d10 Probability

The distribution of World of Darkness dice rolls Ralf H¨ uls uls ([email protected])

August 21, 1996 CAVEAT KITHAIN: Here there be banality!!! Abstract

What follows is a description of the probabilities of dice rolls in the “World of Darkness” line of role playing games by White Wolf Game Studio. This paper is aimed at storytellers who might want this information to review their difficulty rulings as well as players players who might want want to estimate estimate their chances chances of success for a given given difficulty. difficulty. The probability function for the number of successes for given dice pool size and difficulty is given and explained (math alert). A procedure in C code to calculate probabilities for given given combinations combinations of difficulty/dice difficulty/dice pool/number pool/number of successes is presented. presented. Finally extensive tables of relevant values are shown.

1

Intr Introdu oduct ctio ion n

In the World of Darkness line of role playing games by White Wolf Game Studio (Vampire: The Masquerade, Werewolf: The Apocalypse, Mage: The Ascension, Wraith: The Oblivion and Changeling: The Dreaming) conflict is resolved by use of a varying number of ten-sided dice. This number number is called called a characte character’s r’s dice po ol, and is determined determined by the character’s character’s traits. traits. To resolve a critical situation, situation, the player player rolls a number number of dice according according to his dice pool for the problem problem at hand. Prior to the roll the game master (or storyteller) storyteller) sets a difficulty difficulty for the task, which is a number number between between 2 and 10 (usually 6). The number number of dice equal to or higher higher than the selected selected difficulty is counted as successes. successes. The number of ones rolled rolled is subtracted subtracted from this number. number. The final number of successes successes is the result of this subtraction. If the number of ones is greater than the number of successes, the result is called a “botch” and the action has a catastrophic result. This paper examines the probabilities for different numbers of successes under different conditions. Use of terms terms and gam gamee mechan mechanics ics possibly possibly copyri copyrigh ghted ted to White White Wolf Inc. is not intended as a challenge to these copyrights. This document may be freely distributed provided that no charge is made for the distribution. I’m currently working on my thesis for a degree in statistics at Dortmund University, Germany Germany.. My role playing character characterss include include a Malkavi Malkavian, an, a Pooka Pooka and a Sluagh Sluagh (my favorite). 1

2

The The prob probab abil ilit ity y funct functio ion n [. . . ] a man who confine confiness knowled knowledge ge to formu formulae lae necess necessary ary for the solution solution of an algebraic or other perplexity, the same deserves to be shot with a Fusil or old-fashioned light musket. Flann O’Brien — At Swim-Two-Birds

(Math alert: alert: I’ll try to keep keep it simple, simple, but if you’re not interested interested in the theory, theory, skip this chapter!) To score exactly a certain number, say s of successes, you have to roll s dice higher than the difficulty (say d). The remaini remaining ng dice may all be lowe lowerr than than d and higher than 1, or come in pairs of one die that is higher than d and one die that is 1. For example: to roll 5 successes with a dice pool of 10 we may roll any of the following combinations: •

5 successes, no 1

•

6 successes, one 1

•

7 successes, two ones

The maximum number of pairs is the largest whole number smaller than or equal to s (where p is the dice pool). Let that number be denoted by p− 2 2 Thus, in order to calculate the probability of s successes, we have to add up the probabilities of the possible combinations of successes, fails and ones:

p−s

 

[

]  )= (Prob. of rolling p−s

2

P (S = s

otherrs) s + i successes, i ones and p − s − 2 ∗ i othe

(1) (1)

i=0

In the example this is: [

P (S = 5)

=

 ](Prob. of rolling 5 + successes, ones and 10 5 2 others) (Prob. of rolling 5 + successes, ones and 10 5 2 others) 10−5 2

i

i

−

−

∗i

i=0

2

=

i

i

−

−

∗i

i=0

= (Prob. (Prob. of rollin rolling g 5 success successes, es, 0 ones ones and 5 others) others) + (Prob. of rolling 6 successes, 1 one and 3 others) + (Prob. of rolling 7 successes, 2 ones and 1 other)

Now, what we still need to find is the probability for a specific combination of successes, ones, and others. 2

1 The probability of rolling a 1 on a ten-sided die is of course 10 . The probability of 10−d+1 rolling a success is . Finally, the probability of rolling a number that is neither a 1 10 d−2 nor a success is 10 . For example on a difficulty of 6 you may roll 6, 7, 8, 9 or 10 to score a success, which is 10 − 6 + 1 = 5 out of 10. To fail you roll 2, 3, 4 or five, which is d − 2 = 4 out of 10. And you botch on a 1, which is one out of 10. If you roll more than one die and want the probability to roll a success, failure or 1 in a specific sequence, all you have to do is multiply the probabilities for the single roll. Thus, the probability to roll, say, a successes, b failures and c ones in a given sequence would be:

 10

−d+1

10

a



d−2

10

b

c

 1 10

.

This, however, doesn’t take permutations into account. The storyteller doesn’t care in what sequence you roll successes and ones. There are ( a + b + c)! permutations. (n! = 1 · 2 · . . . · n − 1 · n;0! := 1). a! of these are the same, because all you do is shuffle around the successes. b! are the same, because all you do is shuffle the failures. And—you guessed it—c! of the permutations are the same. So the actual number of distinct permutations is: (a + b + c)! . a!b!c! So, we have the probability for a given sequence, and every one of the permutations given above is one such sequence. Thus we have to multiply the probability with the number of permutations to find the probability for the case where sequence is irrelevant: (a + b + c)! P (a,b,c) = a!b!c!

 10

−d+1

10

a



d−2

10

b

c

 1

.

10

A random experiment that follows the above law of probability, by the way, is said to have a Multinomial Distribution. Now all we have to do is remember equation (1) and substitute (s + i) for a, i for c and ( p − s − 2i) for b. We also find that a + b + c = (s + i) + i + ( p − s − 2i) = p which is hardly surprising, as the total number of dice rolled is the dice pool. So finally we’ve reached the conclusion that the probability to score s successes against a difficulty of d with a dice pool of p is: [

P (S = s

]  )= p−s

2

i=0

p! (s + i)! i! ( p − s − 2i)!

s+i

i

 11   1   −d

10

10

d−2

10

p−s−2i



(2)

To continue our example to the bitter end, the probability to score exactly 5 successes against a difficulty of 6 with a dice pool of 10 dice is (hold your hat :-) : [ P (S = 5)

=

]

10−5 2

i=0

10! (5 + i)! i!(10 − 5 − 2i)!

3

5+i

i

 11 6   1   6 2  −

10

10

−

10

10−5−2i

[ ] 5 1 4  10! (5 + )! ! (5 2 )! 10 10 10  3628800  5   1   4  (5 + )! ! (5 2 )! 10 10 10   1 4 3628800 5 + 5!0!5! 10 10 10   1 4 3628800 5 + 6!1!3! 10 10 10   1 4 3628800 5 5 2

=

i=0

i i

i=0

=

7!2!1!

=

i

5−2i

5+i

i

5−2i

− i

2

=

5+i

i i

− i

10

5

0

5

6

1

3

7

2

1

10

10

3628800 · 0.03125 · 1 · 0.01024 + 120 · 1 · 120 3628800 · 0.015625 · 0.1 · 0.064 + 720 · 1 · 6 3628800 · 0.0078125 · 0.01 · 0.4 5040 · 2 · 1

3628800 3628800 3628800 · 0.00032 + · 0.0001 + · 0.00003125 14400 4320 10080 = 252 · 0.00032 + 840 · 0.0001 + 360 · 0.00003125 = 0.08064 + 0.084 + 0.01125 = 0.17589 =

Obviously this is a task for a computer (or a Boggan :-). Now, usually in the game you don’t need to score an exact number of successes, but you’re interested in the probability to score at least s successes. That number is easily calculated as: 10

 )=

P (S ≥ s

P (S = j )

j =s

with P (S = j ) calculated according to equation (2) The formula in equation (2) only works for a non-negative number of successes. If you want to calculate the probability of a botch use the following formula: 10

P (S < 0) = 1 − P (S ≥ 0) = 1 −

 j =0

with P (S = j ) calculated according to equation (2)

4

P (S = j )

3

C code for the calculation of probabilities

I’m not much of a C programmer and this is just a quick and dirty hack. The program should get the idea across though. The program calculates a table of probabilities by successes and size of dice pool for each difficulty from 2 to 10. Its core is the function “double probability(pool,success,difficulty) ” which returns the probability to score exactly “ success” successes against a difficulty of “ difficulty” with a dice pool of “pool”. #include double factorial(n) int n; { int f; if (n<0) { printf("Negative argument in function factorial\n"); }; if (n==0) f=1; else f=n*factorial(n-1); return((double)f); }

double probability(pool,success,difficulty) int pool,success,difficulty; { int i, max; double p,p1,p2,p3,fac,prob,botch; p1=(11.0-difficulty)/10.0; p2=0.1; p3=(difficulty-2.0)/10.0; max=(int)floor(((float)pool-(float)success)/2.0); p=0.0; for (i=0;i<=max;i++) { fac=( factorial(pool)/ (factorial(success+i) * factorial(i) * factorial(pool-success-2*i))); prob=pow(p1,(success+i))* pow(p2,i)* pow(p3,(pool-success-2*i));

5

p+=fac*prob; } return(p); }

main() { int pool, difficulty, success; double p,botch; for (difficulty=2; difficulty<=10;difficulty++) { printf("\n\n Difficulty %d\n Dice Pool",difficulty); for (success=10; success>=0;success--) printf("%11d ",success); printf(" botch\n"); for (pool=1; pool<=10;pool++) { botch=1.0; printf("%2d Dice ",pool); for (success=10; success>=0;success--) { if (success>pool) p=0; else p=probability(pool,success,difficulty); printf("%11.8f ",p*100); botch-=p; } printf("%11.8f\n",botch*100); } } }

6

4

Probability tables

The following tables show probabilities of certain numbers of successes under different conditions. All probabilities are given as percentages. If you want “real” probabilities, divide by 100. The tables in sections 4.1 and 4.2 show the probability of rolling a phenomenal success (five or more successes), a complete success (three or more successes) , any success at all and the probabilities for failure and botch. The tables in sections 4.3 and 4.4 show the probability of rolling exactly a certain number of successes. In section 4.2 and 4.4 there is a table for every difficulty and the rows represent different dice pool sizes. In section 4.1 and 4.3 there is a table for every dice pool size and the rows represent different difficulties. To make the tables in sections 4.3 and 4.4 more compact there are two rows for every dice pool size or difficulty. The first row shows probabilities for 10-5 successes, the second row shows probabilities for 4-0 sucesses and b otch. Thus the probabilities of rolling 10 and 4 successes are in the same field of the table. For example, the probability of rolling at least five successes against a Difficulty of 6 with seven dice is found in table 4.1.7 in the “Phenomenal” column and the row for Dice Pool 7. The same number (16.75%) can be found in table 4.2.5 in the “Phenomenal” column and the row for Difficulty 6. The probability of rolling exactly five successes against a Difficulty of 6 with seven dice is found in table 4.3.7 as the upper number in the column for “5/Botch” and the row for Dice Pool 7. The same number (4.375%) can be found in table 4.4.5 as the upper number in the column for “5/Botch” and the row for Difficulty 6.

4.1

Success classes by Difficulty by Dice Pool

4.1.1 Diff Diff Diff Diff Diff Diff Diff Diff Diff

Dice Pool • 2 3 4 5 6 7 8 9 10

Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

Complete 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

Success 90.00000000 80.00000000 70.00000000 60.00000000 50.00000000 40.00000000 30.00000000 20.00000000 10.00000000

7

Fail 0.00000000 10.00000000 20.00000000 30.00000000 40.00000000 50.00000000 60.00000000 70.00000000 80.00000000

Botch 10.00000000 10.00000000 10.00000000 10.00000000 10.00000000 10.00000000 10.00000000 10.00000000 10.00000000

4.1.2

Dice Pool • •

Diff Diff Diff Diff Diff Diff Diff Diff Diff

Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

2 3 4 5 6 7 8 9 10


2 3 4 5 6 7 8 9 10

Fail 18.00000000 17.00000000 18.00000000 21.00000000 26.00000000 33.00000000 42.00000000 53.00000000 66.00000000

Botch 1.00000000 3.00000000 5.00000000 7.00000000 9.00000000 11.00000000 13.00000000 15.00000000 17.00000000

Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

Complete 72.90000000 51.20000000 34.30000000 21.60000000 12.50000000 6.40000000 2.70000000 0.80000000 0.10000000

Success 97.20000000 92.00000000 86.80000000 81.00000000 74.00000000 65.20000000 54.00000000 39.80000000 22.00000000

Fail 0.00000000 4.90000000 9.20000000 13.50000000 18.40000000 24.50000000 32.40000000 42.70000000 56.00000000

Botch 2.80000000 3.10000000 4.00000000 5.50000000 7.60000000 10.30000000 13.60000000 17.50000000 22.00000000

Success 94.77000000 93.76000000 90.93000000 86.40000000 80.05000000 71.52000000 60.21000000 45.28000000 25.65000000

Fail 4.86000000 4.81000000 6.46000000 9.45000000 13.66000000 19.21000000 26.46000000 36.01000000 48.70000000

Botch 0.37000000 1.43000000 2.61000000 4.15000000 6.29000000 9.27000000 13.33000000 18.71000000 25.65000000

Success 99.14400000 96.80800000 94.05200000 90.12600000 84.40000000 76.24400000 64.90800000 49.40200000 28.37600000

Fail 0.00000000 2.08100000 4.09200000 6.72300000 10.42400000 15.52500000 22.35600000 31.36700000 43.24800000

Botch 0.85600000 1.11100000 1.85600000 3.15100000 5.17600000 8.23100000 12.73600000 19.23100000 28.37600000

Dice Pool • • • • 2 3 4 5 6 7 8 9 10


Success 81.00000000 80.00000000 77.00000000 72.00000000 65.00000000 56.00000000 45.00000000 32.00000000 17.00000000

Dice Pool • • •


Complete 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

Complete 65.61000000 61.44000000 51.45000000 38.88000000 26.25000000 15.36000000 7.29000000 2.40000000 0.33000000

Dice Pool • • • • • 2 3 4 5 6 7 8 9 10

Phenomenal 59.04900000 32.76800000 16.80700000 7.77600000 3.12500000 1.02400000 0.24300000 0.03200000 0.00100000

Complete 91.85400000 78.84800000 66.54200000 53.13600000 38.75000000 24.70400000 12.79800000 4.59200000 0.68600000

8


Dice Pool • • • • • 2 3 4 5 6 7 8 9 10


2 3 4 5 6 7 8 9 10

Phenomenal 85.03056000 64.55296000 47.05960000 30.55968000 16.75000000 7.26016000 2.21616000 0.36640000 0.01408000

2 3 4 5 6 7 8 9 10

Phenomenal 81.31047300 74.18675200 59.41274500 41.99040000 25.21562500 12.03404800 4.04813700 0.73600000 0.03098500

2 3 4 5 6 7 8 9 10

Phenomenal 94.70278620 83.04066560 69.43643980 52.27804800 33.76437500 17.44875520 6.38122860 1.26289280 0.05782300

Fail 1.45800000 1.62410000 2.79240000 4.87890000 8.09960000 12.79050000 19.29960000 27.95090000 39.08040000

Botch 0.12700000 0.61110000 1.27820000 2.39230000 4.25340000 7.26950000 12.02860000 19.37070000 30.45980000

Success 99.72720000 98.71800000 97.22384000 94.59666000 90.12960000 82.91420000 71.79840000 55.39494000 32.08976000

Fail 0.00000000 0.85457000 1.87896000 3.58263000 6.37424000 10.67925000 16.90632000 25.31291000 35.82048000

Botch 0.27280000 0.42743000 0.89720000 1.82071000 3.49616000 6.40655000 11.29528000 19.29215000 32.08976000

Success 99.49756500 99.14400000 98.08150100 95.95584000 92.05948500 85.35344000 74.45884500 57.71913600 33.39324500

Fail 0.45927000 0.60076900 1.29101400 2.65558500 5.06416600 9.00454500 14.96669400 23.19580900 33.21351000

Botch 0.04316500 0.25523100 0.62748500 1.38857500 2.87634900 5.64201500 10.57446100 19.08505500 33.39324500

Fail 0.00000000 0.34896010 0.88856120 1.98251550 4.05289840 7.64995250 13.35557160 21.44486470 31.08504800

Botch 0.08909200 0.17086630 0.44140720 1.06121350 2.36914960 4.96862950 9.88335280 18.80073670 34.45747600

• • •

Complete 96.19082100 93.99910400 88.33038900 79.05859200 65.72112500 48.66969600 29.78766900 12.79414400 2.30819700

Dice Pool • • • • •

Success 98.41500000 97.76480000 95.92940000 92.72880000 87.64700000 79.94000000 68.67180000 52.67840000 30.45980000

• •

Complete 97.43085000 91.11040000 83.43475000 72.60840000 58.35625000 41.54560000 24.31215000 9.93400000 1.69765000



Complete 88.57350000 84.99200000 76.31750000 64.15200000 49.43750000 33.53600000 18.58950000 7.16000000 1.14950000



Phenomenal 53.14410000 45.87520000 31.93330000 18.66240000 9.06250000 3.48160000 0.94770000 0.14080000 0.00490000

•

• • • •

Complete 99.16689060 96.29143040 91.78590820 83.97380160 71.77542500 54.94581760 34.93557540 15.66096320 2.96161060

Success 99.91090800 99.48017360 98.67003160 96.95627100 93.57795200 87.38141800 76.76107560 59.75439860 34.45747600

9


2 3 4 5 6 7 8 9 10

4.2 4.2.1 Pool 1 2 3 4 5 6 7 8 9 10 4.2.2 Pool 1 2 3 4 5 6 7 8 9 10

Dice Pool • • • • • Phenomenal 92.98091736 88.23111680 77.18715592 61.17161472 41.95775000 23.19732736 9.12503880 1.94868992 0.09638872

• • • • •

Complete 98.72048016 97.55217920 94.20146512 87.72004512 76.74410000 60.44886016 39.72816720 18.48410912 3.64173712

Success 99.83650626 99.65983120 99.07262442 97.69888872 94.78372450 89.08484376 78.77814570 61.56786592 35.34301122

Fail 0.14880348 0.23391697 0.61651228 1.48853781 3.26251276 6.53808673 11.99254572 19.96241653 29.31397756

Botch 0.01469026 0.10625183 0.31086330 0.81257347 1.95376274 4.37706951 9.22930858 18.46971755 35.34301122

Success classes by Dice Pool by Difficulty Difficulty 2 Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 59.04900000 53.14410000 85.03056000 81.31047300 94.70278620 92.98091736

Complete 0.00000000 0.00000000 72.90000000 65.61000000 91.85400000 88.57350000 97.43085000 96.19082100 99.16689060 98.72048016

Success 90.00000000 81.00000000 97.20000000 94.77000000 99.14400000 98.41500000 99.72720000 99.49756500 99.91090800 99.83650626

Fail 0.00000000 18.00000000 0.00000000 4.86000000 0.00000000 1.45800000 0.00000000 0.45927000 0.00000000 0.14880348

Botch 10.00000000 1.00000000 2.80000000 0.37000000 0.85600000 0.12700000 0.27280000 0.04316500 0.08909200 0.01469026

Complete 0.00000000 0.00000000 51.20000000 61.44000000 78.84800000 84.99200000 91.11040000 93.99910400 96.29143040 97.55217920

Success 80.00000000 80.00000000 92.00000000 93.76000000 96.80800000 97.76480000 98.71800000 99.14400000 99.48017360 99.65983120

Fail 10.00000000 17.00000000 4.90000000 4.81000000 2.08100000 1.62410000 0.85457000 0.60076900 0.34896010 0.23391697

Botch 10.00000000 3.00000000 3.10000000 1.43000000 1.11100000 0.61110000 0.42743000 0.25523100 0.17086630 0.10625183

Difficulty 3 Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 32.76800000 45.87520000 64.55296000 74.18675200 83.04066560 88.23111680

10

4.2.3 Pool 1 2 3 4 5 6 7 8 9 10 4.2.4 Pool 1 2 3 4 5 6 7 8 9 10 4.2.5 Pool 1 2 3 4 5 6 7 8 9 10


Complete 0.00000000 0.00000000 34.30000000 51.45000000 66.54200000 76.31750000 83.43475000 88.33038900 91.78590820 94.20146512

Success 70.00000000 77.00000000 86.80000000 90.93000000 94.05200000 95.92940000 97.22384000 98.08150100 98.67003160 99.07262442

Fail 20.00000000 18.00000000 9.20000000 6.46000000 4.09200000 2.79240000 1.87896000 1.29101400 0.88856120 0.61651228

Botch 10.00000000 5.00000000 4.00000000 2.61000000 1.85600000 1.27820000 0.89720000 0.62748500 0.44140720 0.31086330

Complete 0.00000000 0.00000000 21.60000000 38.88000000 53.13600000 64.15200000 72.60840000 79.05859200 83.97380160 87.72004512

Success 60.00000000 72.00000000 81.00000000 86.40000000 90.12600000 92.72880000 94.59666000 95.95584000 96.95627100 97.69888872

Fail 30.00000000 21.00000000 13.50000000 9.45000000 6.72300000 4.87890000 3.58263000 2.65558500 1.98251550 1.48853781

Botch 10.00000000 7.00000000 5.50000000 4.15000000 3.15100000 2.39230000 1.82071000 1.38857500 1.06121350 0.81257347

Complete 0.00000000 0.00000000 12.50000000 26.25000000 38.75000000 49.43750000 58.35625000 65.72112500 71.77542500 76.74410000

Success 50.00000000 65.00000000 74.00000000 80.05000000 84.40000000 87.64700000 90.12960000 92.05948500 93.57795200 94.78372450

Fail 40.00000000 26.00000000 18.40000000 13.66000000 10.42400000 8.09960000 6.37424000 5.06416600 4.05289840 3.26251276

Botch 10.00000000 9.00000000 7.60000000 6.29000000 5.17600000 4.25340000 3.49616000 2.87634900 2.36914960 1.95376274

Difficulty 5 Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 7.77600000 18.66240000 30.55968000 41.99040000 52.27804800 61.17161472 Difficulty 6 Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 3.12500000 9.06250000 16.75000000 25.21562500 33.76437500 41.95775000

11

4.2.6 Pool 1 2 3 4 5 6 7 8 9 10 4.2.7 Pool 1 2 3 4 5 6 7 8 9 10 4.2.8 Pool 1 2 3 4 5 6 7 8 9 10


Complete 0.00000000 0.00000000 6.40000000 15.36000000 24.70400000 33.53600000 41.54560000 48.66969600 54.94581760 60.44886016

Success 40.00000000 56.00000000 65.20000000 71.52000000 76.24400000 79.94000000 82.91420000 85.35344000 87.38141800 89.08484376

Fail 50.00000000 33.00000000 24.50000000 19.21000000 15.52500000 12.79050000 10.67925000 9.00454500 7.64995250 6.53808673

Botch 10.00000000 11.00000000 10.30000000 9.27000000 8.23100000 7.26950000 6.40655000 5.64201500 4.96862950 4.37706951

Complete 0.00000000 0.00000000 2.70000000 7.29000000 12.79800000 18.58950000 24.31215000 29.78766900 34.93557540 39.72816720

Success 30.00000000 45.00000000 54.00000000 60.21000000 64.90800000 68.67180000 71.79840000 74.45884500 76.76107560 78.77814570

Fail 60.00000000 42.00000000 32.40000000 26.46000000 22.35600000 19.29960000 16.90632000 14.96669400 13.35557160 11.99254572

Botch 10.00000000 13.00000000 13.60000000 13.33000000 12.73600000 12.02860000 11.29528000 10.57446100 9.88335280 9.22930858

Complete 0.00000000 0.00000000 0.80000000 2.40000000 4.59200000 7.16000000 9.93400000 12.79414400 15.66096320 18.48410912

Success 20.00000000 32.00000000 39.80000000 45.28000000 49.40200000 52.67840000 55.39494000 57.71913600 59.75439860 61.56786592

Fail 70.00000000 53.00000000 42.70000000 36.01000000 31.36700000 27.95090000 25.31291000 23.19580900 21.44486470 19.96241653

Botch 10.00000000 15.00000000 17.50000000 18.71000000 19.23100000 19.37070000 19.29215000 19.08505500 18.80073670 18.46971755

Difficulty 8 Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 0.24300000 0.94770000 2.21616000 4.04813700 6.38122860 9.12503880 Difficulty 9 Phenomenal 0.00000000 0.00000000 0.00000000 0.00000000 0.03200000 0.14080000 0.36640000 0.73600000 1.26289280 1.94868992

12

4.2.9 Pool 1 2 3 4 5 6 7 8 9 10

4.3 4.3.1 Diff 2 3 4 5 6 7 8 9 10


Complete 0.00000000 0.00000000 0.10000000 0.33000000 0.68600000 1.14950000 1.69765000 2.30819700 2.96161060 3.64173712

Success 10.00000000 17.00000000 22.00000000 25.65000000 28.37600000 30.45980000 32.08976000 33.39324500 34.45747600 35.34301122

Fail 80.00000000 66.00000000 56.00000000 48.70000000 43.24800000 39.08040000 35.82048000 33.21351000 31.08504800 29.31397756

Botch 10.00000000 17.00000000 22.00000000 25.65000000 28.37600000 30.45980000 32.08976000 33.39324500 34.45747600 35.34301122

Successes by Difficulty by Dice Pool Dice Pool • 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

8 2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

7 1 0.00000000 90.00000000 0.00000000 80.00000000 0.00000000 70.00000000 0.00000000 60.00000000 0.00000000 50.00000000 0.00000000 40.00000000 0.00000000 30.00000000 0.00000000 20.00000000 0.00000000 10.00000000

13

6 0 0.00000000 0.00000000 0.00000000 10.00000000 0.00000000 20.00000000 0.00000000 30.00000000 0.00000000 40.00000000 0.00000000 50.00000000 0.00000000 60.00000000 0.00000000 70.00000000 0.00000000 80.00000000

5 Botch 0.00000000 10.00000000 0.00000000 10.00000000 0.00000000 10.00000000 0.00000000 10.00000000 0.00000000 10.00000000 0.00000000 10.00000000 0.00000000 10.00000000 0.00000000 10.00000000 0.00000000 10.00000000

4.3.2 Diff 2 3 4 5 6 7 8 9 10

4.3.3 Diff 2 3 4 5 6 7 8 9 10

Dice Pool • • 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

8 2 0.00000000 81.00000000 0.00000000 64.00000000 0.00000000 49.00000000 0.00000000 36.00000000 0.00000000 25.00000000 0.00000000 16.00000000 0.00000000 9.00000000 0.00000000 4.00000000 0.00000000 1.00000000

7 1 0.00000000 0.00000000 0.00000000 16.00000000 0.00000000 28.00000000 0.00000000 36.00000000 0.00000000 40.00000000 0.00000000 40.00000000 0.00000000 36.00000000 0.00000000 28.00000000 0.00000000 16.00000000

6 0 0.00000000 18.00000000 0.00000000 17.00000000 0.00000000 18.00000000 0.00000000 21.00000000 0.00000000 26.00000000 0.00000000 33.00000000 0.00000000 42.00000000 0.00000000 53.00000000 0.00000000 66.00000000

5 Botch 0.00000000 1.00000000 0.00000000 3.00000000 0.00000000 5.00000000 0.00000000 7.00000000 0.00000000 9.00000000 0.00000000 11.00000000 0.00000000 13.00000000 0.00000000 15.00000000 0.00000000 17.00000000

Dice Pool • • • 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000

9 3 0.00000000 72.90000000 0.00000000 51.20000000 0.00000000 34.30000000 0.00000000 21.60000000 0.00000000 12.50000000 0.00000000 6.40000000 0.00000000 2.70000000 0.00000000 0.80000000 0.00000000 0.10000000

8 2 0.00000000 0.00000000 0.00000000 19.20000000 0.00000000 29.40000000 0.00000000 32.40000000 0.00000000 30.00000000 0.00000000 24.00000000 0.00000000 16.20000000 0.00000000 8.40000000 0.00000000 2.40000000

14

7 1 0.00000000 24.30000000 0.00000000 21.60000000 0.00000000 23.10000000 0.00000000 27.00000000 0.00000000 31.50000000 0.00000000 34.80000000 0.00000000 35.10000000 0.00000000 30.60000000 0.00000000 19.50000000

6 0 0.00000000 0.00000000 0.00000000 4.90000000 0.00000000 9.20000000 0.00000000 13.50000000 0.00000000 18.40000000 0.00000000 24.50000000 0.00000000 32.40000000 0.00000000 42.70000000 0.00000000 56.00000000

5 Botch 0.00000000 2.80000000 0.00000000 3.10000000 0.00000000 4.00000000 0.00000000 5.50000000 0.00000000 7.60000000 0.00000000 10.30000000 0.00000000 13.60000000 0.00000000 17.50000000 0.00000000 22.00000000

4.3.4 Diff 2 3 4 5 6 7 8 9 10

4.3.5 Diff 2 3 4 5 6 7 8 9 10

Dice Pool • • • • 10 4 0.00000000 65.61000000 0.00000000 40.96000000 0.00000000 24.01000000 0.00000000 12.96000000 0.00000000 6.25000000 0.00000000 2.56000000 0.00000000 0.81000000 0.00000000 0.16000000 0.00000000 0.01000000

9 3 0.00000000 0.00000000 0.00000000 20.48000000 0.00000000 27.44000000 0.00000000 25.92000000 0.00000000 20.00000000 0.00000000 12.80000000 0.00000000 6.48000000 0.00000000 2.24000000 0.00000000 0.32000000

8 2 0.00000000 29.16000000 0.00000000 24.32000000 0.00000000 25.48000000 0.00000000 28.08000000 0.00000000 29.00000000 0.00000000 26.56000000 0.00000000 20.52000000 0.00000000 12.08000000 0.00000000 3.88000000

7 1 0.00000000 0.00000000 0.00000000 8.00000000 0.00000000 14.00000000 0.00000000 19.44000000 0.00000000 24.80000000 0.00000000 29.60000000 0.00000000 32.40000000 0.00000000 30.80000000 0.00000000 21.44000000

6 0 0.00000000 4.86000000 0.00000000 4.81000000 0.00000000 6.46000000 0.00000000 9.45000000 0.00000000 13.66000000 0.00000000 19.21000000 0.00000000 26.46000000 0.00000000 36.01000000 0.00000000 48.70000000

5 Botch 0.00000000 0.37000000 0.00000000 1.43000000 0.00000000 2.61000000 0.00000000 4.15000000 0.00000000 6.29000000 0.00000000 9.27000000 0.00000000 13.33000000 0.00000000 18.71000000 0.00000000 25.65000000

8 2 0.00000000 0.00000000 0.00000000 10.88000000 0.00000000 17.64000000 0.00000000 22.68000000 0.00000000 26.00000000 0.00000000 26.40000000 0.00000000 22.68000000 0.00000000 14.84000000 0.00000000 5.28000000

7 1 0.00000000 7.29000000 0.00000000 7.08000000 0.00000000 9.87000000 0.00000000 14.31000000 0.00000000 19.65000000 0.00000000 25.14000000 0.00000000 29.43000000 0.00000000 29.97000000 0.00000000 22.41000000

6 0 0.00000000 0.00000000 0.00000000 2.08100000 0.00000000 4.09200000 0.00000000 6.72300000 0.00000000 10.42400000 0.00000000 15.52500000 0.00000000 22.35600000 0.00000000 31.36700000 0.00000000 43.24800000

5 Botch 59.04900000 0.85600000 32.76800000 1.11100000 16.80700000 1.85600000 7.77600000 3.15100000 3.12500000 5.17600000 1.02400000 8.23100000 0.24300000 12.73600000 0.03200000 19.23100000 0.00100000 28.37600000

Dice Pool • • • • • 10 4 0.00000000 0.00000000 0.00000000 20.48000000 0.00000000 24.01000000 0.00000000 19.44000000 0.00000000 12.50000000 0.00000000 6.40000000 0.00000000 2.43000000 0.00000000 0.56000000 0.00000000 0.04000000

9 3 0.00000000 32.80500000 0.00000000 25.60000000 0.00000000 25.72500000 0.00000000 25.92000000 0.00000000 23.12500000 0.00000000 17.28000000 0.00000000 10.12500000 0.00000000 4.00000000 0.00000000 0.64500000

15

4.3.6 Diff 2 3 4 5 6 7 8 9 10

4.3.7 Diff 2 3 4 5 6 7 8 9 10

Dice Pool • • • • • 10 4 0.00000000 35.42940000 0.00000000 25.80480000 0.00000000 24.49020000 0.00000000 22.16160000 0.00000000 16.87500000 0.00000000 10.21440000 0.00000000 4.51980000 0.00000000 1.19520000 0.00000000 0.09660000

9 3 0.00000000 0.00000000 0.00000000 13.31200000 0.00000000 19.89400000 0.00000000 23.32800000 0.00000000 23.50000000 0.00000000 19.84000000 0.00000000 13.12200000 0.00000000 5.82400000 0.00000000 1.04800000

Dice Pool • • • • • 10 4 0.00000000 0.00000000 0.00000000 15.19616000 0.00000000 20.84068000 0.00000000 22.04496000 0.00000000 19.25000000 0.00000000 13.35040000 0.00000000 6.73596000 0.00000000 2.01488000 0.00000000 0.18256000

•

8 2 0.00000000 9.84150000 0.00000000 9.31200000 0.00000000 13.00950000 0.00000000 17.98200000 0.00000000 22.53750000 0.00000000 24.98400000 0.00000000 23.44950000 0.00000000 16.78200000 0.00000000 6.52950000

7 1 0.00000000 0.00000000 0.00000000 3.46080000 0.00000000 6.60240000 0.00000000 10.59480000 0.00000000 15.67200000 0.00000000 21.42000000 0.00000000 26.63280000 0.00000000 28.73640000 0.00000000 22.78080000

6 0 53.14410000 1.45800000 26.21440000 1.62410000 11.76490000 2.79240000 4.66560000 4.87890000 1.56250000 8.09960000 0.40960000 12.79050000 0.07290000 19.29960000 0.00640000 27.95090000 0.00010000 39.08040000

5 Botch 0.00000000 0.12700000 19.66080000 0.61110000 20.16840000 1.27820000 13.99680000 2.39230000 7.50000000 4.25340000 3.07200000 7.26950000 0.87480000 12.02860000 0.13440000 19.37070000 0.00480000 30.45980000

8 2 0.00000000 0.00000000 0.00000000 5.03104000 0.00000000 9.21298000 0.00000000 14.08428000 0.00000000 19.20100000 0.00000000 23.04400000 0.00000000 23.37174000 0.00000000 18.07708000 0.00000000 7.60648000

7 1 47.82969000 2.29635000 20.97152000 2.57656000 8.23543000 4.57611000 2.79936000 7.90398000 0.78125000 12.57235000 0.16384000 18.32460000 0.02187000 24.11451000 0.00128000 27.38386000 0.00001000 22.78563000

6 0 0.00000000 0.00000000 18.35008000 0.85457000 16.47086000 1.87896000 9.79776000 3.58263000 4.37500000 6.37424000 1.43360000 10.67925000 0.30618000 16.90632000 0.03136000 25.31291000 0.00056000 35.82048000

5 Botch 37.20087000 0.27280000 25.23136000 0.42743000 22.35331000 0.89720000 17.96256000 1.82071000 11.59375000 3.49616000 5.66272000 6.40655000 1.88811000 11.29528000 0.33376000 19.29215000 0.01351000 32.08976000

• •

9 3 0.00000000 12.40029000 0.00000000 11.36128000 0.00000000 15.53447000 0.00000000 20.00376000 0.00000000 22.35625000 0.00000000 20.93504000 0.00000000 15.36003000 0.00000000 7.55272000 0.00000000 1.50101000

16

4.3.8 Diff 2 3 4 5 6 7 8 9 10

4.3.9 Diff 2 3 4 5 6 7 8 9 10

Dice Pool • • • • • 10 4 0.00000000 14.88034800 0.00000000 13.13177600 0.00000000 17.27759600 0.00000000 20.41200000 0.00000000 20.03750000 0.00000000 15.61548800 0.00000000 8.83839600 0.00000000 2.95433600 0.00000000 0.29750000

9 3 0.00000000 0.00000000 0.00000000 6.68057600 0.00000000 11.64004800 0.00000000 16.65619200 0.00000000 20.46800000 0.00000000 21.02016000 0.00000000 16.90113600 0.00000000 9.10380800 0.00000000 1.97971200

Dice Pool • • • • • 10 4 0.00000000 0.00000000 0.00000000 8.30914560 0.00000000 13.67417520 0.00000000 18.07686720 0.00000000 19.71900000 0.00000000 17.04729600 0.00000000 10.69180560 0.00000000 3.95277120 0.00000000 0.43888320

• • •

8 2 43.04672100 3.30674400 16.77721600 3.70048000 5.76480100 6.59932000 1.67961600 10.96804800 0.39062500 16.20220000 0.06553600 20.94534400 0.00656100 22.79340000 0.00025600 18.88600000 0.00000100 8.51384800

7 1 0.00000000 0.00000000 16.77721600 1.44441600 13.17668800 3.15179200 6.71846400 5.92920000 2.50000000 10.13616000 0.65536000 15.73840000 0.10497600 21.87777600 0.00716800 26.03899200 0.00006400 22.57120000

6 0 38.26375200 0.45927000 24.11724800 0.60076900 19.76503200 1.29101400 13.99680000 2.65558500 7.62500000 5.06416600 2.99827200 9.00454500 0.75232800 14.96669400 0.08883200 23.19580900 0.00180000 33.21351000

5 Botch 0.00000000 0.04316500 16.51507200 0.25523100 20.70622400 0.62748500 19.59552000 1.38857500 14.70000000 2.87634900 8.31488000 5.64201500 3.18427200 10.57446100 0.63974400 19.08505500 0.02912000 33.39324500

7 1 38.74204890 0.74401740 22.64924160 0.99510480 17.04734010 2.19400020 10.58158080 4.46891580 4.85156250 8.20676700 1.53354240 13.56555240 0.28934010 19.89601380 0.02280960 24.75505620 0.00023130 22.22969580

6 0 0.00000000 0.00000000 17.30150400 0.34896010 19.76503200 0.88856120 16.62819840 1.98251550 10.65000000 4.05289840 4.89062400 7.64995250 1.41717600 13.35557160 0.19084800 21.44486470 0.00435840 31.08504800

5 Botch 17.21868840 0.08909200 14.56865280 0.17086630 18.21206520 0.44140720 19.52553600 1.06121350 16.66125000 2.36914960 10.70346240 4.96862950 4.63731480 9.88335280 1.04757120 18.80073670 0.05322600 34.45747600

• • • •

9 3 38.74204890 4.46410440 13.42177280 4.94161920 4.03536070 8.67529320 1.00776960 13.61888640 0.19531250 18.29205000 0.02621440 20.44976640 0.00196830 17.86254120 0.00005120 10.44529920 0.00000010 2.46490440

8 2 0.00000000 0.00000000 15.09949440 2.19363840 10.37664180 4.69012320 4.53496320 8.51355360 1.40625000 13.59576000 0.29491200 18.87004800 0.03542940 21.92948640 0.00161280 19.33837920 0.00000720 9.26616960

17

4.3.10 Diff 2 3 4 5 6 7 8 9 10

4.4 4.4.1 Dice Pool 1 2 3 4 5 6 7 8 9 10

Dice Pool • • • • • 10 4 34.86784401 5.73956280 10.73741824 6.24107520 2.82475249 10.62874680 0.60466176 15.54694560 0.09765625 18.69975000 0.01048576 17.77390080 0.00059049 12.23757720 0.00001024 4.96075680 0.00000001 0.60291960

• • • • •

9 3 0.00000000 0.00000000 13.42177280 3.07998720 8.07072140 6.38556240 3.02330880 11.00148480 0.78125000 16.08660000 0.13107200 19.47763200 0.01180980 18.36555120 0.00035840 11.57466240 0.00000080 2.94242880

8 2 38.74204890 1.11602610 20.97152000 1.50960960 14.41200250 3.34135410 7.81021440 6.59730420 3.00781250 11.37089250 0.76349440 16.90622160 0.10825650 20.91275010 0.00569600 19.53240660 0.00002890 9.88239570

7 1 0.00000000 0.00000000 17.61607680 0.59804240 18.28265460 1.52980520 13.60488960 3.38153940 7.40625000 6.66873200 2.75251200 11.72976200 0.60229980 18.13722840 0.05429760 23.55135020 0.00062160 21.81887840

6 0 19.37102445 0.14880348 15.64999680 0.23391697 18.40618605 0.61651228 17.76193920 1.48853781 13.07578125 3.26251276 6.88005120 6.53808673 2.27043405 11.99254572 0.34538880 19.96241653 0.00883245 29.31397756

5 Botch 0.00000000 0.01469026 9.83433216 0.10625183 15.19083888 0.31086330 18.36660096 0.81257347 17.58900000 1.95376274 12.65971200 4.37706951 6.13164816 9.22930858 1.54293888 18.46971755 0.08690496 35.34301122

Successes by Dice Pool by Difficulty Difficulty 2 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 65.61000000 0.00000000 0.00000000 0.00000000 35.42940000 0.00000000 0.00000000 0.00000000 14.88034800 0.00000000 0.00000000 34.86784401 5.73956280

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 72.90000000 0.00000000 0.00000000 0.00000000 32.80500000 0.00000000 0.00000000 0.00000000 12.40029000 0.00000000 0.00000000 38.74204890 4.46410440 0.00000000 0.00000000

8 2 0.00000000 0.00000000 0.00000000 81.00000000 0.00000000 0.00000000 0.00000000 29.16000000 0.00000000 0.00000000 0.00000000 9.84150000 0.00000000 0.00000000 43.04672100 3.30674400 0.00000000 0.00000000 38.74204890 1.11602610

18

7 1 0.00000000 90.00000000 0.00000000 0.00000000 0.00000000 24.30000000 0.00000000 0.00000000 0.00000000 7.29000000 0.00000000 0.00000000 47.82969000 2.29635000 0.00000000 0.00000000 38.74204890 0.74401740 0.00000000 0.00000000

6 0 0.00000000 0.00000000 0.00000000 18.00000000 0.00000000 0.00000000 0.00000000 4.86000000 0.00000000 0.00000000 53.14410000 1.45800000 0.00000000 0.00000000 38.26375200 0.45927000 0.00000000 0.00000000 19.37102445 0.14880348

5 Botch 0.00000000 10.00000000 0.00000000 1.00000000 0.00000000 2.80000000 0.00000000 0.37000000 59.04900000 0.85600000 0.00000000 0.12700000 37.20087000 0.27280000 0.00000000 0.04316500 17.21868840 0.08909200 0.00000000 0.01469026

4.4.2 Dice Pool 1 2 3 4 5 6 7 8 9 10

4.4.3 Dice Pool 1 2 3 4 5 6 7 8 9 10

Difficulty 3 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 40.96000000 0.00000000 20.48000000 0.00000000 25.80480000 0.00000000 15.19616000 0.00000000 13.13177600 0.00000000 8.30914560 10.73741824 6.24107520

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 51.20000000 0.00000000 20.48000000 0.00000000 25.60000000 0.00000000 13.31200000 0.00000000 11.36128000 0.00000000 6.68057600 13.42177280 4.94161920 13.42177280 3.07998720

8 2 0.00000000 0.00000000 0.00000000 64.00000000 0.00000000 19.20000000 0.00000000 24.32000000 0.00000000 10.88000000 0.00000000 9.31200000 0.00000000 5.03104000 16.77721600 3.70048000 15.09949440 2.19363840 20.97152000 1.50960960

7 1 0.00000000 80.00000000 0.00000000 16.00000000 0.00000000 21.60000000 0.00000000 8.00000000 0.00000000 7.08000000 0.00000000 3.46080000 20.97152000 2.57656000 16.77721600 1.44441600 22.64924160 0.99510480 17.61607680 0.59804240

6 0 0.00000000 10.00000000 0.00000000 17.00000000 0.00000000 4.90000000 0.00000000 4.81000000 0.00000000 2.08100000 26.21440000 1.62410000 18.35008000 0.85457000 24.11724800 0.60076900 17.30150400 0.34896010 15.64999680 0.23391697

5 Botch 0.00000000 10.00000000 0.00000000 3.00000000 0.00000000 3.10000000 0.00000000 1.43000000 32.76800000 1.11100000 19.66080000 0.61110000 25.23136000 0.42743000 16.51507200 0.25523100 14.56865280 0.17086630 9.83433216 0.10625183

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 34.30000000 0.00000000 27.44000000 0.00000000 25.72500000 0.00000000 19.89400000 0.00000000 15.53447000 0.00000000 11.64004800 4.03536070 8.67529320 8.07072140 6.38556240

8 2 0.00000000 0.00000000 0.00000000 49.00000000 0.00000000 29.40000000 0.00000000 25.48000000 0.00000000 17.64000000 0.00000000 13.00950000 0.00000000 9.21298000 5.76480100 6.59932000 10.37664180 4.69012320 14.41200250 3.34135410

7 1 0.00000000 70.00000000 0.00000000 28.00000000 0.00000000 23.10000000 0.00000000 14.00000000 0.00000000 9.87000000 0.00000000 6.60240000 8.23543000 4.57611000 13.17668800 3.15179200 17.04734010 2.19400020 18.28265460 1.52980520

6 0 0.00000000 20.00000000 0.00000000 18.00000000 0.00000000 9.20000000 0.00000000 6.46000000 0.00000000 4.09200000 11.76490000 2.79240000 16.47086000 1.87896000 19.76503200 1.29101400 19.76503200 0.88856120 18.40618605 0.61651228

5 Botch 0.00000000 10.00000000 0.00000000 5.00000000 0.00000000 4.00000000 0.00000000 2.61000000 16.80700000 1.85600000 20.16840000 1.27820000 22.35331000 0.89720000 20.70622400 0.62748500 18.21206520 0.44140720 15.19083888 0.31086330

Difficulty 4 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 24.01000000 0.00000000 24.01000000 0.00000000 24.49020000 0.00000000 20.84068000 0.00000000 17.27759600 0.00000000 13.67417520 2.82475249 10.62874680

19

4.4.4 Dice Pool 1 2 3 4 5 6 7 8 9 10

4.4.5 Dice Pool 1 2 3 4 5 6 7 8 9 10

Difficulty 5 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 12.96000000 0.00000000 19.44000000 0.00000000 22.16160000 0.00000000 22.04496000 0.00000000 20.41200000 0.00000000 18.07686720 0.60466176 15.54694560

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 21.60000000 0.00000000 25.92000000 0.00000000 25.92000000 0.00000000 23.32800000 0.00000000 20.00376000 0.00000000 16.65619200 1.00776960 13.61888640 3.02330880 11.00148480

8 2 0.00000000 0.00000000 0.00000000 36.00000000 0.00000000 32.40000000 0.00000000 28.08000000 0.00000000 22.68000000 0.00000000 17.98200000 0.00000000 14.08428000 1.67961600 10.96804800 4.53496320 8.51355360 7.81021440 6.59730420

7 1 0.00000000 60.00000000 0.00000000 36.00000000 0.00000000 27.00000000 0.00000000 19.44000000 0.00000000 14.31000000 0.00000000 10.59480000 2.79936000 7.90398000 6.71846400 5.92920000 10.58158080 4.46891580 13.60488960 3.38153940

6 0 0.00000000 30.00000000 0.00000000 21.00000000 0.00000000 13.50000000 0.00000000 9.45000000 0.00000000 6.72300000 4.66560000 4.87890000 9.79776000 3.58263000 13.99680000 2.65558500 16.62819840 1.98251550 17.76193920 1.48853781

5 Botch 0.00000000 10.00000000 0.00000000 7.00000000 0.00000000 5.50000000 0.00000000 4.15000000 7.77600000 3.15100000 13.99680000 2.39230000 17.96256000 1.82071000 19.59552000 1.38857500 19.52553600 1.06121350 18.36660096 0.81257347

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 12.50000000 0.00000000 20.00000000 0.00000000 23.12500000 0.00000000 23.50000000 0.00000000 22.35625000 0.00000000 20.46800000 0.19531250 18.29205000 0.78125000 16.08660000

8 2 0.00000000 0.00000000 0.00000000 25.00000000 0.00000000 30.00000000 0.00000000 29.00000000 0.00000000 26.00000000 0.00000000 22.53750000 0.00000000 19.20100000 0.39062500 16.20220000 1.40625000 13.59576000 3.00781250 11.37089250

7 1 0.00000000 50.00000000 0.00000000 40.00000000 0.00000000 31.50000000 0.00000000 24.80000000 0.00000000 19.65000000 0.00000000 15.67200000 0.78125000 12.57235000 2.50000000 10.13616000 4.85156250 8.20676700 7.40625000 6.66873200

6 0 0.00000000 40.00000000 0.00000000 26.00000000 0.00000000 18.40000000 0.00000000 13.66000000 0.00000000 10.42400000 1.56250000 8.09960000 4.37500000 6.37424000 7.62500000 5.06416600 10.65000000 4.05289840 13.07578125 3.26251276

5 Botch 0.00000000 10.00000000 0.00000000 9.00000000 0.00000000 7.60000000 0.00000000 6.29000000 3.12500000 5.17600000 7.50000000 4.25340000 11.59375000 3.49616000 14.70000000 2.87634900 16.66125000 2.36914960 17.58900000 1.95376274

Difficulty 6 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 6.25000000 0.00000000 12.50000000 0.00000000 16.87500000 0.00000000 19.25000000 0.00000000 20.03750000 0.00000000 19.71900000 0.09765625 18.69975000

20

4.4.6 Dice Pool 1 2 3 4 5 6 7 8 9 10

4.4.7 Dice Pool 1 2 3 4 5 6 7 8 9 10

Difficulty 7 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 2.56000000 0.00000000 6.40000000 0.00000000 10.21440000 0.00000000 13.35040000 0.00000000 15.61548800 0.00000000 17.04729600 0.01048576 17.77390080

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 6.40000000 0.00000000 12.80000000 0.00000000 17.28000000 0.00000000 19.84000000 0.00000000 20.93504000 0.00000000 21.02016000 0.02621440 20.44976640 0.13107200 19.47763200

8 2 0.00000000 0.00000000 0.00000000 16.00000000 0.00000000 24.00000000 0.00000000 26.56000000 0.00000000 26.40000000 0.00000000 24.98400000 0.00000000 23.04400000 0.06553600 20.94534400 0.29491200 18.87004800 0.76349440 16.90622160

7 1 0.00000000 40.00000000 0.00000000 40.00000000 0.00000000 34.80000000 0.00000000 29.60000000 0.00000000 25.14000000 0.00000000 21.42000000 0.16384000 18.32460000 0.65536000 15.73840000 1.53354240 13.56555240 2.75251200 11.72976200

6 0 0.00000000 50.00000000 0.00000000 33.00000000 0.00000000 24.50000000 0.00000000 19.21000000 0.00000000 15.52500000 0.40960000 12.79050000 1.43360000 10.67925000 2.99827200 9.00454500 4.89062400 7.64995250 6.88005120 6.53808673

5 Botch 0.00000000 10.00000000 0.00000000 11.00000000 0.00000000 10.30000000 0.00000000 9.27000000 1.02400000 8.23100000 3.07200000 7.26950000 5.66272000 6.40655000 8.31488000 5.64201500 10.70346240 4.96862950 12.65971200 4.37706951

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 2.70000000 0.00000000 6.48000000 0.00000000 10.12500000 0.00000000 13.12200000 0.00000000 15.36003000 0.00000000 16.90113600 0.00196830 17.86254120 0.01180980 18.36555120

8 2 0.00000000 0.00000000 0.00000000 9.00000000 0.00000000 16.20000000 0.00000000 20.52000000 0.00000000 22.68000000 0.00000000 23.44950000 0.00000000 23.37174000 0.00656100 22.79340000 0.03542940 21.92948640 0.10825650 20.91275010

7 1 0.00000000 30.00000000 0.00000000 36.00000000 0.00000000 35.10000000 0.00000000 32.40000000 0.00000000 29.43000000 0.00000000 26.63280000 0.02187000 24.11451000 0.10497600 21.87777600 0.28934010 19.89601380 0.60229980 18.13722840

6 0 0.00000000 60.00000000 0.00000000 42.00000000 0.00000000 32.40000000 0.00000000 26.46000000 0.00000000 22.35600000 0.07290000 19.29960000 0.30618000 16.90632000 0.75232800 14.96669400 1.41717600 13.35557160 2.27043405 11.99254572

5 Botch 0.00000000 10.00000000 0.00000000 13.00000000 0.00000000 13.60000000 0.00000000 13.33000000 0.24300000 12.73600000 0.87480000 12.02860000 1.88811000 11.29528000 3.18427200 10.57446100 4.63731480 9.88335280 6.13164816 9.22930858

Difficulty 8 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.81000000 0.00000000 2.43000000 0.00000000 4.51980000 0.00000000 6.73596000 0.00000000 8.83839600 0.00000000 10.69180560 0.00059049 12.23757720

21

4.4.8 Dice Pool 1 2 3 4 5 6 7 8 9 10

4.4.9 Dice Pool 1 2 3 4 5 6 7 8 9 10

Difficulty 9 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.16000000 0.00000000 0.56000000 0.00000000 1.19520000 0.00000000 2.01488000 0.00000000 2.95433600 0.00000000 3.95277120 0.00001024 4.96075680

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.80000000 0.00000000 2.24000000 0.00000000 4.00000000 0.00000000 5.82400000 0.00000000 7.55272000 0.00000000 9.10380800 0.00005120 10.44529920 0.00035840 11.57466240

8 2 0.00000000 0.00000000 0.00000000 4.00000000 0.00000000 8.40000000 0.00000000 12.08000000 0.00000000 14.84000000 0.00000000 16.78200000 0.00000000 18.07708000 0.00025600 18.88600000 0.00161280 19.33837920 0.00569600 19.53240660

7 1 0.00000000 20.00000000 0.00000000 28.00000000 0.00000000 30.60000000 0.00000000 30.80000000 0.00000000 29.97000000 0.00000000 28.73640000 0.00128000 27.38386000 0.00716800 26.03899200 0.02280960 24.75505620 0.05429760 23.55135020

6 0 0.00000000 70.00000000 0.00000000 53.00000000 0.00000000 42.70000000 0.00000000 36.01000000 0.00000000 31.36700000 0.00640000 27.95090000 0.03136000 25.31291000 0.08883200 23.19580900 0.19084800 21.44486470 0.34538880 19.96241653

5 Botch 0.00000000 10.00000000 0.00000000 15.00000000 0.00000000 17.50000000 0.00000000 18.71000000 0.03200000 19.23100000 0.13440000 19.37070000 0.33376000 19.29215000 0.63974400 19.08505500 1.04757120 18.80073670 1.54293888 18.46971755

Difficulty 10 10 4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.01000000 0.00000000 0.04000000 0.00000000 0.09660000 0.00000000 0.18256000 0.00000000 0.29750000 0.00000000 0.43888320 0.00000001 0.60291960

9 3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.10000000 0.00000000 0.32000000 0.00000000 0.64500000 0.00000000 1.04800000 0.00000000 1.50101000 0.00000000 1.97971200 0.00000010 2.46490440 0.00000080 2.94242880

8 2 0.00000000 0.00000000 0.00000000 1.00000000 0.00000000 2.40000000 0.00000000 3.88000000 0.00000000 5.28000000 0.00000000 6.52950000 0.00000000 7.60648000 0.00000100 8.51384800 0.00000720 9.26616960 0.00002890 9.88239570

22

7 1 0.00000000 10.00000000 0.00000000 16.00000000 0.00000000 19.50000000 0.00000000 21.44000000 0.00000000 22.41000000 0.00000000 22.78080000 0.00001000 22.78563000 0.00006400 22.57120000 0.00023130 22.22969580 0.00062160 21.81887840

6 0 0.00000000 80.00000000 0.00000000 66.00000000 0.00000000 56.00000000 0.00000000 48.70000000 0.00000000 43.24800000 0.00010000 39.08040000 0.00056000 35.82048000 0.00180000 33.21351000 0.00435840 31.08504800 0.00883245 29.31397756

5 Botch 0.00000000 10.00000000 0.00000000 17.00000000 0.00000000 22.00000000 0.00000000 25.65000000 0.00100000 28.37600000 0.00480000 30.45980000 0.01351000 32.08976000 0.02912000 33.39324500 0.05322600 34.45747600 0.08690496 35.34301122

Contents 1

Introduction

1

2

The probability function

2

3

C code for the calculation of probabilities

5

4

Probability tables

7

4.1 Success classes by Difficulty by Dice Pool 4.1.1 Dice Pool • . . . . . . . . . . . . . 4.1.2 Dice Pool • • . . . . . . . . . . . . 4.1.3 Dice Pool • • • . . . . . . . . . . . 4.1.4 Dice Pool • • • • . . . . . . . . . . 4.1.5 Dice Pool • • • • • . . . . . . . . . 4.1.6 Dice Pool • • • • • • . . . . . . . 4.1.7 Dice Pool • • • • • • • . . . . . . 4.1.8 Dice Pool • • • • • • • • . . . . . 4.1.9 Dice Pool • • • • • • • • • . . . . 4.1.10 Dice Pool • • • • • • • • • • . . 4.2 Success classes by Dice Pool by Difficulty 4.2.1 Difficulty 2 . . . . . . . . . . . . . 4.2.2 Difficulty 3 . . . . . . . . . . . . . 4.2.3 Difficulty 4 . . . . . . . . . . . . . 4.2.4 Difficulty 5 . . . . . . . . . . . . . 4.2.5 Difficulty 6 . . . . . . . . . . . . . 4.2.6 Difficulty 7 . . . . . . . . . . . . . 4.2.7 Difficulty 8 . . . . . . . . . . . . . 4.2.8 Difficulty 9 . . . . . . . . . . . . . 4.2.9 Difficulty 10 . . . . . . . . . . . . . 4.3 Successes by Difficulty by Dice Po ol . . . 4.3.1 Dice Pool • . . . . . . . . . . . . . 4.3.2 Dice Pool • • . . . . . . . . . . . . 4.3.3 Dice Pool • • • . . . . . . . . . . . 4.3.4 Dice Pool • • • • . . . . . . . . . . 4.3.5 Dice Pool • • • • • . . . . . . . 4.3.6 Dice Pool • • • • • • . . . . . . . 4.3.7 Dice Pool • • • • • • • . . . . . . 4.3.8 Dice Pool • • • • • • • • . . . . . 4.3.9 Dice Pool • • • • • • • • • . . . . 4.3.10 Dice Pool • • • • • • • • • • . . 4.4 Successes by Dice Po ol by Difficulty . . . 4.4.1 Difficulty 2 . . . . . . . . . . . . . 4.4.2 Difficulty 3 . . . . . . . . . . . . . 4.4.3 Difficulty 4 . . . . . . . . . . . . . 4.4.4 Difficulty 5 . . . . . . . . . . . . . 4.4.5 Difficulty 6 . . . . . . . . . . . . . 4.4.6 Difficulty 7 . . . . . . . . . . . . . 4.4.7 Difficulty 8 . . . . . . . . . . . . . 4.4.8 Difficulty 9 . . . . . . . . . . . . . 4.4.9 Difficulty 10 . . . . . . . . . . . . .

23

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d10 Probability

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