A Dice Mechanic Riddle

[Jason Lee]

So, I'm sitting around my house eating lentils and praying for divine punishment on whatever dark force is both preventing me from sleeping and denying me the lucidity of wakefulness, when a dice mechanic riddle bubbles up in my tar pit of a brain.  I'd given up on solving it some time ago, but seeing as I'm doing this whole Forge posting thing again perhaps I should pose the question there instead of bang my head into a wall until the riddle sloshes back down into the icky gooey depths.  I'm trying to come up with a dice mechanic with the following requirements:

• Stat (range 1 - 5) + skill (range 1 - 5)

• Opposed resolution.

• Stat and skill having independent functions in the mechanic.  Skill being weighted over stat.

• Each +1 in a stat or skill either contributes more to the end effectiveness result than the previous +1 or remains equivalent. (screws up several die pool ideas)

• Open ended. Meaning, no opposed roll can be impossible.  This can be the result of the interplay between both sides of resolution.

• No complex operations like multiplication or division.  No charts.  Just comparisons, additions and subtractions unless someone can think of an operation equally easy.

• Optimally, four operations or less for one side of the resolution.  For example, add stat + skill, compare the personal importance of the conflict to determine which die to read,  roll 3d10,  compare and take the middle die, add the middle die to stat + skill = 4 operations.

• No more than 5 dice rolled.

• No handling of multiple die types you can't do with only 5 dice in front of you.  For example, Deadlands is way too much interface overhead.

• 1/4 to 1/3 average contribution from the dice in end effectiveness value either per stat/skill unit or of the maximum range.   That may not be a terribly mathematically informative statement.  basically, low "swing" in the randomizer.

• Roll high.  The higher the number on an individual die the better.

• Can be pass/fail.  Success levels, botches, criticals, etc are not needed.  I've decided I prefer authorial gimmicks that act as success levels, like concessions, over ones tied to the randomizer anyway.

•  And the most annoying requirement of all (grr)... has to use only unaltered d10s.  This requirement annoys me something fierce, so I think I'd like to ignore it for this thread... but I thought I ought to mention it in case anyone can come with an idea.

[Darren Hill]

I don't know if this qualifies all your steps.

Can you have Skill = 0?
Assuming yes...

Target Number = some number based on enemy Skill. (Might be 5 + stat; might be variable diff of 1-5 + stat; might be skill*2 = 0/2/4/6/8/10)
Roll dice equal to Stat.
Side with greater number of successes wins.

Might swap roles of stat and skill, to closer achieve goals. Gets a bit funky if you can have zero Skill.

If you used d6's, you wouldn't need an extra diff mod, you could just have it be:
Roll skill [or stat] dice; must exceed target's stat [or skill].

What about external modifiers - do they play a part in your system?

[Matthew Chan]

Hi everyone. Been lurking around for the past couple months and this post happened to look like something I could reply to meaningfully.

Hi Jason:

Holy crap, 5d10 and low randomness? That's crazy talk... or maybe I'm just biased from years of Storyteller. That said, I'll give this a shot anyway. (warning: long example)


Skill: Number added to own roll
Stat: Number added to opposition's TN

Stat is more likely to contribute to a decisive result, given that the conflict is over only when someone fails their roll, but Skill is crucial in getting what one actually wants, as well as granting the player power to steer the conflict's direction.


Resolution:
Each side gives one win condition and one loss condition.

• Win conditions must not be compatible with each other.
• Loss conditions must, however, be compatible with each other.
• Each loss condition must be compatible with the other player's win condition, whether or not it is compatible with one's own.

Each side notes their TN, which is ten plus the stat the opposing player is using.

Players may back out at any point before rolling the dice. When this happens the remaining player's win condition prevails, but loss conditions do not arise unless the win condition necessitates them.

Each player rolls 2d10 plus their own relevant skill.*

• If one pair of dice comes up at 20, roll a d10 and add its result to one's total. If both rolls come up to 20, do not roll any more dice.

Meeting or exceeding the TN counts as success, rolling under it a failure.


Possible outcomes:
Success vs Success: Stalemate - higher roller narrates some non-resolution that is a compromise of all the stated conditions that doesn't fulfill any of them but instead shifts the conflict to something else. Where it is possible to do so, after a stalemate either player may back out, or change their own win or loss conditions. Reroll in case of a tie - whether this is treated as a retcon or a prolonged exchange depends on whether the win/loss conditions given provide time constraints.

Success vs Failure: Win/Lose - higher roller's win condition and lower roller's lose condition are realized into the SIS. Other win condition may still be up for grabs through other means.

Failure vs Failure: Charlie Foxtrot - both lose conditions are realized into the SIS. Neither win condition may be achieved for this scene.

*I'm assuming that the 5-die limit is for five dice per attempt to resolve the conflict (assuming, of course, that a true stalemate != desirable resolution). However, if it's five dice per roll, then instead of 2d10 this could be the best two of 4d10, with an extra d10 in case of a twenty regardless of whether the other player has taken a similar roll. This would help with the low-swing randomizer limit, which I'm having trouble getting around with an opposed roll of no more than five dice among both.


Example:

Pat and Chris are in a swordfight. Both are fighting to win, which in this case involves being the first and only person of the two to land an incapacitating blow.

Win conditions:
Pat hits Chris while remaining safe
Chris hits Pat while remaining safe

Lose conditions:
Pat gets hit
Chris gets hit

Stats:

• Pat's Aggression is 4
• Chris's Aggression is 3

Skills:

• Pat's Capo Ferro is 3
• Chris's Agrippa is 3

Possible Outcomes:
Stalemate: Exchange of attacks and parries that remains inconclusive. Whoever rolled higher gets to initiate another tactic (feint, strategize, reveal non-left-handedness, etc.).
Win/Lose: Someone wins the swordfight.
Clusterfuck: Pat and Chris skewer each other.

Pat rolls +3 vs TN 13 = 14
Chris rolls +3 vs TN 14 = 14
Reroll!
Pat rolls +3 vs TN 13 = 13
Chris rolls +3 vs TN 14 = 21
Two long exchanges without any clear outcome; fighters retreat out of measure. Chris decides for the next exchange to lure Pat into an opening with a feint.

Stats:

• Chris's Cunning is 4
• Pat's Wisdom is 2

Skills:

• Both continue primarily using their swordfighting skills.

Pat rolls +3 vs TN 14 = 15
Chris rolls +3 vs TN 12 = 13
Chris tricks Pat into leaving an opening but underestimates Pat's speed. Chris's sword briefly comes off line and Pat, previously on the retreat, attempts to capitalize on this moment with a sudden change in direction.

Stats:

• Chris's Reflex is 3
• Pat's Prowess is 4

Skills:

• As above.

Pat rolls +3 vs TN 13 = 8
Chris rolls +3 vs TN 14 = 12
Neither fighter remembers to cover themselves as they press on the attack. Chris's recovery cuts across Pat's jugular, at the cost of running straight into Pat's sword.


Self-Analysis, please post if you disagree:

• Stat+skill: Well, not literally stat+skill, given #3 below, but I think it's about right.
• Opposed resolution: Check.
• Stat and skill having independent functions in the mechanic.  Skill being weighted over stat: Stat only affects immediate effectiveness, while Skill helps guide prolonged conflicts towards more effective Stat/Skill combos, and is more important for influencing the SIS overall. Check.
• Synergetic Bonuses: Uh... I think so? The only way I know how to do this is to go value+fixed die, which is what I've done here.
• Open ended: Given that no stat or skill can exceed five, I believe so.
• Simple Arithmetic: Add and compare. Check.
• Four or fewer operations for each side: Lessee... declare, add, roll, add, compare, compare, narrate. Okay, so it's a bit more than four steps, though if you don't count declare and narrate and count the two comparisons as one... then again, I could get rid of the TN (and the "Charlie Foxtrot" outcome, not to mention speeding up resolution and making resolution less dependent on random chance) altogether, use the Stat as the adder and have Skill determine narration rights, but somehow such a mechanic feels unsatisfying...
  [li] No more than 5 dice rolled: See footnote above.
• No multiple die types that require more than five dice total: Check.
• Low "swing" in randomizer: See "No more than 5 dice rolled" above.
• Roll high: Check.
• Pass/Fail: Check, I think, despite there still being four possibilities one of which does not end the conflict.
• Unadulterated d10s: Check.

[Jason Lee]

I'm still a bit fuzzy for calculations, but I wanted to take a moment to reply.

*****

Darren,

Yes, you could have a zero or external modifiers.  I didn't mention that initially, so no need to worry about it.

That does seem to fit the bill.  It qualifies for open ended too, because either side can get zero successes, even though an individual roll wouldn't be.  Though, when I'm a bit less fuzzy I'll have to try to shake out how much randomless is in there and whether or not there is depreciation in the trait used to determine the number of dice (I don't think there is).

*****

Matthew,

First, Welcome to the Forge!

You're correct in assuming 5 dice per roll, so you could certainly bump up the number of dice to make the curve more steep and try to kill some of that unreliability.  As for the synergetic bonuses, my initial impression in that it's been fulfilled.  Even though there is a fixed target number (2d10 + skill ~ opponents stat + 10  =  2d10 + skill - opponents stat ~ 10), which tends to cause traits to depreciate after the mid point of exceeding that target number, I think it actually balances out to 2d10 + stat + skill ~ 2d10 + stat + skill with success levels for how much you beat your opponent by.  I'm honestly having a bit of trouble sorting that out and will ponder it.  They end up carrying the same weight for a single conflict, but if you stick to breaking up each conflict into smaller ones wherein skill remains fixed and stat varies with the sub-conflict, then I agree skill gets more weight.  It nails the whole point, at least for who I'm trying to please, in having stat and skill in the first place - aesthetics.  Without some sort of apparent mechanical distinction the aesthetic distinction doesn't end up working.  It's strong food for thought for looking outside individual task effectiveness to reinforcing that aesthetic distinction.

Overall, I like the flow and flexibility of the mechanic quite a bit.

*****

There is one criteria neither of the above meet, which is that it can't involve exchanging trait values between participants.  However, I forgot to mention that, so ignore it.  It wouldn't be fair to change the rules once we've started.  Just something to think about I suppose.

[Jason Lee]

I wanted to follow up on my unanswered math question on Darren's mechanic.

Assuming all my math is correct:

Top row represents the number that must be met or exceeded to qualify as a success.
Left column represents the number of successes.
Table values are the percentage chance of getting exactly the number of successes.  Calculated by using the SimpleDicer application from JohnDeHope3.

1D10   >= 6   >= 7   >= 8   >= 9   = 10
1   50.0%   40.0%   30.0%   20.0%   10.0%

2D10   >= 6   >= 7   >= 8   >= 9   = 10
1   50.0%   48.0%   42.0%   32.0%   18.0%
2   25.0%   16.0%   9.0%   4.0%   1.0%

3D10   >= 6   >= 7   >= 8   >= 9   = 10
1   37.5%   43.2%   44.1%   38.3%   24.3%
2   37.5%   28.8%   18.9%   9.6%   2.7%
3   12.5%   6.4%   2.7%   0.8%   0.1%

4D10   >= 6   >= 7   >= 8   >= 9   = 10
1   25.0%   34.6%   41.2%   40.9%   29.2%
2   37.6%   34.5%   26.5%   15.4%   4.9%
3   25.0%   15.3%   7.6%   2.6%   0.4%
4   6.2%   2.6%   0.8%   0.2%   0.0%

5D10   >= 6   >= 7   >= 8   >= 9   = 10
1   15.6%   26.0%   36.0%   40.9%   32.8%
2   31.4%   34.6%   30.9%   20.5%   7.3%
3   31.2%   23.0%   13.2%   5.1%   0.8%
4   15.6%   7.6%   2.8%   0.6%   0.0%
5   3.1%   1.0%   0.2%   0.0%   0.0%

So your average number of successes are:

Top row represents the difficulty.
Left column represents the number of dice.
Table values are the average number of successes for a given combination.  Calculated by adding the probabilities above.

   6   7   8   9   10
1D10   0.5   0.4   0.3   0.2   0.1
2D10   1.0   0.8   0.6   0.4   0.2
3D10   1.5   1.2   0.9   0.6   0.3
4D10   2.0   1.6   1.2   0.8   0.4
5D10   2.5   2.0   1.5   1.0   0.5

If I'm reading my own chart right (heh), it means each increase in either trait remains a constant value.  There appears to be a rising diagonal line (blue) wherein the weight of the traits are equivalent.  Above the line the trait that determines number of dice is favored, and below it the trait determining difficulty is favored.  Interesting.

*****

I haven't quite figured the math behind Matthew's mechanic yet as to how the victories and losses play out... still thinking.

[Jason Lee]

I have a couple minutes before game starts, so I thought I'd post my math so far on Matthew's mechanic.

Raw odds on 2D10 summed.  Nothing whacky.

2D10   =
2   1%
3   2%
4   3%
5   4%
6   5%
7   6%
8   7%
9   8%
10   9%
11   10%
12   9%
13   8%
14   7%
15   6%
16   5%
17   4%
18   3%
19   2%
20   1%

What I was having trouble with was getting both stat and skill for a single character to fit on one chart.  Didn't work.  Which is just as well, because my desire to do so seems to have stemmed from not grokking the different roles the traits were playing in the game.  I initially didn't give the mechanic enough credit for distinguishing stat (favors opponent's loss condition) and skill (favors own win condition).  The difference is actually quite significant in terms of how it impacts play.

Top row represents opponents stat.
Left column represents skill.
Table values represent the chance of scoring a success on the top chart, and the chance of scoring a failure on the bottom chart.

>= 10   -1   -2   -3   -4   -5
1   64%   55%   45%   36%   28%
2   72%   64%   55%   45%   36%
3   79%   72%   64%   55%   45%
4   85%   79%   72%   64%   55%
5   90%   85%   79%   72%   64%

< 10   -1   -2   -3   -4   -5
1   36%   45%   55%   64%   72%
2   28%   36%   45%   55%   64%
3   21%   28%   36%   45%   55%
4   15%   21%   28%   36%   45%
5   10%   15%   21%   28%   36%

Again assuming I can interpret my own charts, below the blue pairs the value of skill depreciates by 1% and stat appreciates by 1%.  The situation reverses above the blue pairs.

*****

A further note on Darren's mechanic.  Analyzing it has given be insight into specifically what is meant when people complain of dice pools being to random.  The range of actual values (success) that is used is very small.  The results don't seem terribly unpredictable to me.  However, the actual contribution to the end effectiveness value from an individual point in a trait is quite small.  If we do some funny math with the figures above and assume that all combinations occur in equal and random proportions, then the average contribution from a single trait point is +/- 0.3 successes.  Which isn't going to show up on a player's radar for a single roll.  Thus, it feels more "random" because your traits impact the actual number you use very little.

*****

Gotta scoot.  *prays to the typo gods to be merciful*