AnyDice / probabilities question -- overlapping odds

**Max_Killjoy** · 2017-07-19, 08:43 AM (ISO 8601)

In the AnyDice code, or via our friend mathematics, is there any way to set up the following:

Roll 3d6+X Determine the percentage chance of rolling at least Y, or doubles on any of the three dice.

That is, rolling at least Y, or rolling doubles, counts as a success, and I need to determine the chances of success for Y on 3d6+X.

The odds of rolling doubles on 3d6 are always the same, but the fact that some combinations of dice both total at least Y, and contain doubles, puts a twist in this, at least for me.

**Satinavian** · 2017-07-19, 09:33 AM (ISO 8601)

the obvious way to calculate this is by taking the probability of doubles and adding the probability for reaching Y-X with 3 dices which all show different numbers.

You only take the 6*5*4 combinations out of the total 6*6*6 without doubles and tripples and count, how many are over the total sum.

Another way would be to add the probabilityies for doubles and getting with 3D6 high enough and than substract the probalility for all cases with at least one double which are also high enough. Thaat are far less cases but it is a bit more complicated as you have to make sure to count the tripples the right way.

**malachi** · 2017-07-19, 12:34 PM (ISO 8601)

3d6+X >= Y is the same as saying 3d6 >= Y-X. I am going to say Z = Y-X to simplify typing some.
(A) Find the probability that 3d6 >= Z
(B) Then find all of the instances where 3d6 < Z where you have a double.
(C) Add the values you got in (A) and (B)

I'm going to look at the example where Z = 9
(A) = 74.07%
For (B), we need to add up the following rolls:
3 3 [1-2] :: This could be 33X, 3X3, or X33, and each of the three permutations can have 2 values for X - so we have 6 / 216 rolls here.
2 2 [1-4] :: This could be 222, 22X, 2X2, X22, where X can be 1, 3, or 4. Total of 10 possibilities, for 10 / 216 for a double on 2's.
1 1 [1-6] :: Similar to above: 111, 11X, 1X1, X11, where X can be 2-6. Total of 16 possibilities, for 16/216 for a double on 1's.

Add that all together, and you get 6/216 + 10/216 + 16/216 = 32/216 = 14.814814...%

For (C) We get 74.07% + 14.81% = 88.88%

**Slipperychicken** · 2017-07-19, 01:05 PM (ISO 8601)

The method I learned in school is this: Take the individual probabilities, add them together, and subtract the chance of both happening at the same time. That gives you the "A or B" chance.

So you can use variables. Set the two probabilities to variables A and B, and their intersection to C.The output line will look like A+B-C.

**Max_Killjoy** · 2017-07-19, 01:26 PM (ISO 8601)

Originally Posted by Slipperychicken

The method I learned in school is this: Take the individual probabilities, add them together, and subtract the chance of both happening at the same time. That gives you the "A or B" chance.

So you can use variables. Set the two probabilities to variables A and B, and their intersection to C.The output line will look like A+B-C.

The trick, for me at least, is knowing where they intersect.

**jayem** · 2017-07-19, 02:44 PM (ISO 8601)

Originally Posted by Max_Killjoy

In the AnyDice code, or via our friend mathematics, is there any way to set up the following:

Roll 3d6+X Determine the percentage chance of rolling at least Y, or doubles on any of the three dice.

That is, rolling at least Y, or rolling doubles, counts as a success, and I need to determine the chances of success for Y on 3d6+X.

The odds of rolling doubles on 3d6 are always the same, but the fact that some combinations of dice both total at least Y, and contain doubles, puts a twist in this, at least for me.

I don't think they'll be an easy mathsy way in general.
But there are only 36 non-degenerative cases

Spoiler: working

Show

Die combo	Degeneracy	Total
1,1,1	1	3
1,1,2	3	4
1,1,3	3	5
1,1,4	3	6
1,1,5	3	7
1,1,6	3	8
2,2,1	3	5
2,2,2	1	6
2,2,3	3	7
2,2,4	3	8
2,2,5	3	9
2,2,6	3	10
3,3,1	3	7
3,3,2	3	8
3,3,3	3	9
3,3,4	3	10
3,3,5	3	11
3,3,6	3	12
4,4,1	3	9
4,4,2

At which point you could count the cases of doubles that come to less that Y-X as a total (and you can get that built up into a table once).
Add that to the number of cases (in general) that come to more than Y-X (which is harder but still only 18 rows when built up, and can do by hand)

Add them together, and divide by 6*6*6

Corollary: The total number of doubles rolls in total for 3d6 are 16*6=96 or around 44%

Spoiler

Show

Table for getting less than Y, with D6

Y	1D throws<Y	2D throws<Y	3D throws<Y
1	1	0	0	0
2	2	1	0	0
3	3	3	1	0
4	4	6	4	1
5	5	10	10	5
6	6	15	20	15
7	6	21	35	35
8	6	26	56	70
9	6	30	81	126
10	6	33	108	206
11	6	35	135	310
12	6	36	160	435
13	6	36	181	575
14	6	36	196	721
15	6	36	206	861
16	6	36	212	986
17	6	36	215	1090
18	6	36	216	1170
19	6	36	216	1226
20	6	36	216	1261
21	6	36	216	1281
22	6	36	216	1291
23	6	36	216	1295
24	6	36	216	1296
Infinity	6	36	216	1296

Table for getting less than Y, with D6 that feature a double

Y	1D throws<Y	2D throws<Y	3D throws<Y
1	0	0	0
2	0	1	0
3	0	1	1
4	0	2	4
5	0	2	10
6	0	3	14
7	0	3	23
8	0	4	32
9	0	4	39
10	0	5	48
11	0	5	57
12	0	6	64
13	0	6	73
14	0	6	82
15	0	6	86
16	0	6	92
17	0	6	95
18	0	6	96

Table for getting MORE than Y OR with D6 that feature a double

Y	1D	2D	3D
1	5	36	216
2	4	36	216
3	3	34	216
4	2	32	216
5	1	28	216
6	0	24	210
7	0	18	204
8	0	14	192
9	0	10	174
10	0	8	156
11	0	6	138
12	0	6	120
13	0	6	108
14	0	6	102
15	0	6	96
16	0	6	96
17	0	6	96
18	0	6	96

**Slipperychicken** · 2017-07-19, 03:45 PM (ISO 8601)

Originally Posted by Max_Killjoy

The trick, for me at least, is knowing where they intersect.

I'm AFK right now, but Anydice should have syntax for an "and" statement. You might have something like ((DieRoll>Condition1) & (DieRoll<Condition2)).

EDIT: I just reviewed the syntax. The "|" symbol is for "or" statements. Try something like
output: (DieRoll>Cond1) | (DieRoll<Cond2)

**Tanarii** · 2017-07-19, 04:04 PM (ISO 8601)

Originally Posted by Slipperychicken

I'm AFK right now, but Anydice should have syntax for an "and" statement. You might have something like ((DieRoll>Condition1) & (DieRoll<Condition2)).

EDIT: I just reviewed the syntax. The "|" symbol is for "or" statements. Try something like
output: (DieRoll>Cond1) | (DieRoll<Cond2)

It's not that simple. Mainly, Anydice isn't really written to handle "save DieRoll as variable X then do operations or comparisons on it". If you try to write the statement you're suggesting, you actually get DieRoll 1 % chance of being TRUE under Cond1, and DieRoll 2 % chance of being TRUE under Cond2, and the intersection of those as an OR. Not the intersection of a single value generated for DieRoll, then compared to see if it's TRUE for either condition.

**Nifft** · 2017-07-19, 05:41 PM (ISO 8601)

Not sure about AnyDice, but it's pretty easy in a scripting language.

Here's some Python:

Code:

def f(x):
   L = [(a,b,c) for a in range(1,7) for b in range(1,7) for c in range(1,7)]
   return len([True for (a,b,c) in L if (a==b or b==c or a==c) or (a+b+c > x)]) / len(L)

for i in range(1,21):
   print( i, '=>', 100 * f(i) )

Here's the output:

Code:

1 => 100.0
2 => 100.0
3 => 100.0
4 => 100.0
5 => 100.0
6 => 97.22222222222221
7 => 94.44444444444444
8 => 88.88888888888889
9 => 80.55555555555556
10 => 72.22222222222221
11 => 63.888888888888886
12 => 55.55555555555556
13 => 50.0
14 => 47.22222222222222
15 => 44.44444444444444
16 => 44.44444444444444
17 => 44.44444444444444
18 => 44.44444444444444
19 => 44.44444444444444
20 => 44.44444444444444

The unintuitive results are:

- You can ignore high & low target numbers, since those ranges are covered by rolls which MUST include doubles.
TN3 => 1,1,1
TN4 => 1,1,2 - 1,2,1 - 2,1,1
TN 5 => 1,2,2 - 2,1,2 - 2,2,1

It's not until TN6 (1,2,3) that you get a combo which does not include doubles.

The same is true at the high end. There's no difference between needing raw 17 vs. raw 18, since rolling 17 always requires doubles and is therefore always a success anyway. Same for raw 16.

**Max_Killjoy** · 2017-07-19, 05:49 PM (ISO 8601)

Thank you for those who've offered help on this.

I'm going to see if I can plug all this into table and compare to just 3d6+X, >= Y.

**Tanarii** · 2017-07-19, 09:59 PM (ISO 8601)

Nifft, is that the percentage chance including the 3d6 => X, OR doubles? Because if so, that chart is the answer if you truncate it at 3 to 18. (And it sure doesn't look like its doubles only to me.)

**Max_Killjoy** · 2017-07-19, 10:27 PM (ISO 8601)

Originally Posted by Tanarii

Nifft, is that the percentage chance including the 3d6 => X, OR doubles? Because if so, that chart is the answer if you truncate it at 3 to 18. (And it sure doesn't look like its doubles only to me.)

I think that every +1 to the Target Number is going to bump the percentages down "one spot", and every +1 to the roll is going to bump the percentages up "one spot"...

**Tanarii** · 2017-07-19, 10:30 PM (ISO 8601)

Originally Posted by Max_Killjoy

I think that every +1 to the Target Number is going to bump the percentages down "one spot", and every +1 to the roll is going to bump the percentages up "one spot"...

Of for sure. But it means you've got your numbers. % chance of 3d6 => N, is the same as % chance of 3d6 + X => N + X

**Max_Killjoy** · 2017-07-19, 10:42 PM (ISO 8601)

I think this is how it works out. Top table is with the "doubles count as success". Bottom table is normal.

Horizontal axis across the top is Target Number, vertical axis across the left hand is the "skill rank" added onto the base 3d6. "50/50" is the TN against which the roll has a 50% chance of success.

3d6+	Avg	50/50	5+	6+	7+	8+	9+	10+	11+	12+	13+	14+	15+	16+	17+	18+	19+	20+	21+	22+	23+	24+	25+	26+	27+	28+	29+	30+	31+	32+	33+	34+
0	10.5	13	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
1	11.5	14	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
2	12.5	15	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
3	13.5	16	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
4	14.5	17	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
5	15.5	18	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
6	16.5	19	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
7	17.5	20	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
8	18.5	21	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
9	19.5	22	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
10	20.5	23	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
11	21.5	24	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
12	22.5	25	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
13	23.5	26	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
14	24.5	27	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%	44.44%
15	25.5	28	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	97.22%	94.44%	88.89%	80.56%	72.22%	63.89%	55.56%	50.00%	47.22%	44.44%	44.44%	44.44%	44.44%	44.44%

3d6+	Avg	50/50	5+	6+	7+	8+	9+	10+	11+	12+	13+	14+	15+	16+	17+	18+	19+	20+	21+	22+	23+	24+	25+	26+	27+	28+	29+	30+	31+	32+	33+	34+
0	10.5	11	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
1	11.5	12	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
2	12.5	13	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
3	13.5	14	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
4	14.5	15	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
5	15.5	16	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
6	16.5	17	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
7	17.5	18	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
8	18.5	19	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
9	19.5	20	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
10	20.5	21	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%	0.00%
11	21.5	22	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%	0.00%
12	22.5	23	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%	0.00%
13	23.5	24	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%	0.00%
14	24.5	25	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%	0.00%
15	25.5	26	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	100.00%	99.54%	98.15%	95.37%	90.74%	83.80%	74.07%	62.50%	50.00%	37.50%	25.93%	16.20%	9.26%	4.63%	1.85%	0.46%	0.00%

(Since it's probably not commonly recognizable, I'm trying to analyze the effect of a particular Weapon Quality on the odds of hitting in the Planet Mercenary RPG.)

**Nifft** · 2017-07-19, 11:53 PM (ISO 8601)

Originally Posted by Tanarii

Nifft, is that the percentage chance including the 3d6 => X, OR doubles? Because if so, that chart is the answer if you truncate it at 3 to 18. (And it sure doesn't look like its doubles only to me.)

Doubles or greater than X. (Not ">=", just ">".) I went above and below the possible results so if you want >= instead, just scale by one.

Originally Posted by Max_Killjoy

I think this is how it works out. Top table is with the "doubles count as success". Bottom table is normal.

Horizontal axis across the top is Target Number, vertical axis across the left hand is the "skill rank" added onto the base 3d6. "50/50" is the TN against which the roll has a 50% chance of success.

[===8<-----]

(Since it's probably not commonly recognizable, I'm trying to analyze the effect of a particular Weapon Quality on the odds of hitting in the Planet Mercenary RPG.)

Wow that's a lot of cells.

You know you're just linearly translating the same SMALL curve up & down, right?

You can get all the same info by moving around the X & Y values, while keeping the probability distribution function constant, like so:

Code:

f(3d6) = {
    true if doubles or sum(3d6) > Y-X;
    else false
}

Then you get a target number TN = (Y - X), and you only need a chart with one set of numbers. :)

**jayem** · 2017-07-20, 02:16 AM (ISO 8601)

Originally Posted by Max_Killjoy

I think this is how it works out. Top table is with the "doubles count as success". Bottom table is normal.

Horizontal axis across the top is Target Number, vertical axis across the left hand is the "skill rank" added onto the base 3d6. "50/50" is the TN against which the roll has a 50% chance of success.

...

(Since it's probably not commonly recognizable, I'm trying to analyze the effect of a particular Weapon Quality on the odds of hitting in the Planet Mercenary RPG.)

Makes sense, you have the graph shifting left/right by 1 as you increase the offset (X). Limits at 3,15 seem to make sense.
Bottom graph looks vague symmetric.

How did you get the table so nice. I got bored typing with a much smaller table. I tried copy and paste, in the hope that the tabs would form bearable columns but the tabs disappeared after it left the page, and than realised could add a spreadsheet that added "[TD]" "/[TD]" to each cell, which worked ok, but feels a bit inelegant.

**Max_Killjoy** · 2017-07-20, 06:47 AM (ISO 8601)

Originally Posted by jayem

Makes sense, you have the graph shifting left/right by 1 as you increase the offset (X). Limits at 3,15 seem to make sense.
Bottom graph looks vague symmetric.

How did you get the table so nice. I got bored typing with a much smaller table. I tried copy and paste, in the hope that the tabs would form bearable columns but the tabs disappeared after it left the page, and than realised could add a spreadsheet that added "[TD]" "/[TD]" to each cell, which worked ok, but feels a bit inelegant.

Excel.

Copy-Paste into post writing window.

Originally Posted by Nifft

Doubles or greater than X. (Not ">=", just ">".) I went above and below the possible results so if you want >= instead, just scale by one.

Wow that's a lot of cells.

You know you're just linearly translating the same SMALL curve up & down, right?

You can get all the same info by moving around the X & Y values, while keeping the probability distribution function constant, like so:

Code:

f(3d6) = {
    true if doubles or sum(3d6) > Y-X;
    else false
}

Then you get a target number TN = (Y - X), and you only need a chart with one set of numbers. :)

I often need to lay things out like that table to really get my head around them.

It's a bit more elegant looking in Excel.

**Max_Killjoy** · 2017-07-20, 03:56 PM (ISO 8601)

BTW, again, thank you to those who offered help and pointers.

This has been bugging me for a while, and it's good to have it worked out.

Thread: AnyDice / probabilities question -- overlapping odds

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