# Skill vs. Skill matrix?

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Having skimmed through the 6th ed pdfs last night, I was appreciative of the 3d6 roll breakdowns in the back of volume 2. I was curious how a "skill vs. skill" resolution breaks down in terms of affecting the overall chance of success. With a calculator, pen and post-it note, I've worked out that a skill vs. skill contest involving an 11- roll vs. another 11- roll averages out to a 40% chance of success for the person attempting over the person resisting.

I think it'd be useful to do up a chart from, say a 3- to a 20- (since 3 is the minimum chance, and 20- is considered a legendary/superhuman level of skill) vs. a 3 to 20, so GMs and players have some concept of what the percentages are.

If it's at all useful, it looks like that 40% chance equates to a 9- chance of success. I suspect that a 12- vs. an 11- might bump you up to a 50% chance, but I haven't checked that yet.

Edit: yep. Works out to about 50.4% for a 12- vs. an 11-. Feel free to check and add some matchups.

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Re: Skill vs. Skill matrix?

So far:

11- vs. 11-: 40%

12- vs. 11-: 50.4%

13- vs. 11-: 60.8%

14- vs. 11-: 70.25%

4 down, 320 to go...

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Re: Skill vs. Skill matrix?

This link might be of help to you

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Re: Skill vs. Skill matrix?

Gotta love a quick little Java program for calculating something like this. Here it is in CSV format. The left column is the aggressor's skill roll. The top row is the defender's skill roll. The values are in terms of the probability from 0 to 1, not a percent.

```-,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
3,0.0046,0.0045,0.0044,0.0042,0.0039,0.0034,0.0029,0.0023,0.0017,0.0012,0.0008,0.0004,0.0002,8.6e-05,2.1e-05,0
4,0.0185,0.0182,0.0178,0.0170,0.0158,0.0142,0.0121,0.0098,0.0075,0.0053,0.0035,0.0020,0.0011,0.0005,0.0002,2.1e-05
5,0.0462,0.0457,0.0447,0.0430,0.0403,0.0364,0.0315,0.0260,0.0203,0.0147,0.0098,0.0060,0.0033,0.0016,0.0006,0.0002
6,0.0924,0.0916,0.0899,0.0867,0.0818,0.0746,0.0654,0.0547,0.0434,0.0323,0.0222,0.0141,0.0082,0.0042,0.0018,0.0006
7,0.1617,0.1605,0.1578,0.1529,0.1449,0.1332,0.1180,0.1001,0.0807,0.0614,0.0435,0.0287,0.0173,0.0095,0.0045,0.0018
8,0.2588,0.2571,0.2533,0.2461,0.2344,0.2169,0.1940,0.1666,0.1365,0.1059,0.0771,0.0525,0.0332,0.0191,0.0099,0.0045
9,0.3745,0.3724,0.3675,0.3583,0.3430,0.3201,0.2893,0.2519,0.2100,0.1665,0.1247,0.0878,0.0579,0.0353,0.0197,0.0099
10,0.4994,0.4971,0.4916,0.4809,0.4630,0.4356,0.3982,0.3518,0.2987,0.2424,0.1868,0.1363,0.0936,0.0602,0.0359,0.0197
11,0.6244,0.6221,0.6164,0.6050,0.5857,0.5556,0.5138,0.4607,0.3987,0.3311,0.2627,0.1984,0.1420,0.0959,0.0608,0.0359
12,0.7402,0.7380,0.7325,0.7214,0.7020,0.6714,0.6280,0.5716,0.5041,0.4287,0.3499,0.2734,0.2037,0.1442,0.0965,0.0608
13,0.8375,0.8356,0.8307,0.8207,0.8029,0.7740,0.7322,0.6766,0.6081,0.5293,0.4444,0.3589,0.2779,0.2055,0.1446,0.0965
14,0.9071,0.9057,0.9019,0.8938,0.8789,0.8543,0.8175,0.7669,0.7026,0.6261,0.5406,0.4509,0.3621,0.2792,0.2058,0.1446
15,0.9535,0.9525,0.9498,0.9439,0.9325,0.9132,0.8832,0.8406,0.7843,0.7146,0.6336,0.5449,0.4530,0.3630,0.2794,0.2058
16,0.9814,0.9808,0.9790,0.9750,0.9671,0.9531,0.9306,0.8971,0.8510,0.7915,0.7191,0.6362,0.5461,0.4535,0.3631,0.2794
17,0.9953,0.9950,0.9940,0.9916,0.9867,0.9774,0.9618,0.9375,0.9023,0.8546,0.7937,0.7204,0.6368,0.5464,0.4536,0.3631
18,1.0000,0.9998,0.9994,0.9982,0.9955,0.9901,0.9803,0.9641,0.9392,0.9035,0.8554,0.7942,0.7206,0.6369,0.5464,0.4536
```

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Re: Skill vs. Skill matrix?

Gotta love a quick little Java program for calculating something like this. Here it is in CSV format. The left column is the aggressor's skill roll. The top row is the defender's skill roll. The values are in terms of the probability from 0 to 1, not a percent.

```-,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18
3,0.0046,0.0045,0.0044,0.0042,0.0039,0.0034,0.0029,0.0023,0.0017,0.0012,0.0008,0.0004,0.0002,8.6e-05,2.1e-05,0
4,0.0185,0.0182,0.0178,0.0170,0.0158,0.0142,0.0121,0.0098,0.0075,0.0053,0.0035,0.0020,0.0011,0.0005,0.0002,2.1e-05
5,0.0462,0.0457,0.0447,0.0430,0.0403,0.0364,0.0315,0.0260,0.0203,0.0147,0.0098,0.0060,0.0033,0.0016,0.0006,0.0002
6,0.0924,0.0916,0.0899,0.0867,0.0818,0.0746,0.0654,0.0547,0.0434,0.0323,0.0222,0.0141,0.0082,0.0042,0.0018,0.0006
7,0.1617,0.1605,0.1578,0.1529,0.1449,0.1332,0.1180,0.1001,0.0807,0.0614,0.0435,0.0287,0.0173,0.0095,0.0045,0.0018
8,0.2588,0.2571,0.2533,0.2461,0.2344,0.2169,0.1940,0.1666,0.1365,0.1059,0.0771,0.0525,0.0332,0.0191,0.0099,0.0045
9,0.3745,0.3724,0.3675,0.3583,0.3430,0.3201,0.2893,0.2519,0.2100,0.1665,0.1247,0.0878,0.0579,0.0353,0.0197,0.0099
10,0.4994,0.4971,0.4916,0.4809,0.4630,0.4356,0.3982,0.3518,0.2987,0.2424,0.1868,0.1363,0.0936,0.0602,0.0359,0.0197
11,0.6244,0.6221,0.6164,0.6050,0.5857,0.5556,0.5138,0.4607,0.3987,0.3311,0.2627,0.1984,0.1420,0.0959,0.0608,0.0359
12,0.7402,0.7380,0.7325,0.7214,0.7020,0.6714,0.6280,0.5716,0.5041,0.4287,0.3499,0.2734,0.2037,0.1442,0.0965,0.0608
13,0.8375,0.8356,0.8307,0.8207,0.8029,0.7740,0.7322,0.6766,0.6081,0.5293,0.4444,0.3589,0.2779,0.2055,0.1446,0.0965
14,0.9071,0.9057,0.9019,0.8938,0.8789,0.8543,0.8175,0.7669,0.7026,0.6261,0.5406,0.4509,0.3621,0.2792,0.2058,0.1446
15,0.9535,0.9525,0.9498,0.9439,0.9325,0.9132,0.8832,0.8406,0.7843,0.7146,0.6336,0.5449,0.4530,0.3630,0.2794,0.2058
16,0.9814,0.9808,0.9790,0.9750,0.9671,0.9531,0.9306,0.8971,0.8510,0.7915,0.7191,0.6362,0.5461,0.4535,0.3631,0.2794
17,0.9953,0.9950,0.9940,0.9916,0.9867,0.9774,0.9618,0.9375,0.9023,0.8546,0.7937,0.7204,0.6368,0.5464,0.4536,0.3631
18,1.0000,0.9998,0.9994,0.9982,0.9955,0.9901,0.9803,0.9641,0.9392,0.9035,0.8554,0.7942,0.7206,0.6369,0.5464,0.4536
```

thanks a bunch--quick question, is the "-" used for a column for the "base" unopposed chance?

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Re: Skill vs. Skill matrix?

Just to double-check, does the algorithm you used reduce the defender's chance for every 1 that the aggressor makes their roll by? Because the column for defender skill of 18 probably should be less absolute, then.

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Re: Skill vs. Skill matrix?

The '-' is simply filler, for the column that has the aggressor's roll in it. The algorithm I used is this: the defender wins if either the aggressor fails the roll or the defender makes the roll by at least the same amount as the aggressor. The source code is below, if it helps.

The 18- vs. 3- is probably not an exact 1 but is so close that the rounding makes it look that way. The only way for the aggressor to lose is if he rolls an 18 and the defender rolls a 3. The only absolute I know of is the 3- vs. 18-, and you'll notice that one is listed without a decimal place. That's because the aggressor can ONLY make the roll exactly, and the defender ALWAYS makes the roll by at least zero.

I am the original author of the following source code, and hereby release the code to the public domain. You may copy, modify, and redistribute it in any fashion you desire, and need not include any information about the origin or authorship of the content unless you wish to do so. However, by using (or misusing) the content, you assume full responsibility for any damages or hurt feelings that such use may incur. --Prestidigitator

```import java.util.ArrayList;
import java.util.List;

public class ProbSkillVsSkill
{
public static void main(String[] args)
{
ProbSkillVsSkill app = new ProbSkillVsSkill();
app.mainf();
}

public void mainf()
{
java.util.Formatter formatter = new java.util.Formatter();

System.out.println("-,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18");

for (int oRoll = 3; oRoll <= 18; ++oRoll)
{
System.out.print(String.valueOf(oRoll));

for (int dRoll = 3; dRoll <= 18; ++dRoll)
{
double oWinProb = 0.0;

for (int roll = 3; roll <= oRoll; ++roll)
{
int margin = oRoll-roll;
if (margin > dRoll-3)
{
oWinProb += probForRolling(roll, 3);
} else
{
oWinProb += probForRolling(roll, 3)
*(1.0-probForRollingUnder(dRoll-margin, 3));
}
}

if (oWinProb == 0.0)
{
System.out.print(",0");
} else if (oWinProb < 0.0001)
{
System.out.format(",%1.1e", oWinProb);
} else
{
System.out.format(",%1.4f", oWinProb);
}
}

System.out.println();
}
}

private List countsNd6 = new ArrayList();
private List countsNd6Under = new ArrayList();

private void precalc(int n)
{
if (countsNd6.size() >= n)
{
return;
}

if (n == 1)
{
countsNd6.add(new int[] { 1, 1, 1, 1, 1, 1 });
countsNd6Under.add(new int[] { 1, 2, 3, 4, 5, 6 });
return;
}

if (countsNd6.size() < n-1)
{
precalc(n-1);
}

int[] countsNMinus1 = countsNd6.get(n-2);

int maxRoll = 5*n;
int maxRollNMinus1 = maxRoll-5;
int[] counts = new int[maxRoll+1];
int[] countsUnder = new int[maxRoll+1];

int count = 0;
int countUnder = 0;
for (int i = 0; i <= maxRoll; ++i)
{
if (i <= maxRollNMinus1)
{
count += countsNMinus1[i];
}
if (i > 5)
{
count -= countsNMinus1[i-6];
}

counts[i] = count;

countUnder += count;
countsUnder[i] = countUnder;
}

}

private int countForRolling(int value, int nDice)
{
if (nDice < 1 || value < nDice || value > 6*nDice)
{
return 0;
}

if (countsNd6.size() < nDice)
{
precalc(nDice);
}

int[] counts = countsNd6.get(nDice-1);

return counts[value-nDice];
}

private double probForRolling(int value, int nDice)
{
return ((double)countForRolling(value, nDice))/Math.pow(6, nDice);
}

// "Under" actually means less than or equal to here
private int countForRollingUnder(int value, int nDice)
{
if (nDice < 1 || value < nDice)
{
return 0;
}
if (value > 6*nDice)
{
value = 6*nDice;
}

if (countsNd6Under.size() < nDice)
{
precalc(nDice);
}

int[] countsUnder = countsNd6Under.get(nDice-1);

return countsUnder[value-nDice];
}

// "Under" actually means less than or equal to here
private double probForRollingUnder(int value, int nDice)
{
return ((double)countForRollingUnder(value, nDice))/Math.pow(6, nDice);
}
}
```

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Re: Skill vs. Skill matrix?

The '-' is simply filler, for the column that has the aggressor's roll in it. The algorithm I used is this: the defender wins if either the aggressor fails the roll or the defender makes the roll by at least the same amount as the aggressor. The source code is below, if it helps.

The 18- vs. 3- is probably not an exact 1 but is so close that the rounding makes it look that way. The only way for the aggressor to lose is if he rolls an 18 and the defender rolls a 3. The only absolute I know of is the 3- vs. 18-, and you'll notice that one is listed without a decimal place. That's because the aggressor can ONLY make the roll exactly, and the defender ALWAYS makes the roll by at least zero.

I am the original author of the following source code, and hereby release the code to the public domain. You may copy, modify, and redistribute it in any fashion you desire, and need not include any information about the origin or authorship of the content unless you wish to do so. However, by using (or misusing) the content, you assume full responsibility for any damages or hurt feelings that such use may incur. --Prestidigitator

The only problem is, in hero, a roll of 18 always fails, so in the 3 vs. 18 scenario, there is still a tiny chance the aggressor wins. Otherwise this is an excellent program. The one thing I notice is that even "legendary" skill levels (14+) still face a significant chance of failure, even against a basic 11- defender roll.

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Re: Skill vs. Skill matrix?

The only problem is' date=' in hero, a roll of 18 always fails, so in the 3 vs. 18 scenario, there is still a tiny chance the aggressor wins. Otherwise this is an excellent program. The one thing I notice is that even "legendary" skill levels (14+) still face a significant chance of failure, even against a basic 11- defender roll.[/quote']

True. Of course, it's also possible to have a Skill of 37- or (modified) -7-, and that would certainly affect the probabilities. I can chance the auto-success/failure if you want, and see how that changes things.

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Re: Skill vs. Skill matrix?

True. Of course' date=' it's also possible to have a Skill of 37- or (modified) -7-, and that would certainly affect the probabilities. I can chance the auto-success/failure if you want, and see how that changes things.[/quote']

I think any number over 17- just reduces the defender's starting roll (e.g., a 20- effectively means that aggressor makes his roll by 3 on a roll of 17, meaning the defender starts out having to make their roll by 3, rather than starting out at just making their roll). A 3 is also always the minimum roll for success, but I think a chart from 3 to 37(aggressor) vs. 3 to 24-(defender) might be somewhat useful (a 37- should be pretty close to auto-success vs. everything except the 24-). Generally, I think in the rare instance someone has a near-godlike roll, the opposing party's probably not going to be operating in the same ballpark.

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Re: Skill vs. Skill matrix?

Hmm. Okay. I'll do that. But here's a question for you. While a roll of 3 always succeeds on a skill roll, are we going to consider it such a great success that it always wins a skill vs. skill contest, no matter what margin of success it actually gives? What if both offender and defender roll 3s?

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Re: Skill vs. Skill matrix?

Hmm. Okay. I'll do that. But here's a question for you. While a roll of 3 always succeeds on a skill roll' date=' are we going to consider it such a great success that it always wins a skill vs. skill contest, no matter what margin of success it actually gives? What if both offender and defender roll 3s?[/quote']

If that ever happend in a game, I'd rule in favor of whoever had the higher Skill. If that's still a tie, then they'd re-roll it.

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Re: Skill vs. Skill matrix?

Okay. So if the aggressor has an 17- roll and rolls a 5, and the defender has a 6- roll and rolls a 3, who wins?

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Re: Skill vs. Skill matrix?

Okay, after a re-read of the skill-vs-skill section (6e1 pg57) I'd say the defender wins. I'd also have to revise my previous answer to the same. The reason is the order of steps taken in a SvS contest:

1. The actor rolls and determine the amount of his success.
2. The reactor rolls, using the attackers AoS as a negative modifier.
3. A roll of 3 always succeeds regardless of modifiers.

So, any time the reactor rolls a 3, the reactor will win regardless of what the actor rolled.

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Re: Skill vs. Skill matrix?

Perhaps. Except that the next sentence also says:

In other words' date=' the second character must succeed by the same or a greater margin as the first.[/quote']

Hmm. Maybe I'll ask Steve what his take on it is.

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Re: Skill vs. Skill matrix?

Perhaps. Except that the next sentence also says:

Hmm. Maybe I'll ask Steve what his take on it is.

Eh, to my mind there is no margin of success greater than rolling a natural 3, regardless of what the relative skills of the people involved are. So if the second person rolls a natural 3 they have automatically succeeded by a margin greater or equal to the success of the first person. Obviously YMMV.

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Re: Skill vs. Skill matrix?

Fortunately, that situation only occurs once every 46,656 rolls, or about once per lifetime of RP. I'd rule that it depends on whether a "3" was the only number a defender could roll to succeed and whether the aggressor's "3" was a natural critical (i.e., their base chance was 7- or better, so a 3 would be a natural critical success using that optional rule). If the defender's chance is 5- and they roll a 3, it's not a natural crit, so if the aggressor's chance is 7- and they roll a 3, the aggressor should prevail, imo.

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Re: Skill vs. Skill matrix?

Steve's happy to leave it up to the GM: http://www.herogames.com/forums/showthread.php?t=74897

I can live with that.

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Re: Skill vs. Skill matrix?

Prestidigitator,

Does the CSV you put together consider auto failure and auto success or is ti based exclusively on margin of success?

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Re: Skill vs. Skill matrix?

Prestidigitator,

Does the CSV you put together consider auto failure and auto success or is ti based exclusively on margin of success?

So far, margin of success only.

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