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Old 12-24-2020, 10:23 PM   #1
Raekai
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Default If 4d hits 50% of the time, is it ≈ 8d-24?

It's hard for me to explain what I'm looking for in a short title (and I'm admittedly not totally sober).

I ask because I like the combat approach of Into the Odd (another tabletop RPG), which makes all attacks hit, which takes boring misses out of combat. However, taking defenses out also means that there's not a way to avoid damage entirely. I want every attack to hit, but I don't want every attack to do damage.

So, is there a way to do something like that in GURPS (even if it would be too much trouble)? If every attack hits, it seems like you would modify damage based on the chance that the attack would hit (in addition to DR and such). Which is where I got 50% chance of 4d ≈ 8d-24.

It seems like there'd have to be an easy way to calculate the odds of an attacking doing damage based on skill and active defense (and I doubt there is other than a hard formula or a large table). Otherwise, I haven't figured out to how to calculate 4d hitting 25% of the time, 75% of the time, and so on. It doesn't seem like this would be very granular either. You could map it to the steps of the 3d success roll, but it seems like partial dice would have to be used, which wouldn't work.

Thanks!
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Old 12-24-2020, 10:39 PM   #2
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

Not even slightly.

The average result for 4d is 14, and that's also the single most probable result. The average result for 8d-24 is somewhat annoying to calculate (because negative values presumably count as zero) but is certainly less. And the most probable result (other than zero) is 4.
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Old 12-24-2020, 11:26 PM   #3
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

In GURPS every attack already does hit, sort of. Even skill 12 has a 74% chance and 16 is 98%. Misses are from automatic and critical failures on 17-18, taking penalties for attacking smaller targets (e.g. -7 to hit skull) or environmental conditions (light, footing), or especially because the target successfully defended.

I can't find anything encouraging to say about trying to replace that with an automatic hit rule, and that's not the end of it. Armor is subtracted from damage, so trying to adjust the damage to reflect hit chance messes up that subsystem. And the subsytem for major wounds and crippling injuries. And probably more.

You're basically trying to pull one gear out of a dynamic system and you're probably better off starting from scratch.
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Old 12-25-2020, 12:58 AM   #4
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

If you go to https://anydice.com/program/1f832 you will find the dirce roll distributions of 4d6 and 8d6-24 for any comparisons you might like. And you can change them and add others as your heart desires.
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Old 12-25-2020, 01:44 AM   #5
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

Quote:
Originally Posted by Raekai View Post
It's hard for me to explain what I'm looking for in a short title (and I'm admittedly not totally sober).

I ask because I like the combat approach of Into the Odd (another tabletop RPG), which makes all attacks hit, which takes boring misses out of combat. However, taking defenses out also means that there's not a way to avoid damage entirely. I want every attack to hit, but I don't want every attack to do damage.

So, is there a way to do something like that in GURPS (even if it would be too much trouble)? If every attack hits, it seems like you would modify damage based on the chance that the attack would hit (in addition to DR and such). Which is where I got 50% chance of 4d ≈ 8d-24.

It seems like there'd have to be an easy way to calculate the odds of an attacking doing damage based on skill and active defense (and I doubt there is other than a hard formula or a large table). Otherwise, I haven't figured out to how to calculate 4d hitting 25% of the time, 75% of the time, and so on. It doesn't seem like this would be very granular either. You could map it to the steps of the 3d success roll, but it seems like partial dice would have to be used, which wouldn't work.

Thanks!
The problem can be divided into two parts to make tackling it easier: first, we want to get 0 damage 50% of the time and second, we want to achieve the same average damage as our original dice spread.

1d-3 will give 0 damage on a 1,2, or 3 thereby neatly giving us damage above 0, only 50% of the time.

1d-3 gives an average damage for multiplication purposes of 3.5 - 3 = 0.5.

Therefore to find the number of 1d-3 dice we need to roll to have an average damage of 14, we need to divide 14 by 0.5, giving us 28.

Hence 4d = 28x(1d-3) = 28d-(28x3) = 28d-84, which will give us 0 damage 50% of the time and keep our average damage at 14.

Achieving your aim of always hitting while keeping the damage the same does require quite a few dice. Two other points are germane. In order to get 0 damage, you will have to abandon the rule that cutting and impaling attacks do a minimum of 1 point of damage regardless of the damage roll, assuming that the hit was successful. Second, removing the boring misses doesn't exactly solve the problem as it simply shifts it from I'm bored because I missed to I'm bored because I rolled low damage. Fixing that problem should require that you always hit doing average damage which would be even more boring as it reduces the amount of die rolling which reduces the opportunity for player agency by affecting the situation through chance. The predictability of combat would be beneficial to those players with a natural/educated bent for tactics, but would be detrimental to those players whose proclivities lie elsewhere.

Last edited by Curmudgeon; 12-25-2020 at 01:58 AM. Reason: additional thought
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Old 12-25-2020, 08:02 AM   #6
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

Do the adversary NPCs always hit the PCs, too?
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Old 12-25-2020, 08:22 AM   #7
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

If you just subtract the average damage from a bunch of dice you are not making 50%o of the time 0 damage AND making the average damage something else. You are making average damage 0. Because for the rest you are using only half of the probability curve, so the lower damages (the higher in the curve after the subtraction) will be more common than the higher rolls (lower in the curve). The damage after the subtraction is skewed in favor of the 0.

To make 50% of the time 0 damage and then have an average damage you need to make all attack roll 10 or less, and then roll damage normally.

In this way 50% of the time you make 0 damage (miss, but you may call it a 0 damage hit if you want) and then the average damage from a bunch of dice is normal.
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Old 12-25-2020, 08:39 AM   #8
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

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Originally Posted by Curmudgeon View Post
Second, removing the boring misses doesn't exactly solve the problem as it simply shifts it from I'm bored because I missed to I'm bored because I rolled low damage.
Also, very likely, "I'm bored because we have spent the last five minutes cross referencing the original damage, attack skill, and defense, and counting the resulting bucket of dice."
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Old 12-25-2020, 08:45 AM   #9
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

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Originally Posted by Ulzgoroth View Post
Not even slightly.

The average result for 4d is 14, and that's also the single most probable result. The average result for 8d-24 is somewhat annoying to calculate (because negative values presumably count as zero) but is certainly less. And the most probable result (other than zero) is 4.
It's actually not hard to calculate the average - each die has an average roll of 3.5, so 8d has an average roll of 3.5x8=28, subtracting 24 the average of 8d-24 is 4. I'll also note that if you want to renormalize that to 4d6 you need to subtract 4*3.5=14 from the result, not 24. So 8d6-14 is approximately equal to 4d6, but only very approximately. 8d6-14 still allows for more extreme highs and lows, but at the same time the bell curve for 8d6 is packed much more tightly around the middle results.

As you allude to, the shape of the bell curve is much more difficult to calculate and visualize for 8d vs 4d, and the zero results do skew the actual average somewhat. I did such a breakdown for my Cards vs Dice article, and you can look at the 4d6 and 8d6 graphs and corresponding tables; just subtract 24 (or 14) from the 8d6 table and ignore the dotted blue line (since that's for cards, if using a deck of cards from the article).

Using the correct 8d6-14, the chances of rolling a 0 or less is pretty miniscule - it only happens 0.18% of the time - not to be confused 1.8% or even 18%. 0.18% is 0.18 times out of 100, or 18 times out of 10,000, or approximately 1 in 556 rolls. This is statistically very unlikely, and barely affects the overall average.
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Last edited by ericbsmith; 12-25-2020 at 08:51 AM.
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Old 12-25-2020, 09:03 AM   #10
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Default Re: If 4d hits 50% of the time, is it ≈ 8d-24?

Quote:
Originally Posted by ericbsmith View Post
It's actually not hard to calculate the average - each die has an average roll of 3.5, so 8d has an average roll of 3.5x8=28, subtracting 24 the average of 8d-24 is 4.
It's easy to miscalculate the average, yes.

The average of 8d-24 is 4, yes...if you allow negative results. Damage rolls don't. The average of Max(8d - 24, 0) is what's not so easy.
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