How do I Get This System to Work?

[Lord Lemming]

I've been working on a homebrew system for a while, and while I have most of the mechanics nailed down for now, I'm trying to get a method for rolling attacks to meet my general requirements and am coming up empty.

The general requirements I'm looking for are:

-The system should require as few dice rolls as possible. Two dice rolls maximum, with d20 or d6 rolls preferred. I have a dice roll system where you roll 2d6, with one d6 being positive and the other negative, so that you get a range between -5 and 5, with 0 being the most likely outcome and -5 and 5 being the least likely, so that's an option.

-Two opponents with evenly matched offense and defense stats have a roughly 50% chance of hitting the other.

-The complicated part: I want someone who has twice as much attack as the target has defense to have half as much chance of missing. For instance, an attack of 2 against a defense of 1 has a 75% chance of hitting. An attack of 5 against a defense of 1 has a 90% chance of missing.

-Conversely, having half as much attack as the enemy's defense means your chance to HIT is cut in half. Attack 1, defense 2, your chance to hit is 25%. Attack 1, defense 5, your chance to hit is 10%.

-For simplicity, we can assume that attack and defense go from 1 to 6, and that you'll never meet someone with an attack-defense stat lower than 1 or higher than 6.

The chart of 'chance to hit' looks something like this, with the column on the far left being the attack rating, the top row being the defense rating, and the numbers being percentage chance (rounded to the nearest degree).

--- -1- -2- -3- -4- -5- -6-
-1- 50 25 17 13 10 8
-2- 75 50 33 25 20 17
-3- 84 67 50 38 30 25
-4- 88 75 64 50 40 33
-5- 90 80 70 60 50 42
-6- 92 83 75 67 58 50

The general idea is that I want a system where getting higher and higher numbers provides diminishing returns. In 3.5, someone with an attack rating of 0 has a 50% chance of hitting someone with an AC of 11, and a 45% chance of hitting someone with an AC of 12. The chance to hit has only gone down by 10%. Meanwhile, if the defender's AC is 19 and goes up to 20, the chance to hit is cut in half. This means that getting higher and higher numbers provides increasing returns against the same foe. I want to do the opposite.

In theory, I could do this by just having everyone keep this table and roll percentage dice. I can't use a d20 because it doesn't have small enough increments, and leads to me having to make more rules. But I don't really LIKE percentage dice, so I'm coming to you to ask if you can think of an easier way to do this, or something similar to this. I'm not married to this percentage table; if you can think of an easier way to provide diminishing returns on higher numbers, I'd like to hear it.

[olskool]

I've been working on a homebrew system for a while, and while I have most of the mechanics nailed down for now, I'm trying to get a method for rolling attacks to meet my general requirements and am coming up empty.

The general requirements I'm looking for are:

-The system should require as few dice rolls as possible. Two dice rolls maximum, with d20 or d6 rolls preferred. I have a dice roll system where you roll 2d6, with one d6 being positive and the other negative, so that you get a range between -5 and 5, with 0 being the most likely outcome and -5 and 5 being the least likely, so that's an option.

-Two opponents with evenly matched offense and defense stats have a roughly 50% chance of hitting the other.

-The complicated part: I want someone who has twice as much attack as the target has defense to have half as much chance of missing. For instance, an attack of 2 against a defense of 1 has a 75% chance of hitting. An attack of 5 against a defense of 1 has a 90% chance of missing.

-Conversely, having half as much attack as the enemy's defense means your chance to HIT is cut in half. Attack 1, defense 2, your chance to hit is 25%. Attack 1, defense 5, your chance to hit is 10%.

-For simplicity, we can assume that attack and defense go from 1 to 6, and that you'll never meet someone with an attack-defense stat lower than 1 or higher than 6.

The chart of 'chance to hit' looks something like this, with the column on the far left being the attack rating, the top row being the defense rating, and the numbers being percentage chance (rounded to the nearest degree).

--- -1- -2- -3- -4- -5- -6-
-1- 50 25 17 13 10 8
-2- 75 50 33 25 20 17
-3- 84 67 50 38 30 25
-4- 88 75 64 50 40 33
-5- 90 80 70 60 50 42
-6- 92 83 75 67 58 50

The general idea is that I want a system where getting higher and higher numbers provides diminishing returns. In 3.5, someone with an attack rating of 0 has a 50% chance of hitting someone with an AC of 11, and a 45% chance of hitting someone with an AC of 12. The chance to hit has only gone down by 10%. Meanwhile, if the defender's AC is 19 and goes up to 20, the chance to hit is cut in half. This means that getting higher and higher numbers provides increasing returns against the same foe. I want to do the opposite.

In theory, I could do this by just having everyone keep this table and roll percentage dice. I can't use a d20 because it doesn't have small enough increments, and leads to me having to make more rules. But I don't really LIKE percentage dice, so I'm coming to you to ask if you can think of an easier way to do this, or something similar to this. I'm not married to this percentage table; if you can think of an easier way to provide diminishing returns on higher numbers, I'd like to hear it.

What about using 2D12 as your dice? Would that give you a smaller breakdown? A game using 2 to 24 slots would slightly reduce your increments. 2D20 could work but your back to percentile rolling those.

[Composer99]

If you were willing to go with a slightly less clean implementation, what about 2d10?

Let's say, if your Attack and Defence are the same, the attacker needs to roll 10 or better on 2d10 in order to hit. That's 55% to hit.

Then, for every point of Attack you have higher than your target's Defence, or if you want more scalability, each time you hit a particular threshold of Attack:Defence ratio, you hit on a result 1 lower than before. (The baseline is Attack:Defence is 1:1, needing 10 to hit.)

Attack - Defence
So if your Attack - Defence is +2, you hit on an 8 or better, for a 72% to hit (55 + 9 + 8). If it's +5, you hit on a 5 or better, for a 90% to hit (55 + 9 + 8 + 7 + 6 + 5). Have a cap on the die roll modifier if you want to avoid having a 100% to hit. The system works the same way in reverse. This could work well enough with maximum Attack and Defence ratings of 6 or so, since in that case the absolute cap would be 90% hit or miss chance.

Attack:Defence Ratio
With this, your chance of hitting goes up (or down) based on the ratio of Attack to Defence. If your Attack is higher than the target's Defence, you can have a threshold at 3:2 and then at each odds ratio with an integer (2:1, 3:1, and so on), where each such threshold you cross allows you to hit on a result 1 lower than before. So you hit on a 9 or higher with 3:2, an 8 or higher with 2:1, a 7 or higher with 3:1, and so on. It works the same way in reverse: if your Attack:Defence ratio is no better than 2:3, you hit on an 11 or higher, if it's no better than 1:2, you hit on a 12 or higher, and so on.

Either method includes diminishing returns. <Attack-Defence> means your chance of hitting increases by a lower amount each time, <Attack:Defence> includes that and needing progressively more Attack or Defence to hit a new ratio threshold. The former is probably better if you have a tight spread of stat numbers. The latter is better if you can have a larger spread of numbers, especially if there is a wide numerical gulf between creatures at different power levels.

(This also works with any other implementation of multiple dice: 3d6, 2d20, what have you. I just picked 2d10 because it has the same number of results, overall, as percentile dice, while spreading them differently.)

[Lord Lemming]

Attack - Defence
So if your Attack - Defence is +2, you hit on an 8 or better, for a 72% to hit (55 + 9 + 8). If it's +5, you hit on a 5 or better, for a 90% to hit (55 + 9 + 8 + 7 + 6 + 5). Have a cap on the die roll modifier if you want to avoid having a 100% to hit. The system works the same way in reverse. This could work well enough with maximum Attack and Defence ratings of 6 or so, since in that case the absolute cap would be 90% hit or miss chance.



I like this. It's relatively simple, doesn't involve charts or having to recalculate based on relative scores. I think I'll try this. Thanks!

EDIT: I mean, it doesn't QUITE do what I wanted it to do, but I think it's about as close as I can get while keeping it simple.

[Maat Mons]

Option 1
Roll 1 die depending on your rank in the relevant ability
Rank 1: d2
Rank 2: d4
Rank 3: d6
Rank 4: d8
Rank 5: d10
Rank 6: d12
You opponent also rolls 1 die depending on his rank in his ability.
Highest roll wins.
In case of a tie, flip a coin.

Option A
Roll 1d6 and multiply by your ability score.
Your opponent rolls 1d6 and multiplies by his ability score.
Highest roll wins.
Ties go to whoever has the lowest ability score.
If that's tied too, flip a coin.

[PhantomSoul]

Option 1
Roll 1 die depending on your rank in the relevant ability
Rank 1: d2
Rank 2: d4
Rank 3: d6
Rank 4: d8
Rank 5: d10
Rank 6: d12
You opponent also rolls 1 die depending on his rank in his ability.
Highest roll wins.
In case of a tie, flip a coin.


I was going to see if something similar worked, but with some other (partial) resolution systems. I did a quick simulation (3736 rolls per dice pairing) to see what the numbers were like at different comparisons. Column 1 tells you the dice, column 2 tells you how often you win out of non-tie rolls (tie rate in parentheses), column 3 tells you how often you win if the character with the largest die wins (tie rate in parentheses), column 3 tells you how often you win if the character with the smallest die wins (tie rate in parentheses). So basically, baseline vs. rich get richer / strength bias vs. poor get poorer / underdog bias.

Do not resolve ties Largest die wins Smallest die wins
You at d4 vs. other at d4: 51.68% (23.73% tie) 51.68% (23.73% tie) 51.68% (23.73% tie)
You at d4 vs. other at d6: 29.59% (16.34% tie) 24.75% (0% tie) 41.09% (0% tie)
You at d4 vs. other at d8: 21.64% (13.71% tie) 18.67% (0% tie) 32.38% (0% tie)
You at d4 vs. other at d10: 16.67% (10.65% tie) 25.54% (0% tie) 14.89% (0% tie)
You at d4 vs. other at d12: 12.09% (8.65% tie) 19.69% (0% tie) 11.05% (0% tie)
You at d4 vs. other at d20: 7.89% (5.06% tie) 12.56% (0% tie) 7.5% (0% tie)
You at d6 vs. other at d4: 69.35% (17.62% tie) 74.75% (0% tie) 57.13% (0% tie)
You at d6 vs. other at d6: 49.74% (17.98% tie) 49.74% (17.98% tie) 49.74% (17.98% tie)
You at d6 vs. other at d8: 36.21% (12.39% tie) 31.72% (0% tie) 44.12% (0% tie)
You at d6 vs. other at d10: 28.82% (10.45% tie) 36.26% (0% tie) 25.81% (0% tie)
You at d6 vs. other at d12: 22.01% (8.74% tie) 28.83% (0% tie) 20.09% (0% tie)
You at d6 vs. other at d20: 11.73% (4.73% tie) 15.91% (0% tie) 11.18% (0% tie)
You at d8 vs. other at d4: 77.2% (13.21% tie) 80.21% (0% tie) 67% (0% tie)
You at d8 vs. other at d6: 65.36% (13.08% tie) 69.89% (0% tie) 56.8% (0% tie)
You at d8 vs. other at d8: 50.5% (11.34% tie) 50.5% (11.34% tie) 50.5% (11.34% tie)
You at d8 vs. other at d10: 38.79% (9.83% tie) 44.81% (0% tie) 34.98% (0% tie)
You at d8 vs. other at d12: 33.14% (8.55% tie) 38.86% (0% tie) 30.31% (0% tie)
You at d8 vs. other at d20: 18.9% (5.39% tie) 23.27% (0% tie) 17.88% (0% tie)
You at d10 vs. other at d4: 82.78% (10.26% tie) 74.29% (0% tie) 84.55% (0% tie)
You at d10 vs. other at d6: 72.09% (10.12% tie) 64.79% (0% tie) 74.92% (0% tie)
You at d10 vs. other at d8: 61.64% (10.78% tie) 55% (0% tie) 65.78% (0% tie)
You at d10 vs. other at d10: 49.5% (10.42% tie) 49.5% (10.42% tie) 49.5% (10.42% tie)
You at d10 vs. other at d12: 42.84% (8.38% tie) 39.25% (0% tie) 47.63% (0% tie)
You at d10 vs. other at d20: 21.11% (4.54% tie) 20.15% (0% tie) 24.69% (0% tie)
You at d12 vs. other at d4: 86.87% (8.35% tie) 79.62% (0% tie) 87.97% (0% tie)
You at d12 vs. other at d6: 77.5% (7.82% tie) 71.43% (0% tie) 79.26% (0% tie)
You at d12 vs. other at d8: 68.24% (8.19% tie) 62.66% (0% tie) 70.84% (0% tie)
You at d12 vs. other at d10: 59.37% (8.65% tie) 62.89% (0% tie) 54.24% (0% tie)
You at d12 vs. other at d12: 51.51% (8.28% tie) 51.51% (8.28% tie) 51.51% (8.28% tie)
You at d12 vs. other at d20: 29.59% (4.8% tie) 28.17% (0% tie) 32.97% (0% tie)
You at d20 vs. other at d4: 92.56% (5.06% tie) 87.87% (0% tie) 92.93% (0% tie)
You at d20 vs. other at d6: 86.61% (5% tie) 82.28% (0% tie) 87.28% (0% tie)
You at d20 vs. other at d8: 81.67% (5.13% tie) 77.48% (0% tie) 82.61% (0% tie)
You at d20 vs. other at d10: 74.93% (5.06% tie) 76.2% (0% tie) 71.14% (0% tie)
You at d20 vs. other at d12: 71.12% (5.19% tie) 72.62% (0% tie) 67.42% (0% tie)
You at d20 vs. other at d20: 49.14% (4.73% tie) 49.14% (4.73% tie) 49.14% (4.73% tie)

(Pasting a table should really be possible... :/ I guess I could have the simulation output 'code' for a table on the side, but oh well. It should be easy to paste into a spreadsheet program.)

[Maat Mons]

I like to use AnyDice (https://anydice.com/) for these sorts of things.

I'm pretty sure that site uses convolution (https://en.wikipedia.org/wiki/Convolution) to determine probabilities. It can be a very efficient way of getting the answer. Though writing a good, fast convolution algorithm is by no means trivial. Maybe your preferred programming language already has one that someone's made?

As an example of how you can use that website, if you want to have 1 person roll a d12, and another roll a d6, and see who gets the higher number, you'd type "output 1d12 - 1d6" (no quotes). Clicking on "At Least" and looking at the "1" row on the table, you see that there's a 70.83% chance that the sum of 1d12 - 1d6 is 1 or more. That is, there's a 70.83% chance that the d12 rolls higher than the d6. Clicking on "At Most" and looking at the "-1" row, you can see there's a 20.83% chance that the d6 rolls higher than the d12. Then clicking on "Normal" and looking at the "0" row, you can see there's an 8.33% chance of a tie.

This is sort of why I wanted to resolve ties with a coin flip for this method. That means half of the ties (4.17% of rolls) add to the chance of each side winning, so it's a 75% chance for one, and a 25% chance for the other.

[MoiMagnus]

Attack - Defence
So if your Attack - Defence is +2, you hit on an 8 or better, for a 72% to hit (55 + 9 + 8). If it's +5, you hit on a 5 or better, for a 90% to hit (55 + 9 + 8 + 7 + 6 + 5). Have a cap on the die roll modifier if you want to avoid having a 100% to hit. The system works the same way in reverse. This could work well enough with maximum Attack and Defence ratings of 6 or so, since in that case the absolute cap would be 90% hit or miss chance.


Am I missing something, or are you just describing "D&D, but with 2d10 instead of a d20"?
Because here the computation seems to simply be equivalent to "2d10+Attack VS 10+Defence".

[Composer99]

Am I missing something, or are you just describing "D&D, but with 2d10 instead of a d20"?
Because here the computation seems to simply be equivalent to "2d10+Attack VS 10+Defence".

Basically yes. Roll + Attack vs. Defence (with or without a base value) is a pretty solid mechanic for streamlined combat resolution.

The two main differences are that 2d10 has 100 possible outcomes, while a d20 has 20, and the 2d10 has increasing returns as one goes from having a low chance of hitting to a middling chance, and diminishing returns as one goes from having a middling chance to having a high chance, where the d20 has the same returns no matter what.

[clash]

I mean the easiest way to do this is with multiple dice. Use d6s. Count each as a d2. You need at least 1 success. 1 dice rolls 50% chance. 2 roll for 75% and so on. You roll one dice plus one for each in the difference between attack and defense.