of 12 for 2d +2 cr....lets assume he hits him in the head...what are the odds/percentage of it resulting in a knockout? or even killing him?

Or lets assume that little Johnny with a HP/HT of 10 is playing with some dynamite when it goes off doing 12d cr....even if some miracle he "rolls" all ones, he's still going to be at -2 HP...but it's more likely that he will be brought so low he will need to make multiple rolls just to survive...what are his odds?

of course even this is a bit simplified...I realize other factors like damage type and DR will skew the odds, but just trying to get started
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Old 02-29-2024, 12:39 PM   #2
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

You can see the probabilities of dice rolls at a variety of places online, although anydice.com is probably the best option if you want to see a lot of options. For example, this gives the spreads for 1d, 2d, and 3d, and you can pick a variety of displays (for knockout/kill, you'll probably be looking at the At Least option).

Of course, what the goal number is will depend on things like the target's HP and DR, the wounding modifiers involved, and where you're hitting - that 2d+2 cr has a far better chance of knocking out (or killing) the target if you swing at the unarmored skull of an average man than at the heavily-armored arm of a big beefy knight.

EDIT: Here are the spreads for the two scenarios you mentioned, the baseball bat to head (which I'm treating as Skull) and dynamite explosion. For the first, a roll of 4+ (8+ HP) calls for a roll against HT-10 (Major Wound to Skull) to avoid Knockdown and Stunning, a roll of 5+ (12+ HP) adds in an unmodified HT roll each second of activity to stay conscious (at or below 0 HP), a roll of 8+ (24+ HP) imposes a -1 and calls for an unmodified HT roll to avoid death, and a roll of 11 or 12 (48 or 52 HP) makes that -2 and calls for two death checks. For the second, a roll of 12-19 means an HT roll against knockdown/stunning and a per-second HT roll to stay conscious, 20-29 gives a -1 to the latter and calls for a death check, and every +10 is a further -1 to stay conscious and calls for an additional death check, until you reach 60, at which point Johnny is simply dead.

To determine the probability of stun/knockout/passout/death, multiply the probability of such a result on the 3d roll and the probability of the relevant damage results together. If something calls for multiple death checks, raise the probability of passing the death check to the power of the number of said checks, then subtract that from 1 to get the probability you'll fail at least once. If looking at multiple potential results, you can add, so long as there isn't overlap. Let's look at Johnny; to save time, I'm only looking at the probability of failing a death check, and ignoring the rule that a death check that's failed by only 1 or 2 is a Mortal Wound rather than instant death.

12-19 is below the resolution of anydice, meaning less than a 0.01% chance, but we'll round up to 0.01% (12-20 does show a 0.01% chance, so it's close at least). 20-29 is around 1.65%, 30-39 is around 32.15%, 40-49 is around 55.83%, 50-59 is around 10.25%, and 60+ is around 0.11%. The probability Johnny will fail with a single death check (20-29) is 50%; the probability with two (30-39) is 75%, with three (40-49) is 87.5%, with four (50-59) is 93.75%, and with 60+ damage is 100%. So, this works out to (0.0165*0.5) + (0.3215*0.75) + (0.5583*0.875) + (0.1025*0.9375) + (0.0011*1) ~= 0.835, for an 83.5% chance Johnny will snuff it - and thus a 16.5% chance he'll survive. Note this will be a lot easier to work with if you use a spreadsheet or similar.
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Old 02-29-2024, 12:47 PM   #3
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

You can find probabilities of individual events, but you won't find them for things like "sword 55% more deadly than spear" or anything like that. Deadliness is dependent on far too many factors to resolve into a simple number.

If what you're doing is trying to find "encounter balance," the key to this isn't to measure absolute combat ability, but rather relative combat ability. "I do more damage, but the enemy hits more often." Stuff like that. In total, if you have more features of combat in your favor than your opponent does, the combat should be fairly easy for you. If your opponent has more features in his favor, combat will be fairly hard for you.

This is the method behind Kromm's book How To Be a GURPS GM: Combat Encounters, which sadly hasn't been released generally yet but has only had a special bundled release a few years ago. It really ought to be published now. People are constantly asking for exactly what this book deals with.
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Old 02-29-2024, 01:02 PM   #4
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

There's no easy way to do this as a single pass, you need to do it as a state machine.
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Old 02-29-2024, 01:13 PM   #5
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

Probability of the attack (PoA) succeeding multiplied by the probability of the defense (PoD) succeeding gives you how likely the attack will hit.

Take the average damage of the attackers attack (AvgA) and subtract the targets DR (AvgD) (If any) to get how much damage the defender takes. Then take THAT average and multiple it by the Wound modifier and/or hit location modifier, then divide it by any injury tolerance (AvgDIT)to get how much injury the target takes.

Compare that Injury number to the thresholds of the Defender to determine what would happen.

The GM Screen has the chart for probability of success.

So you have:

PoA x PoD = Hit Ratio

(AvgA - AvgD) x WoundORLocation / AvgDIT = Injury Ratio


Using your example:

Ignoring Hit Ratio, since you said assume it hits.

2d+2 average is 9.

Skull has DR 2

(9 - 2) x 4 / 1 = 28 injury.

Knockdown roll is at -10 for skull hit.

HT roll is 12 -10 = 2 which means you will always fail, but if you roll a 7 or more its worse, roll a 12 or more and its a crit fail.
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Old 02-29-2024, 01:13 PM   #6
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

Its mostly just a matter of doing math. having various xd6 percentages memorized helps. I find memorizing 10 = 50% failure, 12 = 25% failure, 14 = 10% failure is really helpful.

Quote:
Originally Posted by Bathawk View Post
For example. take a ST: 14 opponent with a baseball bat hitting a target HP/HT of 12 for 2d +2 cr....lets assume he hits him in the head...what are the odds/percentage of it resulting in a knockout? or even killing him?
"Head" could mean either skull or face, with VERY different outcomes...

a face hit will do between 4 and 14 damage, and never result in death.

on a roll of 2-4 (thus doing 4-6 damage) you get a single knockdown roll (for a face hit) against 12, which has ~25% chance of "knockdown"... which just knocks them to the ground. only a critical failure knocks them out cold, so that's a 4/216 = 1/54. This damage range occurs 6/36ths of the time.

A face hit needs to do 7 or more damage to get a -5 to the knockdown roll. it does this on a roll of 5 or higher, which happens... 30/36 = 5/6 of the time. on a roll worse than 12(so 25% of the time), this results in a knockout. on a roll worse than 7 (I think that's 5/6 of the time) you have a "knockdown".

A face hit doing 12 or more damage will require the opponent to additionally roll HT every turn they take real actions or suffer unconsciousness. This will make them effectively unconscious... but its complex. a roll of 10-12 on 2d makes this happen... so 1/6th of the time, and it will always overlap with the 7+ damage category. the 7-11 damage category is a roll of 5-9, which is 4/6 of the time. If we only want to know how often this results in unconsciousness immediately (instead of in a few seconds, we have one more HT roll vs 12, with 25% chance of failure).

So for strict unconsciousness you add 1/6*1/54 + 4/6*1/4+ 1/6.

If we say the crit is irrelevant, then that's 1/6 + 1/6 = 2/6 = 1/3.

I suppose that wasn't very quick, was it?
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Old 02-29-2024, 01:34 PM   #7
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

Doing skull just because:

The skull has DR 2, so effective damage drops to 2d6.

but all damage will also be multiplied by 4, so...

All skull hits will do 8 injury or more, and get -10 for a major wound to the skull on the knockdown roll. They will fail the knockdown roll (target is 2) on anything other than a crit (1/54). They will fail by five or more on anything higher than an 7 (5/6 of the time).


They will also be in the roll for unconsciousness range for any roll that is not a 2, so 35/36 of the time.

So a skull hit results in immediate unconsciousness 5/6 of the time, and sticks them in the roll for unconsciousness range 35/36 of the time.

The guy still being standing is around a 1/1500 chance.

Death... you've got to do at least 24 damage to force a death check. that means roll 6 on the 2d or better... a 26/36 chance.... but they roll against 12, so they only die 25% (1/4) of the time. If 36 damage is done (rolled a 9 or better, a 10/36 chance) then that roll must be made twice (7/16 chance of death), and 48 damage will force three rolls (1/36 chance of happening, and 37/64 chance of dying).

The total chance of death is 16/36*1/4 + 9/36*7/16 + 1/36*37/64 = 1/9 +~7/64+ ~1/64 = 4/36+8/64 = 1/9 + 1/8 = 17/72 =~1/4


It occurs to me that if you wanted to run a bunch of tables on damage to chance of knockdown, death, and unconsciousness, you could. Or at least a calculator.
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Old 02-29-2024, 01:42 PM   #8
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

Assuming 'head' means 'face' (the logic is similar for skull, just different numbers)

First, split the damage possibilities into the three relevant states, which are:
  • Not a major wound (4-6 damage; 6/36 chance). This prompts a knockdown roll, which is a HT roll (at +3 for high pain threshold); on a 15- no effect, on a normal failure (16) the target is stunned and knocked down, on a critical failure or failure by 5+ (17-18, 4/216) the target is KOed.
  • Major wound (7-11 damage; 24/36 chance). The same as above, but the roll is at -5, and thus it's 10- no effect, 11-14 knockdown, 15-18 (20/216) KO.
  • Target 0 HP or less (12-14 damage; 6/36). The same as major wound, but in addition the target must make a HT roll to avoid unconsciousness at the start of its next turn (56/216 to fail), and must repeat the roll every turn unless they Do Nothing.

The prompt odds of KO is 6/36*4/216 + 24/36*20/216 + 6/36*20/216 = 104/1296 = 8.02%. The odds of a subsequent KO at start of turn is 6/36 * 196/216 * 56/216 = 3.92%, and thus the total odds of KO is 11.94%.
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Old 02-29-2024, 01:48 PM   #9
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

Quote:
Originally Posted by Stormcrow View Post
You can find probabilities of individual events, but you won't find them for things like "sword 55% more deadly than spear" or anything like that. Deadliness is dependent on far too many factors to resolve into a simple number.

If what you're doing is trying to find "encounter balance," the key to this isn't to measure absolute combat ability, but rather relative combat ability. "I do more damage, but the enemy hits more often." Stuff like that. In total, if you have more features of combat in your favor than your opponent does, the combat should be fairly easy for you. If your opponent has more features in his favor, combat will be fairly hard for you.

This is the method behind Kromm's book How To Be a GURPS GM: Combat Encounters, which sadly hasn't been released generally yet but has only had a special bundled release a few years ago. It really ought to be published now. People are constantly asking for exactly what this book deals with.
It's mainly for being able to describe functionality to those not super familiar with RPG's If a newbie with a sword doing 1d +3 cuting, goes up against an Ogre who does 4d cr. with his club. I'd like to say something like "you'll have a 50% chance to put him dwn in four hits, but he has a 90% chance of knocking you out in one his, and a 50% chance of killing you in one go"

...and as I thought of it, I thought it would just be cool way to look at dice of damage compared to HP?HT....a "7d attack has a 50% chance of forcing a HT roll, with a 50 chance of surviving...so a 25% of a kill" for example, but perhaps a bit more precise (I like numbers)
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Old 02-29-2024, 01:56 PM   #10
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Default Re: Is There An "Easy" Formula To Figue KO/Kill Odds?

Quote:
Originally Posted by Bathawk View Post
It's mainly for being able to describe functionality to those not super familiar with RPG's If a newbie with a sword doing 1d +3 cuting, goes up against an Ogre who does 4d cr. with his club. I'd like to say something like "you'll have a 50% chance to put him dwn in four hits, but he has a 90% chance of knocking you out in one his, and a 50% chance of killing you in one go"

...and as I thought of it, I thought it would just be cool way to look at dice of damage compared to HP?HT....a "7d attack has a 50% chance of forcing a HT roll, with a 50 chance of surviving...so a 25% of a kill" for example, but perhaps a bit more precise (I like numbers)
One set of numbers that helps with this is the ability to get the average on d6's. its 3.5. So the ogre will do on average 14 damage, and the sword guy 6.5. Getting beyond that is a lot harder.
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