Single Roll Opposed 3d Dice Roll Tables

[Pursuivant]

These are tables I originally created as an experimental method of speeding combat.

They allow one 3d roll to substitute for the usual attack and active defense rolls. In theory, this eliminates a common source of slowness and allows more "player focused" play, since the player typically rolls the dice.

They can be also be used for other types of opposed 3d rolls, like Quick Contests.

I abandoned the idea because the percentage chance of the attacker's action succeeding multiplied by the defender's percentage chance of making a successful Active Defense resulted in numbers which weren't sufficiently "granular" or intuitive to work well with 3d (see the third table).

An additional weakness is that the table doesn't have a quick method of determining or resolving ties.

I present them as an idea for others to avoid or to develop into a more workable system.

I apologize for the crappy Code tag formatting. Cut and paste into your favorite spreadsheet for better legibility.

3d Probability Table
Bog standard 3d Probability Table used as a basis for the next two tables.

Number	Individual %	Rounded individual %	Total %	Times Occurring	Total Rounded %
3	0.4	0.50%	0.4	1	1%
4	1.3	1%	1.7	3	2%
5	2.7	3%	4.4	6	5%
6	4.7	5%	9	10	9%
7	6.9	7%	15.9	15	16%
8	9.7	10%	25.6	21	26%
9	11.6	12%	37.2	25	37%
10	12.5	13%	49.7	27	50%
11	12.5	13%	62.2	27	62%
12	11.6	12%	73.8	25	74%
13	9.7	10%	83.5	21	84%
14	6.9	7%	90.4	15	90%
15	4.7	5%	95	10	95%
16	2.7	3%	97.7	6	98%
17	1.3	1%	99	3	99%
18	0.4	0.50%	99.4	1	100%

Opposed 3d Roll Percentage Table
First Column/Row is 3-18 on 3d. Second Column/Row is cumulative percentage chance of rolling a particular number or less on 3d.

Top row can be taken as the Attacker's skill, while the first column can be taken as the Defender's Active Defense or skill.

Cross index to find percentage probability of the "attacker's" action overcoming the "defender's" counteraction. This is equal to Attacker's % chance of success * Defender's % chance of success.

3d	x	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
x	Cum. %	0.4	1.7	4.4	9	15.9	25.6	37.2	49.7	62.2	73.8	83.5	90.4	95	97.7	99	99.4
3	0.4	0.4	0.4	0.4	0.4	0.3	0.3	0.3	0.2	0.2	0.1	0.1	0.0	0.0	0.0	0.0	0.0
4	1.7	1.7	1.7	1.6	1.5	1.4	1.3	1.1	0.9	0.6	0.4	0.3	0.2	0.1	0.0	0.0	0.0
5	4.4	4.4	4.3	4.2	4.0	3.7	3.3	2.8	2.2	1.7	1.2	0.7	0.4	0.2	0.1	0.0	0.0
6	9	9.0	8.8	8.6	8.2	7.6	6.7	5.7	4.5	3.4	2.4	1.5	0.9	0.5	0.2	0.1	0.1
7	15.9	15.8	15.6	15.2	14.5	13.4	11.8	10.0	8.0	6.0	4.2	2.6	1.5	0.8	0.4	0.2	0.1
8	25.6	25.5	25.2	24.5	23.3	21.5	19.0	16.1	12.9	9.7	6.7	4.2	2.5	1.3	0.6	0.3	0.2
9	37.2	37.1	36.6	35.6	33.9	31.3	27.7	23.4	18.7	14.1	9.7	6.1	3.6	1.9	0.9	0.4	0.2
10	49.7	49.5	48.9	47.5	45.2	41.8	37.0	31.2	25.0	18.8	13.0	8.2	4.8	2.5	1.1	0.5	0.3
11	62.2	62.0	61.1	59.5	56.6	52.3	46.3	39.1	31.3	23.5	16.3	10.3	6.0	3.1	1.4	0.6	0.4
12	73.8	73.5	72.5	70.6	67.2	62.1	54.9	46.3	37.1	27.9	19.3	12.2	7.1	3.7	1.7	0.7	0.4
13	83.5	83.2	82.1	79.8	76.0	70.2	62.1	52.4	42.0	31.6	21.9	13.8	8.0	4.2	1.9	0.8	0.5
14	90.4	90.0	88.9	86.4	82.3	76.0	67.3	56.8	45.5	34.2	23.7	14.9	8.7	4.5	2.1	0.9	0.5
15	95	94.6	93.4	90.8	86.5	79.9	70.7	59.7	47.8	35.9	24.9	15.7	9.1	4.8	2.2	1.0	0.6
16	97.7	97.3	96.0	93.4	88.9	82.2	72.7	61.4	49.1	36.9	25.6	16.1	9.4	4.9	2.2	1.0	0.6
17	99	98.6	97.3	94.6	90.1	83.3	73.7	62.2	49.8	37.4	25.9	16.3	9.5	5.0	2.3	1.0	0.6
18	99.4	99.0	97.7	95.0	90.5	83.6	74.0	62.4	50.0	37.6	26.0	16.4	9.5	5.0	2.3	1.0	0.6

3d Conversion of % Chance of Opposed Success

This is where it all goes pear-shaped. I converted percentage chances into 3d probabilities, rounding percentages up to the next highest number on 3d. For example, any percentage chance to hit greater than 0.4% but less than 1.7% is listed as a "4", while any percent chance to hit between 49.8% and 62.2% is treated as an "11."

In far too many cases this results in a 5-10% increase in chance of success as compared to the percentage-based table, which is why I abandoned the effort.

3d	x	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
x	Cum. %	0.4	1.7	4.4	9	15.9	25.6	37.2	49.7	62.2	73.8	83.5	90.4	95	97.7	99	99.4
3	0.4	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3
4	1.7	4	4	4	4	4	4	4	4	4	3	3	3	3	3	3	3
5	4.4	5	5	5	5	5	5	5	5	4	4	4	3	3	3	3	3
6	9	6	6	6	6	6	5	5	5	5	5	4	4	3	3	3	3
7	15.9	7	7	7	7	7	7	7	6	6	5	5	4	4	3	3	3
8	25.6	8	8	8	8	8	8	7	7	6	6	5	5	4	4	3	3
9	37.2	9	9	9	9	9	9	8	8	8	6	6	5	5	4	3	3
10	49.7	10	10	10	10	10	9	9	8	8	7	6	6	5	4	4	3
11	62.2	11	11	11	11	11	10	10	9	8	8	7	6	5	4	4	3
12	73.8	12	12	12	12	11	10	10	9	8	8	7	6	5	4	4	3
13	83.5	13	12	12	12	11	10	10	9	8	8	7	6	5	4	4	4
14	90.4	14	13	13	13	12	11	10	9	8	8	7	6	5	4	4	4
15	95	15	14	14	14	12	11	10	9	8	8	7	6	5	4	4	4
16	97.7	16	15	15	14	12	11	10	9	8	8	8	6	5	4	4	4
17	99	17	16	15	14	12	11	11	10	9	9	8	6	5	4	4	4
18	99.4	18	16	15	15	12	12	11	10	9	9	8	6	5	4	4	4

Takeaways

To speed play the GM could ignore defenses/opposing skill if the modified success number is 5 or less. Assume that the chance of a Critical Failure by the Attacker covers both the chance of CF by the attacker and CS by the defender.

Against a defender with modified skill of 16+, the GM could rule that the the attacker's action fails automatically on anything but a CS.

For effective skill levels of 9-13, it might be possible to model the effects of successful counteraction by just subtracting -1 or -2 from the attacker's dice roll.