Author Topic: D10 Dice Pools  (Read 3309 times)

snakefing

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D10 Dice Pools
« on: September 22, 2006, 06:15:57 PM »
Okay, I broke down and wrote a program to generate these, so they are easier to generate. Here are some fairly complete tables for cumulative probabilities using d10 dice pools.

[table=1 Successes]
[tr][th]Net Target[/th][th]2[/th][th]3[/th][th]4[/th][th]5[/th][th]6[/th][th]7[/th][th]8[/th][th]9[/th][th]10[/th][/tr]
[tr][th]DicePool(2,d10)[/th][td]99%[/td][td]96%[/td][td]91%[/td][td]84%[/td][td]75%[/td][td]64%[/td][td]51%[/td][td]36%[/td][td]19%[/td][/tr]
[tr][th]DicePool(3,d10)[/th][td]99.9%[/td][td]99.2%[/td][td]97%[/td][td]94%[/td][td]88%[/td][td]78%[/td][td]66%[/td][td]49%[/td][td]27%[/td][/tr]
[tr][th]DicePool(4,d10)[/th][td]100%[/td][td]99.8%[/td][td]99.2%[/td][td]97%[/td][td]94%[/td][td]87%[/td][td]76%[/td][td]59%[/td][td]34%[/td][/tr]
[tr][th]DicePool(5,d10)[/th][td]100%[/td][td]100%[/td][td]99.8%[/td][td]99%[/td][td]97%[/td][td]92%[/td][td]83%[/td][td]67%[/td][td]41%[/td][/tr]
[tr][th]DicePool(6,d10)[/th][td]100%[/td][td]100%[/td][td]99.9%[/td][td]99.6%[/td][td]98%[/td][td]95%[/td][td]88%[/td][td]74%[/td][td]47%[/td][/tr]
[tr][th]DicePool(7,d10)[/th][td]100%[/td][td]100%[/td][td]100%[/td][td]99.8%[/td][td]99.2%[/td][td]97%[/td][td]92%[/td][td]79%[/td][td]52%[/td][/tr]
[tr][th]DicePool(8,d10)[/th][td]100%[/td][td]100%[/td][td]100%[/td][td]99.9%[/td][td]99.6%[/td][td]98%[/td][td]94%[/td][td]83%[/td][td]57%[/td][/tr]
[/table]

[table=2 Successes]
[tr][th]Net Target[/th][th]2[/th][th]3[/th][th]4[/th][th]5[/th][th]6[/th][th]7[/th][th]8[/th][th]9[/th][th]10[/th][/tr]
[tr][th]DicePool(2,d10)[/th][td]81%[/td][td]64%[/td][td]49%[/td][td]36%[/td][td]25%[/td][td]16%[/td][td]9%[/td][td]4.0%[/td][td]1.0%[/td][/tr]
[tr][th]DicePool(3,d10)[/th][td]97%[/td][td]90%[/td][td]78%[/td][td]65%[/td][td]50%[/td][td]35%[/td][td]22%[/td][td]10%[/td][td]2.8%[/td][/tr]
[tr][th]DicePool(4,d10)[/th][td]99.6%[/td][td]97%[/td][td]92%[/td][td]82%[/td][td]69%[/td][td]52%[/td][td]35%[/td][td]18%[/td][td]5%[/td][/tr]
[tr][th]DicePool(5,d10)[/th][td]100%[/td][td]99.3%[/td][td]97%[/td][td]91%[/td][td]81%[/td][td]66%[/td][td]47%[/td][td]26%[/td][td]8%[/td][/tr]
[tr][th]DicePool(6,d10)[/th][td]100%[/td][td]99.8%[/td][td]99%[/td][td]96%[/td][td]89%[/td][td]77%[/td][td]58%[/td][td]34%[/td][td]11%[/td][/tr]
[tr][th]DicePool(7,d10)[/th][td]100%[/td][td]100%[/td][td]99.6%[/td][td]98%[/td][td]94%[/td][td]84%[/td][td]67%[/td][td]42%[/td][td]15%[/td][/tr]
[tr][th]DicePool(8,d10)[/th][td]100%[/td][td]100%[/td][td]99.9%[/td][td]99.1%[/td][td]96%[/td][td]89%[/td][td]74%[/td][td]50%[/td][td]19%[/td][/tr]
[/table]

[table=3 Successes]
[tr][th]Net Target[/th][th]2[/th][th]3[/th][th]4[/th][th]5[/th][th]6[/th][th]7[/th][th]8[/th][th]9[/th][th]10[/th][/tr]
[tr][th]DicePool(3,d10)[/th][td]73%[/td][td]51%[/td][td]34%[/td][td]22%[/td][td]13%[/td][td]6%[/td][td]2.7%[/td][td]0.8%[/td][td]0.1%[/td][/tr]
[tr][th]DicePool(4,d10)[/th][td]95%[/td][td]82%[/td][td]65%[/td][td]48%[/td][td]31%[/td][td]18%[/td][td]8%[/td][td]2.7%[/td][td]0.4%[/td][/tr]
[tr][th]DicePool(5,d10)[/th][td]99.1%[/td][td]94%[/td][td]84%[/td][td]68%[/td][td]50%[/td][td]32%[/td][td]16%[/td][td]6%[/td][td]0.9%[/td][/tr]
[tr][th]DicePool(6,d10)[/th][td]99.9%[/td][td]98%[/td][td]93%[/td][td]82%[/td][td]66%[/td][td]46%[/td][td]26%[/td][td]10%[/td][td]1.6%[/td][/tr]
[tr][th]DicePool(7,d10)[/th][td]100%[/td][td]99.5%[/td][td]97%[/td][td]90%[/td][td]77%[/td][td]58%[/td][td]35%[/td][td]15%[/td][td]2.6%[/td][/tr]
[tr][th]DicePool(8,d10)[/th][td]100%[/td][td]99.9%[/td][td]99%[/td][td]95%[/td][td]86%[/td][td]68%[/td][td]45%[/td][td]20%[/td][td]3.8%[/td][/tr]
[/table]

[table=4 Successes]
[tr][th]Net Target[/th][th]2[/th][th]3[/th][th]4[/th][th]5[/th][th]6[/th][th]7[/th][th]8[/th][th]9[/th][th]10[/th][/tr]
[tr][th]DicePool(4,d10)[/th][td]66%[/td][td]41%[/td][td]24%[/td][td]13%[/td][td]6%[/td][td]2.6%[/td][td]0.8%[/td][td]0.2%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(5,d10)[/th][td]92%[/td][td]74%[/td][td]53%[/td][td]34%[/td][td]19%[/td][td]9%[/td][td]3.1%[/td][td]0.7%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(6,d10)[/th][td]98%[/td][td]90%[/td][td]74%[/td][td]54%[/td][td]34%[/td][td]18%[/td][td]7%[/td][td]1.7%[/td][td]0.1%[/td][/tr]
[tr][th]DicePool(7,d10)[/th][td]99.7%[/td][td]97%[/td][td]87%[/td][td]71%[/td][td]50%[/td][td]29%[/td][td]13%[/td][td]3.3%[/td][td]0.3%[/td][/tr]
[tr][th]DicePool(8,d10)[/th][td]100%[/td][td]99%[/td][td]94%[/td][td]83%[/td][td]64%[/td][td]41%[/td][td]19%[/td][td]6%[/td][td]0.5%[/td][/tr]
[/table]

[table=5 Successes]
[tr][th]Net Target[/th][th]2[/th][th]3[/th][th]4[/th][th]5[/th][th]6[/th][th]7[/th][th]8[/th][th]9[/th][th]10[/th][/tr]
[tr][th]DicePool(5,d10)[/th][td]59%[/td][td]33%[/td][td]17%[/td][td]8%[/td][td]3.1%[/td][td]1.0%[/td][td]0.2%[/td][td]0.0%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(6,d10)[/th][td]89%[/td][td]66%[/td][td]42%[/td][td]23%[/td][td]11%[/td][td]4.1%[/td][td]1.1%[/td][td]0.2%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(7,d10)[/th][td]97%[/td][td]85%[/td][td]65%[/td][td]42%[/td][td]23%[/td][td]10%[/td][td]2.9%[/td][td]0.5%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(8,d10)[/th][td]99.5%[/td][td]94%[/td][td]81%[/td][td]59%[/td][td]36%[/td][td]17%[/td][td]6%[/td][td]1.0%[/td][td]0.0%[/td][/tr]
[/table]

And for damage dice:
[table=Average Damage]
[tr][th]Net Target[/th][th]3[/th][th]4[/th][th]5[/th][th]6[/th][th]7[/th][th]8[/th][th]9[/th][th]10[/th][/tr]
[tr][th]DicePool(3,d10)[/th][td]2.4[/td][td]2.1[/td][td]1.8[/td][td]1.5[/td][td]1.2[/td][td]0.9[/td][td]0.6[/td][td]0.3[/td][/tr]
[tr][th]DicePool(4,d10)[/th][td]3.2[/td][td]2.8[/td][td]2.4[/td][td]2.0[/td][td]1.6[/td][td]1.2[/td][td]0.8[/td][td]0.4[/td][/tr]
[tr][th]DicePool(5,d10)[/th][td]4.0[/td][td]3.5[/td][td]3.0[/td][td]2.5[/td][td]2.0[/td][td]1.5[/td][td]1.0[/td][td]0.5[/td][/tr]
[tr][th]DicePool(6,d10)[/th][td]4.8[/td][td]4.2[/td][td]3.6[/td][td]3.0[/td][td]2.4[/td][td]1.8[/td][td]1.2[/td][td]0.6[/td][/tr]
[tr][th]DicePool(7,d10)[/th][td]5.6[/td][td]4.9[/td][td]4.2[/td][td]3.5[/td][td]2.8[/td][td]2.1[/td][td]1.4[/td][td]0.7[/td][/tr]
[tr][th]DicePool(8,d10)[/th][td]6.4[/td][td]5.6[/td][td]4.8[/td][td]4.0[/td][td]3.2[/td][td]2.4[/td][td]1.6[/td][td]0.8[/td][/tr]
[/table]

Note that average damage is always directly proportional to the size of dice pool and likelihood of damaging with a single die.
« Last Edit: September 26, 2006, 11:56:59 AM by Thanuir »
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beejazz

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« Reply #1 on: September 22, 2006, 06:29:02 PM »
Woah... After only a cursory glance, I'm seeing a much smoother transition. I think d10s might actually be worth a shot.

By the way, thanks. You know most of this math is beyond me.
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« Reply #2 on: September 22, 2006, 08:40:59 PM »
Okay, I'm going to go on the assumption of abilities between seven and ten, target numbers between twelve and sixteen, and 5d10 dicepools, with successes between one and five (though keep in mind that combat is generally between 12 and 15 with between two and four successes to hit). That said, I'll start with ability scores to see how difficult a number of tasks may be.

7

1DC12=99%->99.6%->99.8%-99.9%
2DC12=91%->96%->98%->99.1%
3DC12=68%->82%->90%->95%
4DC12=34%->54%->71%->83%
5DC12=8%->23%->42%->59%

1DC13=97%->98%->99.2%->99.6%
2DC13=81%->89%->94%->96%
3DC13=50%->66%->77%->86%
4DC13=19%->34%->54%->71%->83%
5DC13=3.1%->11%->23%->36%

1DC14=92%->95%->97%->98%
2DC14=66%->77%->84%->89%
3DC14=32%->46%->58%->68%
4DC14=9%->18%->29%->41%
5DC14=1%->4.1%->10%->17%

1DC15=83%->88%->92%->94%
2DC15=47%->58%->67%->74%
3DC15=16%->26%->35%->45%
4DC15=3.1%->7%->13%->19%
5DC15=0.2%->1.1%->2.9%->6%

1DC16=67%->74%->79%->83%
2DC16=26%->34%->42%->50%
3DC16=6%->10%->15%->20%
4DC16=0.7%->1.7%->3.3%->6%
5DC16=0%->0.2%->0.5%->1%
[close]

8

1DC12=99.8%->99.9%->100%->100%
2DC12=97%->99%->99.6%->99.9%
3DC12=84%->93%->97%->99%
4DC12=53%->74%->87%->94%
5DC12=17%->42%->65%->81%

1DC13=99%->99.6%->99.8%->99.9%
2DC13=91%->96%->98%->99.1%
3DC13=68%->82%->90%->95%
4DC13=34%->54%->71%->83%
5DC13=8%->23%->42%->65%->81%

1DC14=97%->98%->99.2%->99.6%
2DC14=81%->89%->94%->96%
3DC14=50%->66%->77%->86%
4DC14=19%->34%->50%->64%
5DC14=3.1%->11%->23%->36%

1DC15=92%->95%->97%->98%
2DC15=66%->77%->84%->89%
3DC15=32%->46%->58%->68%
4DC15=9%->18%->29%->41%
5DC15=1%->4.1%->10%->17%

1DC16=83%->88%->92%->94%
2DC16=47%->58%->67%->74%
3DC16=16%->26%->35%->45%
4DC16=3.1%->7%->13%->19%
5DC16=0.2%->1.1%->2.9%->6%
[close]

9

1DC12=100%->100%->100%->100%
2DC12=99.3%->99.8%->100%->100%
3DC12=94%->98%->99.5%->99.9%
4DC12=74%->90%->97%->99%
5DC12=33%->66%->85%->94%

1DC13=99.8%->99.9%->100%->100%
2DC13=97%->99%->99.6%->99.9%
3DC13=84%->93%->97%->99%
4DC13=53%->74%->87%->94%
5DC13=17%->42%->65%->81%

1DC14=99%->99.6%->99.8%->99.9%
2DC14=91%->96%->98%->99.1%
3DC14=68%->82%->90%->95%
4DC14=34%->54%->71%->83%
5DC14=8%->23%->42%->59%

1DC15=97%->98%->99.2%->99.6%
2DC15=81%->89%->94%->96%
3DC15=50%->66%->77%->86%
4DC15=19%->34%->50%->64%
5DC15=3.1%->11%->23%->36%

1DC16=92%->95%->97%->98%
2DC16=66%->77%->84%->89%
3DC16=32%->46%->58%->68%
4DC16=9%->18%->29%->41%
5DC15=1%->4.1%->10%->17%
[close]

10

1DC12=100%->100%->100%->100%
2DC12=100%->100%->100%->100%
3DC12=99.1%->99.9%->100%->100%
4DC12=92%->98%->99.7%->100%
5DC12=59%->89%->97%->99.5%

1DC13=100%->100%->100%->100%
2DC13=99.3%->99.8%->100%->100%
3DC13=94%->98%->99.5%->99.9%
4DC13=74%->90%->97%->99%
5DC13=33%->66%->85%->94%

1DC14=99.8%->99.9%->100%->100%
2DC14=97%->99%->99.6%->99.9%
3DC14=84%->93%->97%->99%
4DC14=53%->74%->87%->94%
5DC14=17%->42%->65%->81%

1DC15=99%->99.6%->99.8%->99.9%
2DC15=91%->96%->98%->99.1%
3DC15=68%->82%->90%->95%
4DC15=34%->54%->71%->83%
5DC15=8%->23%->42%->59%

1DC16=97%->98%->99.2%->99.6%
2DC16=81%->89%->94%->96%
3DC16=50%->66%->77%->86%
4DC16=19%->34%->50%->64%
5DC16=3.1%->11%->23%->36%
[close]
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« Reply #3 on: September 25, 2006, 03:24:09 AM »
Um, snake? When you get the time, would you mind updating 2s. When it comes to 10, they may become important.
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« Reply #4 on: September 25, 2006, 05:15:56 AM »
Heh. For Exalted, I'd need tables for dice pools up to 30 dice...
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« Reply #5 on: September 25, 2006, 08:48:01 AM »
Well, I'm not going to post tables for 30 dice. But I do have a little Java program to generate as many as you please.

I'll update the tables with 2's, I'll just need to find the time.
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« Reply #6 on: September 25, 2006, 08:59:43 AM »
Quote from: snakefing

Well, I'm not going to post tables for 30 dice. But I do have a little Java program to generate as many as you please.

I'll update the tables with 2's, I'll just need to find the time.


Thanks, but please don't bother on my behalf - I don't really need them.

Besides, Exalted further complicated things by equating a rolled "10" with two successes..
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« Reply #7 on: September 25, 2006, 04:26:52 PM »
Oh God... is this really starting to look like Exalted?
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« Reply #8 on: September 26, 2006, 12:04:32 PM »
Okay, I edited the tables to include more data.

I think d10 pools might work okay. We need to run through mock combat or stat analysis for a bunch of scenarios. I'm thinking things like the following (for melee only, right now):

A couple of schlubs, unarmored, slugging each other with fists.

A couple of evenly matched average guards/soldiers.

An average guard against a low-level PC character.

A couple well-matched high-level fighting types.

Well-matched fighting types, but who have taken different approaches to combat (e.g., tank vs. duelist, tank vs. damage machine, etc.).

Low level character against an animal or monster like a wolf or something.

Once we think we've got something that works okay for one-on-one combats, then we could start looking at mock combats with two-on-one, ten-on-one, etc. But start out with the simple stuff to make sure we understand the basics.
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« Reply #9 on: September 26, 2006, 12:45:13 PM »
Okay, I'm going to put up 10 soon.

Here's a breakdown of how combat should work:

Melee Attack: Pool and Strength vs. Ref+5
Ranged Attack: Pool and Coord vs. Ref+5

Required successes is determined by armor (2 for light, 3 for medium, 4 for heavy). On a roll of five, damage roll is for instakill (see weapon stats).

Melee damage: Pool and strength vs. Tough+5
Ranged damage: Pool and Coord vs. Tough+5

Damage equals number of successes.

Instakills are rolled like damage, except that a certain number of successes (determined by the weapon) kills. Instakills are rolled on five attack successes (see above) or when the attacked has no hit points.

Weapons: Weapons that deal less damage should also cost fewer action points to use. Characters can also buy AP decreases to attack more frequently.

Armor: Armor penalizes action points. Defense slightly impairs offense.

Action out of turn: Characters can reserve up to five action points to act out of turn later. If their next turn comes and they have not spent their points, they do not carry over. On the flipside, a character can act out of turn unprepared, but it costs five action points to do so.

Just some thoughts.
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« Reply #10 on: September 26, 2006, 01:49:02 PM »
[blockquote=Armor]Required successes is determined by armor (2 for light, 3 for medium, 4 for heavy).

...Damage equals number of successes.[/blockquote]
Seems like it makes more sense to say that armor absorbs the indicated number of successes/damage. Otherwise you have the odd situation where it is very hard to hit someone in good armor, but if you do, it is automatically devastating.

[blockquote=Insta-kill]On a roll of five, damage roll is for instakill (see weapon stats).[/blockquote]
Would this make more sense to treat it like a WP/VP critical - bypassing the vitality points? I'm not fond of insta-kill.

[blockquote=Weapons]Weapons that deal less damage should also cost fewer action points to use. Characters can also buy AP decreases to attack more frequently.[/blockquote]
I'm open to this. But you have to be careful - reducing AP costs for weapons can sometimes have drastic effects. Maybe better to just buy more AP.

Simple, basic AP systems are okay, but it can get out of hand pretty quickly. Ysgarth used an AP system for attack, defense, movement, spells - everything - and it was one of the most heavily criticized aspects in playtest.
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« Reply #11 on: September 26, 2006, 02:08:25 PM »
In terms of armor, it only goes as high as four successes... nobody's becoming impossible to hit... it's just that one success, even at an exaggerated target number, is pretty freaking likely. I say we try out "number of successes" armor before we move on to straight DR. Though the latter does mesh better with a couple of my variant ideas (see discussion thread).
In terms of AP... I guess we don't *have* to have out of turn action... but I'm just so fond of it. Lots of my favorite tactics in DnD concern readied actions and AoOs. I would stick with reducing costs. You might only get so far with it (two attacks for an uber-damager, maybe three with something lighter)... but it just feels more right. IMHO it's a little easier than how DnD does it, determining how much you can do in a round.

As for instakill vs. VP/WP... I don't know so much. I'm a big fan of it in d20, but for us? If we do, it might have to be more or less often. Even five successes is pretty common at target number 2. But REALLY freaking rare for anyon else.
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I don't believe in it anyway.
What?
England.
Just a conspiracy of cartographers, then?

beejazz

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« Reply #12 on: September 26, 2006, 02:33:40 PM »
Also on successes, I have to say you're quoting out of context. You roll to hit separately from your roll to damage. Hell, the pools aren't even necessarily the same size.

Let's say I attack. I roll 5d10. I succeed three times. That's enough, I hit.

I roll damage. This is a nice little 10d10 weapon, so I roll that. This guy's got low toughness, so I get seven successes. Therefore seven damage.

Understand?
Beejazz's Homebrew System
 Beejazz's Homebrew Discussion

Quote
I don't believe in it anyway.
What?
England.
Just a conspiracy of cartographers, then?

snakefing

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« Reply #13 on: September 26, 2006, 03:38:20 PM »
Gotcha. I misread your earlier post - I thought you were suggesting changing that. It makes more sense this way.
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My Unitarian Jihad name is: The Dagger of the Short Path.
And no, I don't understand it.

beejazz

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« Reply #14 on: September 26, 2006, 06:08:54 PM »
Okay, score ten is up.
I might also rehash these by difficulty/score.
Beejazz's Homebrew System
 Beejazz's Homebrew Discussion

Quote
I don't believe in it anyway.
What?
England.
Just a conspiracy of cartographers, then?