Steve Jackson Games Forums Bell Curve on 1D6 [math]
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06-08-2013, 06:52 AM   #21
martinl

Join Date: Jan 2006
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by Gnomasz My houserule derived from Modifying Dice + Adds: keep subtracting flat bonuses and adding dice until minimal roll is as close to 1 as possible. That rifle gets +2d-7 (average 0) for 8d-7 of damage.
I like to do similar, but I will point out that the odds of rolling 1 on 8d6-7 are literally less than one in a million. IMO over belling is even more annoying than under belling. (Although some take it as a feature - the KE of guns is pretty reliable.)

You could go with (2d6-2)*4+1, but you players might revolt.

You might get some relief from the AD bullets approach of 4d-3(2), but if your players are smart, they won't like that either.

Randomness is not in favor of the PCs in the long term, usually.

06-08-2013, 09:03 AM   #22
jacobmuller

Join Date: Feb 2006
Location: Not in your time zone:D
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by Anthony My actual preference is to just have wound levels based on MoS, but that introduces its own complexities.
Houserule
Success is Damage
Instead of rolling dice for damage, use Margin of Victory (MoV): subtract the Defender’s Margin of Success from the Attacker’s Margin of Success – Rule of 16 applies, ie maximum effective attacking skill is treated as 16 unless the defending skill is higher than 16.
Basically, the MoS difference is treated as the die or dice result:
• MoV (Margin of Victory): the attacker’s MoS (0 is ˝) minus the Defender’s MoS (0 is ˝);
• an MoV ≥ 6 is treated as 6;
• MoV 0 is treated as a ˝; round damage down; min dam is 1 unless Cr where min dam is 0;
• -ve MoV, if ≤ defender’s shield DB, the blow was stopped by the shield;
• Critical Success table results 6 and 15 become: The blow does maximum normal damage +50%;
• Effects of Attacker failure are unchanged & Defender failure subtracts 0 from Attackers MoS.
• Rapid Fire: is unchanged; Attacker’s MoS determines number of hits; Defender’s MoS determines number of hits avoided; Damage is rolled randomly.

YMMV. Making it strictly MoS is more RAW. It just Really annoys me when an attack succeeds by 9 and is blocked by a MoS 0:/
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06-08-2013, 09:10 AM   #23
Gnomasz

Join Date: Aug 2009
Location: Poland
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by martinl You could go with (2d6-2)*4+1, but you players might revolt.
I'd rather just stop caring about being accurate and made it (2d-2)×n for any firearm (so 1 point of damage less for the rifle), with a roll of 0 being able to inflict 1 point of injury. Which is just ericthered's idea with fractions omitted for convenience. I have to agree that it looks better then over belling. But I'm usually dealing with muscle-powered weapons and it's not very common to get past 3 dice (after modifying adds). +1 is a big deal here and I wouldn't drop it.

So, each way has it's cons. No wonder why the writers chose simple Xd+Y.
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06-11-2013, 02:29 AM   #24
JCurwen3

Join Date: Dec 2007
Location: Brooklyn, NY
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by ericthered yes, 3.5 is the average value. I choose 4 because it means every damage step increases damage taken by 1 point with no .5 steps and it make the math cleaner. It increases the damage, but not by much, What I said above. I use the 2d for all damage. if the table says 5d, its an average 20 damage, multiplied by (2d-2)*.2. 3d is 12*(2d-2)*.2. If you want everything to be a 3d shaped curve (for when damage should be more consistent) take the average damage and multiply it by (3d *.1). That will increase the damage by a little bit, but if that effects your HP-Damage-DR balance, you're walking a tightrope as it is and the change in the curve shape will hurt you as much as the increase in damage.
Thanks! Using the 2d formula, you can end up with 0 damage though (if you roll snake eyes), but maybe that doesn't happen often enough to be a problem.

What would you use to get results on 4d, 5d, or 6d curves? I'm considering a house rule to make damage for higher skill level fighters increasingly consistent.
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06-11-2013, 09:11 AM   #25
Captain Joy

Join Date: Nov 2006
Location: Heartland, U.S.A.
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by Landwalker If you're bothered by 2d distributions...
If you actually like the 2d distribution, you might like my 2d Damage House Rule. Click the button towards the bottom of the page to access these rules. The introductory text reads:
Quote:
 For purposes of determining damage, GURPS makes use one or several 6-sided dice. 1d6 gives you a flat random distribution. 2d6 gives you linear up --> peak --> linear down. 3d6 (or nd6 where n >= 3) gives you a bell curve. I.e. when you graph these results, 1d6 is flat, 2d6 looks like a pyramid, and 3d6 looks like a bell curve. I prefer the distribution given by using two dice. Also, I want the minimum possible damage to be about 15% average and the maximum possible damage to be about 185% average. To that end, the following charts may be used to determine damage.
Myself, I use 2d4-1 instead of 1d6
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Last edited by Captain Joy; 06-11-2013 at 09:16 AM. Reason: Trimmed quoted text. Added quote from my house rule.

 06-12-2013, 09:13 AM #26 BaHalus     Join Date: Mar 2011 Location: Belém, Pará, Amazônia, Brasil. Re: Bell Curve on 1D6 [math] It may be an interesting idea. I imagine that we could just roll 2 or 3 dice and add more dices as skill rises (and/or depending of the weapon) to represent more consistent results (as extremes results will be less likely to occur as you keep adding dices). But using a table or formula for the damage (not direct dice results). A formula could work fine if you use the aid computers. And print a table based in the formula if otherwise. As stabilizing the damage will tend to make getting high damages less likely, a small increase in damage as skill rises may be interesting too. Or, throwing more dices, but discarding the lower values and staying with 3 dices (you could do the opposite with lower Skill leves and throw more dices and discard higher values).
06-12-2013, 10:40 AM   #27
Pmandrekar
Careful Wisher

Join Date: Jun 2005
Location: Oregon, WI
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by martinl One of the things that bugs me about GURPS is that the damage probability distributions vary so much with how many dice you roll. The worst offender is the 1d6 - if it was just a bit more bell-shaped, it would make me happier. So here's my idea: When rolling 1d6 damage, actually roll 3d6 and take the middle value. I don't think this is too hard. Code: ```1 16 7.4% 2 40 18.5% 3 52 24.1% 4 52 24.1% 5 40 18.5% 6 16 7.4%``` Thoughts? It's not as sharply belled as 3d6, but it is belled.
In another thread, Ze proposed this one:
Quote:
 Originally Posted by Ze'Manel Cunha Do you want to substitute MoS for damage rolls altogether? From the Crit table we have up to triple damage in the RAW, which happens on a Crit roll on a Crit/+10 MoS. Margin of Success Result -1 to -2 barely contact, 0 dmg, +2 to defense roll 0 a graze, 1 dmg, +2 to defense roll +1, flesh wound, min dmg -1, +1 to defense roll +2, barely hit, min dmg, +1 to defense roll +3, dmg as if rolled all 2s +4 to +5, dmg as if rolled all 3s +6 to +7, dmg as if rolled all 4s, -1 to defense roll +7 to +8, dmg as if rolled all 5s, -1 to defense roll +9 to +10, dmg as if rolled all 6s, -2 to defense roll +11 to +13, dmg as if rolled all 6s, -2 to defense roll +14 to +17, dmg as if rolled all 6s, halve DR, -3 to defense roll +18 to +21, dmg as if rolled all 6s, halve DR, -3 to defense roll
I like this general approach, since it incorporates the Margin of success directly into the amount of damage, and hey, if your opponent nails you with +9 over the required hit, then the damage shouldn't come out as 5-7 points on a (bad) 3d6 roll. Like I did a few times two weeks ago when you ran the combat clinic at gaming and my 9d6 Sunbolts sputtered out 11 points of damage.

I'm not saying that we should adopt this for our gaming group (martinl and I are in the same group on Tuesday nights in Madison) , and maybe the exact impact of the margin of success is up for discussion, but I like the general idea here. Unless, of course, you're taking away from the fun of people rolling out their 36d6's to simulate an FGMP-15 blast in Traveller. :)

Obviously, I'm not the first in the thread to suggest MOS = damage, but I saw something that Ze posted that made me wonder if this was applicable to what you're getting at. Although maybe not, since the *range* of damage is still the same, and the possible outcomes is actually reduced.
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06-12-2013, 10:42 AM   #28
Pmandrekar
Careful Wisher

Join Date: Jun 2005
Location: Oregon, WI
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by martinl Randomness is not in favor of the PCs in the long term, usually.
Speaking as a player in the same GURPS games as you, I am definitely warming up to the idea of buying Luck at every opporunity in character creation. :)
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P. Mandrekar, Geneticist and Gamer
Rational Centrist
"Everyone is entitled to his own opinion, but not his own facts"- Daniel P. Moynihan

06-12-2013, 01:08 PM   #29
martinl

Join Date: Jan 2006
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by Pmandrekar MOS = damage
I go back and forth on MOS=damage.

On one hand, it is satisfying to know that a big MOS on your hit means high damage. Whiffy crits in GURPS are particularly unsatisfying.

On the other hand, GURPS RAW assumes that trade offs between skill and damage come in as voluntary choices before the hit roll, not as side effects of the MOS. If you change that, a lot of ground shifts under existing rules and rules interactions. I'm not sure how bad it would be, or even if it would be bad at all, but it is a fundamental change.

Here's one proposal:

For 1d6+Y damage, use the middle value of 1d, 1d, and your MOS as the D6 roll.

For Xd6+Y where 1<X<4, replace one of the dice with your MOS (or 1 if MOS=0, 6 if MOS>6).

If X>4, dome some sort of divide - roll - multiply thing.

06-12-2013, 01:11 PM   #30
martinl

Join Date: Jan 2006
Re: Bell Curve on 1D6 [math]

Quote:
 Originally Posted by Pmandrekar Speaking as a player in the same GURPS games as you, I am definitely warming up to the idea of buying Luck at every opporunity in character creation. :)
I amuses me weirdly that Luck is such a requirement for players who don't like to rely on luck.

 Tags math, modifying dice + adds

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