If 4d hits 50% of the time, is it ≈ 8d-24?

[Daigoro]

1d12-6 gives 50% chance of 0, 50% chance of 1-6. Wouldn't 4d12-24 have the same distro as the target?

[Daigoro]

Originally Posted by Daigoro

1d12-6 gives 50% chance of 0, 50% chance of 1-6. Wouldn't 4d12-24 have the same distro as the target?

Fzzzt. Of course not.

If you want to avoid rolling twice, you need a little trick. You have a "trigger die", either the d12 or a coloured d6.

Roll 1d12 + 3d6, only counting the 3d6 if the d12 is 6 or less, and adding them together.

Or roll 1d6 coloured and 4d6, counting the result of the 4d6 if the coloured die is 4 or more.

[Raekai]

Oh my god. I forgot that I made this thread. Amazing. Thank you all for the great insight. I don't think I'd want to port this idea to GURPS—if I wanted something like that, I'd just play a different game—, but I thought it was an interesting thing to ponder. I've always had the problem of my players feeling like GURPS combat was too slow or cumbersome, so it got me thinking.

Of course, there are more GURPS-appropriate solutions like trying to do a very-small-scale Mass Combat workaround or using the BATTLE system from Action 7 (which I really like).

Thank you to all of those that humored me and taught me even more about numbers, probability, and dice. I'll have to take some more time tomorrow to really sift through for the most useful tidbits, but, again, I don't think this seems even remotely feasible to apply this to GURPS.

[Anaraxes]

Originally Posted by Daigoro

You have a "trigger die", either the d12 or a coloured d6.

Or you could use a color-coded set of three trigger d6s, along with whatever damage dice you need. And you'd keep the GURPS bell curve. This technique is just rolling the attack and damage at the same time, rather than combining them into a single roll.

Mathematically, I don't think you're going to get a single dice pool roll that replicates the two separate rolls. You can find a distribution with the same average as your original damage (when that's multiple dice). But if you cut off the bottom half of that normal-ish distribution to represent a miss, you're left not with a shape that peaks around its average with symmetry above and below, but has a heavily weighted low end, with a long tail of higher values. It will become highly likely to roll a little less than average, or a little more than average, with a small chance of high damage values. (Maybe that's even something players would find desirable; it's a lot like whether or not you like the excitement of a critical hit -- at least the relatively dull "2x damage" kind, as opposed to the tables or decks with elaborate descriptions of every result.)

Seems like you'd need to start with a bimodal distribution so that you keep the bell curve after you cut off the bottom.

Or, you know, just roll the dice again, because that's way easier than doing advanced statistics modelling just to avoid rolling a dice roll. Rolling the dice twice isn't what slows combat down. It's players hemming and hawing over what they're going to do, counting every hex multiple ways for the absolutely optimal path, skimming through rule books trying to glean every modifier, and waiting until it's their turn to do any of this after they have to get a little recap of what happened on everyone else's turn because they weren't paying attention (a problem aggravated by those players doing all that boring delay, so it's a problem that snowballs). Players still have plenty to do when it's not their turn so that they're ready when it is. That's not the time to work on a backup character or read some rules or check your email.

Faster games come from players being willing to decisively pick an action as soon as their turn starts and competently execute it, hopefully with some level of real-world verve, even though later thought might reveal that there had been a better option. If combat is boring, try moving a bit toward the "roll and shout" end of the spectrum.

[Plane]

Originally Posted by Daigoro

What happens to the bell curve with 4d12? Heretical, I know...

We get less random on high-ST thrust too (10d instead of 1d*10) so it's kind of a larger concern.

That's why I liked toying with something like thrust = 1d*ST/10 w/ +10% for committed:strong, +20% for aoa:strong, -20% for defensive

Rather than "0 ST touches" you could specify amounts smaller than 1 ST (which does 0.1 to 0.6 thrust) like 0.5 ST (0.05 to 0.5) but at some point it should require a DX roll to reduce to very low %s. Like maybe to "pull punch" (hit with low ST) you roll your technique at +10 (easy task difficulty modifier) with a -1 penalty for each halving of ST.

So for ST 10, you'd be DX+9 for ST 5, DX+8 for ST 2.5, DX+7 for ST 1.25, DX+8 for ST 0.75, DX+7 for 0.375 ...

Not that hard for a human, but some ST 10,000 creature with only DX 3 might eventually encounter some problems trying to do a "non-damaging touch".

To account for "sometimes grapples hurt too" you could maybe do something like grapples inflict 1 crushing damage per 5 control points. Hitting at 1/5 damage is about what blunt force trauma does. Grapplers who want to avoid harming something could pull the ST to reduce that damage similarly.

[ericbsmith]

Originally Posted by Daigoro

What happens to the bell curve with 4d12? Heretical, I know...

Instead of what, 8d6?

First thing that happens is you wind up lowering the average result by 2 points. Average result of 8d6 = 3.5*8 = 28 while the average of 4d12 = 6.5*4 = 26.

Assuming you make it 4d12+2 vs 8d6, here's the bell curves.

[Daigoro]

Originally Posted by ericbsmith

Instead of what, 8d6?

I was thinking of 4d12-26 instead of 8d6-28 to get the 50% chance of hitting, but yeah, I nixed that idea.