Author Topic: Dice Pool Crunching  (Read 4834 times)

beejazz

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« Reply #30 on: September 19, 2006, 06:29:10 PM »
Well... It is an *altenate* system after all. Point is a greater degree of realism, and checkboxes on character sheets would minimize any extra complexity. With any luck. It also minimizes bookkeeping on armor stats.

In terms of armor providing no progressive benefit... not to difficulty to hit, but for number of successes. Tradeoff in AP, I guess.

In settings without armor (modern, etc.) we might use reflex+luck for defense and above hit point system. Just a thought.
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snakefing

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« Reply #31 on: September 19, 2006, 06:41:03 PM »
Some simulated combat numbers:

Two chumps swinging their fists in anger. Assume that COORD attack bonuses and REACT defense cancel each other out. No armor. 3d6 pools, 2 successes to hit. Each turn they have a 74% chance to hit, Damage would be 1d6 dice pool, non-lethal. No armor means TOUGH is the target for damage. Assume this is 4 out of range 3 to 6. Then for each hit their is 50% chance of doing 1 VP damage.

Average damage per round is 0.37 points.

Now, we have an adventurer fighting a conscript guard. Assume that the adventurer has a +1 advantage in both COORD and REACT. The adventurer has medium armor, but average TOUGH and STRENGTH, and 4d6 attack pool with his sword. The guard has 3d6 attack pool and only light armor.

The adventurer still has a target number of 3. His COORD advantage cancels out the armor defense. With 4d6 he's got an 89% chance to score 2+ successes each round. The guard has 3d6, but he needs a target number of 6 (increased by two for the armor and one for the adventurer's REACT advantage). With 3d6 dice pool he's only got a 7.5% chance to hit.

The adventurer has 3d6 dice pool against 5 target number to hit (TOUGH + light armor). His average damage (assuming he hits) is exactly 1.0. The guard has 3d6 dice pool against 6 target number. Assuming he hits, his average damage is 0.50.

So taking all into consideration, the adventurer averages 0.89 damage per round, while the guard averages 0.04 damage per round.

This is a pretty heavy 20:1 advantage for the adventurer. The advantages I gave him were:
1d6 extra attack die
+1 additional COORD
+1 additional REACT
+1 additional ARMOR

If we assume that armor does not affect attack rolls, we can get some different numbers. In this case I'm just assuming that any defensive advantage supplied by armor is negated by its encumbrance effects. It still affects damage rolls.

In this case the adventurer's attack target number decreases to 2, nearly a sure thing, but he doesn't gain much advantage from that because his probability of success was pretty high anyway. The guard's target number goes down to 5, but that's a bigger gain for him - his chance to hit goes up to 26%. In this case the adventurer's average damage per round goes to 1.0 more or less, while the guard's is not .13. Still a high advantage for the adventurer, but more like 8:1.

Obviously the advantages would increase all the more if I gave the adventurer more advantages on defense, making it effectively impossible for the guard to damage him at all.

Anyway, that's something to look at. It helps to show the level of granularity of the system.
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beejazz

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« Reply #32 on: September 19, 2006, 07:11:58 PM »
Before I write up an example of my own and check, could we get an update back on the probabilities to include progressive dice increases for one required success, target number two and 6d6 for two successes, and result:2 for three successes.

Also, remember that granularity need not be limited to the probability of hitting or missing but in the number of possible outcomes. There is zero granularity in chess, after all. You move into your opponent's square and you capture their piece. But the number of possible results? Infinite.

Likewise, penalties to a player in armor applying to action points (and the necessary max reflex to keep defenses in the nine-and-under range) could limit the number of times you can attack, whether you can attack and move in the same turn, how far you can move, whether you can afford to attack or defend out-of-turn, etc.

Also... this is an obviously inferior opponent. Probably faced in groups of twenty. Point is, if he's falling short in two places, he's probably compensating... in this case in Strength and Toughness. Or maybe just one of the two.
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beejazz

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« Reply #33 on: September 20, 2006, 05:45:05 PM »
Okay, another new system. Greater 'granularity' as you put it.

Start with 5d10 dicepools.

Ability scores range from 7 to 10 (start at seven, three points to distribute).

Target numbers from 12 to 16 (5 possible numbers).

Target number of successes from one to five (five possible numbers.)

25 possible difficulties for four possible ability values (a total of 100 possibilities, not counting further dice progression).

Base defense modifier is +5.

Three types of armor require 2, 3, or 4 successes. Armor penalties apply to action points only.

Vital weapon stats are damage dice, weapon group, and action point cost to attack (to account for reload times and make less damaging weapons still attractive).

Note that while d10s are less accessible than d6s, they offer a greater range of possibilities, and can double as percentile rolls as the need arises.

...Just some thoughts.
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snakefing

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« Reply #34 on: September 20, 2006, 07:01:59 PM »
Okay, I went back and edited the original probability tables to add some additional data. Just to keep it all in one place.

As far as my example combat goes: This is clearly a case of a superior opponent vs. inferior. But in DnD terms it is like a level 2 PC fighter vs. a level 1 standard array warrior. The adventurer has purchased the following advantages:
Used his initial character points to give him above average COORD and REACT.
Spent some of his initial XP on +1d6 added to his dice pool for his weapon.
Spent some of his initial wealth on medium armor.

It really isn't out of the question, in my mind, that a PC character could be this good right out of the gate - without ever having earned an XP in anger. I'm not surprised that he is superior to John Q. Henchman, but I was a little surprised to see how much of a difference it makes.

As for granularity, what I mean by this is the size of the "grains", that is, the smallest possible adjustments you can make - like increasing the task difficulty by 1, or adding one die to the pool, or reducing the required successes by one. It's not about number of possible outcomes, but rather how much a GM can "fine-tune" the difficulty of an encounter.

Your latest proposal will be more granular in this sense in several ways. Changing to d10 means that adding or subtracting +/- 1 to net target numbers makes a smaller difference. Using larger dice pools will be more granular - adding or removing one die will make less difference out of a large dice pool than a smaller one. And introducing larger numbers of required successes also makes it more granular.

At the same time, it makes the system a little more unwieldy.
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beejazz

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« Reply #35 on: September 20, 2006, 09:16:59 PM »
Quote from: snakefing

Okay, I went back and edited the original probability tables to add some additional data. Just to keep it all in one place.

As far as my example combat goes: This is clearly a case of a superior opponent vs. inferior. But in DnD terms it is like a level 2 PC fighter vs. a level 1 standard array warrior. The adventurer has purchased the following advantages:
Used his initial character points to give him above average COORD and REACT.
Spent some of his initial XP on +1d6 added to his dice pool for his weapon.
Spent some of his initial wealth on medium armor.

It really isn't out of the question, in my mind, that a PC character could be this good right out of the gate - without ever having earned an XP in anger. I'm not surprised that he is superior to John Q. Henchman, but I was a little surprised to see how much of a difference it makes.

As for granularity, what I mean by this is the size of the "grains", that is, the smallest possible adjustments you can make - like increasing the task difficulty by 1, or adding one die to the pool, or reducing the required successes by one. It's not about number of possible outcomes, but rather how much a GM can "fine-tune" the difficulty of an encounter.

Your latest proposal will be more granular in this sense in several ways. Changing to d10 means that adding or subtracting +/- 1 to net target numbers makes a smaller difference. Using larger dice pools will be more granular - adding or removing one die will make less difference out of a large dice pool than a smaller one. And introducing larger numbers of required successes also makes it more granular.

At the same time, it makes the system a little more unwieldy.


In terms of buying extra ability scores with CP in the d6 system... increases to ability scores *are* a pretty big deal. Even if we were to allow it... sure as hell not right off the bat. In terms of the dice pools, keep in mind that extra dice apply only to attacking. Not damage.

In terms of the d10s... I actually think this might work better. Defense values and armor both have a slightly more intuitive feel. Also, we have more to work with from a design standpoint. Small bonuses to dice and abilities won't mean a 20:1 advantage. Also, like I said before, 2d10 can be used for percentile rolls as neccessary.

anyway, d6 is a little clunky. d10 really only looks good so far I know, but at least it's got that much. Unless you have some alternate proposal?
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snakefing

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« Reply #36 on: September 20, 2006, 09:22:30 PM »
One other point:

More or less granular is not necessarily better or worse. It's just different. A combat system that is less granular means that combat will be a little less prominent I think - it is more likely that the side with the statistical advantage will just be overwhelmingly more likely to win. So there won't be as much uncertainty or drama in the combats themselves.

This just means that the game will play a little differently. Players will have to scheme and plan to try to gain that statistical advantage, or counteract the opponent's advantage. This isn't necessarily a bad thing, but it does change the focus of the game.
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beejazz

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« Reply #37 on: September 20, 2006, 09:30:57 PM »
Err... Yeah. "Superior Opponent Wins (Always)" does not mesh with "Tactical Movement" or "Fighting Kills People." The latter two are really what I'm looking for. Again, 'granularity' means a couple of things, as I see it. First, we need to go into more detail because there are more possible outcomes. Second, we have a little more freedom in design because little things aren't 20:1 nor does "one rank" in a skill increase the likelihood of success twofold or what have you. It's hard to represent anything numerically when "+1" equals "win"...

I'm seeing merit in the granular, myself.
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Thanuir

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« Reply #38 on: October 23, 2006, 07:36:22 AM »
First, is there a reason for building entirely new RPG? There are tons of existing ones out there. I can give pointers towards free ones.
I personally enjoy system crafting, so this is not complaining. Just curious.

Some scattered thoughts:
The chance of success can be manipulated in several ways: Number of dice, target number, number of successes required/taken away (e.g. shooting a skeleton with a bow will give normal sucesses, but two of them will be simply ignored). This is not necessary. One method is usually enough, two should be sufficient for most purposes.

Changing the TN (target number) is dangerous, due to 7 being impossible and 1 automatic. My suggestion is to make target number fixed or uniquely determined by single number (attribute, skill, equipment, but only single thing).

This would leave number of dice and number of successes as the variables.

One option: Positive circumstances give bonus dice, negative ones increase the successes needed.

beejazz

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« Reply #39 on: October 23, 2006, 11:19:54 AM »
Umm... This particular thread has been pretty much abandoned in favor of one for 5d10 pools.
Also, we know you can shift both TN and number of successes. Lately, we've been discussing roll-unders, where you roll under your ability score and aim to hit a variable number of successes. Number of dice would start at five and increase with skill ranks.

Except for CYMRO. He's gone on some kind of wild percentile roll tangent. Which is fine; I'll still participate in that too... I just wanna make use of these pools and such.

As for why a new system... I prefer to ask "why not?"
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beejazz

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« Reply #40 on: November 07, 2006, 03:52:51 PM »
One final request and I won't bug you anymore on pools:

Pool size between 6d6 and 9d6.
Roll at or under numbers between 2 and 5.
Successes between one and nine (just to be sure).

I just need to see how it'd work. Won't bug ya no more after that.
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snakefing

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« Reply #41 on: November 07, 2006, 05:03:50 PM »
Will do. My memory stick is not with me right now, so I'll have to wait till I get home.
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beejazz

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« Reply #42 on: November 07, 2006, 07:44:52 PM »
Thanks man. I owe ya for all this.


Math.
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snakefing

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« Reply #43 on: November 09, 2006, 03:53:03 PM »
D6 dice pools, roll low. Dice pool sizes ranging from 6d6 to 9d6, for all target numbers

[table=1+ Success]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(6,d6)[/th][td]100%[/td][td]99.9%[/td][td]98%[/td][td]91%[/td][td]67%[/td][/tr]
[tr][th]DicePool(7,d6)[/th][td]100%[/td][td]100%[/td][td]99.2%[/td][td]94%[/td][td]72%[/td][/tr]
[tr][th]DicePool(8,d6)[/th][td]100%[/td][td]100%[/td][td]99.6%[/td][td]96%[/td][td]77%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]100%[/td][td]100%[/td][td]99.8%[/td][td]97%[/td][td]81%[/td][/tr]
[/table]

[table=2+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(6,d6)[/th][td]99.9%[/td][td]98%[/td][td]89%[/td][td]65%[/td][td]26%[/td][/tr]
[tr][th]DicePool(7,d6)[/th][td]100%[/td][td]99.3%[/td][td]94%[/td][td]74%[/td][td]33%[/td][/tr]
[tr][th]DicePool(8,d6)[/th][td]100%[/td][td]99.7%[/td][td]96%[/td][td]80%[/td][td]40%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]100%[/td][td]99.9%[/td][td]98%[/td][td]86%[/td][td]46%[/td][/tr]
[/table]

[table=3+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(6,d6)[/th][td]99.1%[/td][td]90%[/td][td]66%[/td][td]32%[/td][td]6%[/td][/tr]
[tr][th]DicePool(7,d6)[/th][td]99.8%[/td][td]95%[/td][td]77%[/td][td]43%[/td][td]10%[/td][/tr]
[tr][th]DicePool(8,d6)[/th][td]100%[/td][td]98%[/td][td]86%[/td][td]53%[/td][td]13%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]100%[/td][td]99.2%[/td][td]91%[/td][td]62%[/td][td]18%[/td][/tr]
[/table]

[table=4+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(6,d6)[/th][td]94%[/td][td]68%[/td][td]34%[/td][td]10%[/td][td]0.9%[/td][/tr]
[tr][th]DicePool(7,d6)[/th][td]98%[/td][td]83%[/td][td]50%[/td][td]17%[/td][td]1.8%[/td][/tr]
[tr][th]DicePool(8,d6)[/th][td]99.5%[/td][td]91%[/td][td]64%[/td][td]26%[/td][td]3.1%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]99.9%[/td][td]96%[/td][td]75%[/td][td]35%[/td][td]4.8%[/td][/tr]
[/table]

[table=5+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(6,d6)[/th][td]74%[/td][td]35%[/td][td]11%[/td][td]1.8%[/td][td]0.1%[/td][/tr]
[tr][th]DicePool(7,d6)[/th][td]90%[/td][td]57%[/td][td]23%[/td][td]4.5%[/td][td]0.2%[/td][/tr]
[tr][th]DicePool(8,d6)[/th][td]97%[/td][td]74%[/td][td]36%[/td][td]9%[/td][td]0.5%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]99.1%[/td][td]86%[/td][td]50%[/td][td]14%[/td][td]0.9%[/td][/tr]
[/table]

[table=6+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(6,d6)[/th][td]33%[/td][td]9%[/td][td]1.6%[/td][td]0.1%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(7,d6)[/th][td]67%[/td][td]26%[/td][td]6%[/td][td]0.7%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(8,d6)[/th][td]87%[/td][td]47%[/td][td]14%[/td][td]2.0%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]95%[/td][td]65%[/td][td]25%[/td][td]4.2%[/td][td]0.1%[/td][/tr]
[/table]

[table=7+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(7,d6)[/th][td]28%[/td][td]6%[/td][td]0.8%[/td][td]0.0%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(8,d6)[/th][td]60%[/td][td]20%[/td][td]3.5%[/td][td]0.3%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]82%[/td][td]38%[/td][td]9%[/td][td]0.8%[/td][td]0.0%[/td][/tr]
[/table]

[table=8+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(8,d6)[/th][td]23%[/td][td]3.9%[/td][td]0.4%[/td][td]0.0%[/td][td]0.0%[/td][/tr]
[tr][th]DicePool(9,d6)[/th][td]54%[/td][td]14%[/td][td]2.0%[/td][td]0.1%[/td][td]0.0%[/td][/tr]
[/table]

[table=9+ Successes]
[tr][th]Net Target[/th][th]5[/th][th]4[/th][th]3[/th][th]2[/th][th]1[/th][/tr]
[tr][th]DicePool(9,d6)[/th][td]19%[/td][td]2.6%[/td][td]0.2%[/td][td]0.0%[/td][td]0.0%[/td][/tr]
[/table]
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beejazz

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« Reply #44 on: November 09, 2006, 05:11:32 PM »
Yay!
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