d10 Probability

The distribution of World of Darkness dice rolls

Ralf Huls([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 Dark-ness” line of role playing games by White Wolf Game Studio. This paper is aimed atstorytellers who might want this information to review their difficulty rulings as well asplayers who might want to estimate their chances of success for a given difficulty. Theprobability function for the number of successes for given dice pool size and difficulty isgiven and explained (math alert). A procedure in C code to calculate probabilities forgiven combinations of difficulty/dice pool/number of successes is presented. Finallyextensive tables of relevant values are shown.

1 Introduction

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 Oblivionand Changeling: The Dreaming) conflict is resolved by use of a varying number of ten-sideddice. This number is called a character’s dice pool, and is determined by the character’straits. To resolve a critical situation, the player rolls a number of dice according to hisdice pool for the problem at hand. Prior to the roll the game master (or storyteller) setsa difficulty for the task, which is a number between 2 and 10 (usually 6). The number ofdice equal to or higher than the selected difficulty is counted as successes. The number ofones rolled is subtracted from this number. The final number of successes is the result ofthis subtraction. If the number of ones is greater than the number of successes, the resultis called a “botch” and the action has a catastrophic result.

This paper examines the probabilities for different numbers of successes under differentconditions.

Use of terms and game mechanics possibly copyrighted to White Wolf Inc. is notintended as a challenge to these copyrights.

This document may be freely distributed provided that no charge is made for the dis-tribution.

I’m currently working on my thesis for a degree in statistics at Dortmund University,Germany. My role playing characters include a Malkavian, a Pooka and a Sluagh (myfavorite).

1

2 The probability function

[. . . ] a man who confines knowledge to formulae necessary for the solution ofan algebraic or other perplexity, the same deserves to be shot with a Fusil orold-fashioned light musket.

Flann O’Brien — At Swim-Two-Birds

(Math alert: I’ll try to keep it simple, but if you’re not interested in the theory, skipthis chapter!)

To score exactly a certain number, say s of successes, you have to roll s dice higher thanthe difficulty (say d). The remaining dice may all be lower than d and higher than 1, orcome 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 followingcombinations:

• 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 top−s2 (where p is the dice pool). Let that number be denoted by

[p−s2

]Thus, in order to calculate the probability of s successes, we have to add up the proba-

bilities of the possible combinations of successes, fails and ones:

P (S = s) =[ p−s

2 ]∑i=0

(Prob. of rolling s + i successes, i ones and p− s− 2 ∗ i others) (1)

In the example this is:

P (S = 5) =[ 10−5

2 ]∑i=0

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

=2∑

i=0

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

= (Prob. of rolling 5 successes, 0 ones and 5 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

The probability of rolling a 1 on a ten-sided die is of course 110 . The probability of

rolling a success is 10−d+110 . Finally, the probability of rolling a number that is neither a 1

nor a success is d−210 . 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 = 4out 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 aspecific 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 + 110

)a (d− 210

)b (110

)c

.

This, however, doesn’t take permutations into account. The storyteller doesn’t care inwhat 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 aroundthe successes. b! are the same, because all you do is shuffle the failures. And—you guessedit—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 givenabove is one such sequence. Thus we have to multiply the probability with the number ofpermutations to find the probability for the case where sequence is irrelevant:

P (a, b, c) =(a + b + c)!

a!b!c!

(10− d + 1

10

)a (d− 210

)b (110

)c

.

A random experiment that follows the above law of probability, by the way, is said tohave 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 hardlysurprising, 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 againsta 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)!

(11− d

10

)s+i (110

)i (d− 210

)p−s−2i

(2)

To continue our example to the bitter end, the probability to score exactly 5 successesagainst 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)!

(11− 6

10

)5+i (110

)i (6− 210

)10−5−2i

3

=[ 52 ]∑

i=0

10!(5 + i)! i! (5− 2i)!

(510

)5+i (110

)i (410

)5−2i

=2∑

i=0

3628800(5 + i)! i! (5− 2i)!

(510

)5+i (110

)i (410

)5−2i

=36288005! 0! 5!

(510

)5 (110

)0 (410

)5

+

36288006! 1! 3!

(510

)6 (110

)1 (410

)3

+

36288007! 2! 1!

(510

)7 (110

)2 (410

)1

=3628800

120 · 1 · 120· 0.03125 · 1 · 0.01024 +

3628800720 · 1 · 6

· 0.015625 · 0.1 · 0.064 +

36288005040 · 2 · 1

· 0.0078125 · 0.01 · 0.4

=362880014400

· 0.00032 +3628800

4320· 0.0001 +

362880010080

· 0.00003125

= 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 easilycalculated as:

P (S ≥ s) =10∑

j=s

P (S = j)

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:

P (S < 0) = 1− P (S ≥ 0) = 1−10∑

j=0

P (S = j)

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

4

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 programshould get the idea across though. The program calculates a table of probabilities bysuccesses and size of dice pool for each difficulty from 2 to 10. Its core is the func-tion “double probability(pool,success,difficulty)” which returns the probabilityto score exactly “success” successes against a difficulty of “difficulty” with a dice poolof “pool”.

#include <math.h>

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 differentconditions. 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 alland the probabilities for failure and botch.

The tables in sections 4.3 and 4.4 show the probability of rolling exactly a certain numberof successes.

In section 4.2 and 4.4 there is a table for every difficulty and the rows represent differentdice pool sizes.

In section 4.1 and 4.3 there is a table for every dice pool size and the rows representdifferent difficulties.

To make the tables in sections 4.3 and 4.4 more compact there are two rows for everydice pool size or difficulty. The first row shows probabilities for 10-5 successes, the secondrow shows probabilities for 4-0 sucesses and botch. Thus the probabilities of rolling 10 and4 successes are in the same field of the table.

For example, the probability of rolling at least five successes against a Difficulty of 6with seven dice is found in table 4.1.7 in the “Phenomenal” column and the row for DicePool 7. The same number (16.75%) can be found in table 4.2.5 in the “Phenomenal” columnand the row for Difficulty 6.

The probability of rolling exactly five successes against a Difficulty of 6 with seven diceis found in table 4.3.7 as the upper number in the column for “5/Botch” and the row forDice Pool 7. The same number (4.375%) can be found in table 4.4.5 as the upper numberin the column for “5/Botch” and the row for Difficulty 6.

4.1 Success classes by Difficulty by Dice Pool

4.1.1 Dice Pool •Phenomenal Complete Success Fail Botch

Diff 2 0.00000000 0.00000000 90.00000000 0.00000000 10.00000000Diff 3 0.00000000 0.00000000 80.00000000 10.00000000 10.00000000Diff 4 0.00000000 0.00000000 70.00000000 20.00000000 10.00000000Diff 5 0.00000000 0.00000000 60.00000000 30.00000000 10.00000000Diff 6 0.00000000 0.00000000 50.00000000 40.00000000 10.00000000Diff 7 0.00000000 0.00000000 40.00000000 50.00000000 10.00000000Diff 8 0.00000000 0.00000000 30.00000000 60.00000000 10.00000000Diff 9 0.00000000 0.00000000 20.00000000 70.00000000 10.00000000Diff 10 0.00000000 0.00000000 10.00000000 80.00000000 10.00000000

7

4.1.2 Dice Pool • •Phenomenal Complete Success Fail Botch


4.1.3 Dice Pool • • •Phenomenal Complete Success Fail Botch


4.1.4 Dice Pool • • • •Phenomenal Complete Success Fail Botch


4.1.5 Dice Pool • • • • •Phenomenal Complete Success Fail Botch


8

4.1.6 Dice Pool • • • • • •Phenomenal Complete Success Fail Botch


4.1.7 Dice Pool • • • • • • •Phenomenal Complete Success Fail Botch


4.1.8 Dice Pool • • • • • • • •Phenomenal Complete Success Fail Botch


4.1.9 Dice Pool • • • • • • • • •Phenomenal Complete Success Fail Botch


9

4.1.10 Dice Pool • • • • • • • • • •Phenomenal Complete Success Fail Botch


4.2 Success classes by Dice Pool by Difficulty

4.2.1 Difficulty 2

Pool Phenomenal Complete Success Fail Botch

1 0.00000000 0.00000000 90.00000000 0.00000000 10.000000002 0.00000000 0.00000000 81.00000000 18.00000000 1.000000003 0.00000000 72.90000000 97.20000000 0.00000000 2.800000004 0.00000000 65.61000000 94.77000000 4.86000000 0.370000005 59.04900000 91.85400000 99.14400000 0.00000000 0.856000006 53.14410000 88.57350000 98.41500000 1.45800000 0.127000007 85.03056000 97.43085000 99.72720000 0.00000000 0.272800008 81.31047300 96.19082100 99.49756500 0.45927000 0.043165009 94.70278620 99.16689060 99.91090800 0.00000000 0.0890920010 92.98091736 98.72048016 99.83650626 0.14880348 0.01469026

4.2.2 Difficulty 3


1 0.00000000 0.00000000 80.00000000 10.00000000 10.000000002 0.00000000 0.00000000 80.00000000 17.00000000 3.000000003 0.00000000 51.20000000 92.00000000 4.90000000 3.100000004 0.00000000 61.44000000 93.76000000 4.81000000 1.430000005 32.76800000 78.84800000 96.80800000 2.08100000 1.111000006 45.87520000 84.99200000 97.76480000 1.62410000 0.611100007 64.55296000 91.11040000 98.71800000 0.85457000 0.427430008 74.18675200 93.99910400 99.14400000 0.60076900 0.255231009 83.04066560 96.29143040 99.48017360 0.34896010 0.1708663010 88.23111680 97.55217920 99.65983120 0.23391697 0.10625183

10

4.2.3 Difficulty 4


1 0.00000000 0.00000000 70.00000000 20.00000000 10.000000002 0.00000000 0.00000000 77.00000000 18.00000000 5.000000003 0.00000000 34.30000000 86.80000000 9.20000000 4.000000004 0.00000000 51.45000000 90.93000000 6.46000000 2.610000005 16.80700000 66.54200000 94.05200000 4.09200000 1.856000006 31.93330000 76.31750000 95.92940000 2.79240000 1.278200007 47.05960000 83.43475000 97.22384000 1.87896000 0.897200008 59.41274500 88.33038900 98.08150100 1.29101400 0.627485009 69.43643980 91.78590820 98.67003160 0.88856120 0.4414072010 77.18715592 94.20146512 99.07262442 0.61651228 0.31086330

4.2.4 Difficulty 5


1 0.00000000 0.00000000 60.00000000 30.00000000 10.000000002 0.00000000 0.00000000 72.00000000 21.00000000 7.000000003 0.00000000 21.60000000 81.00000000 13.50000000 5.500000004 0.00000000 38.88000000 86.40000000 9.45000000 4.150000005 7.77600000 53.13600000 90.12600000 6.72300000 3.151000006 18.66240000 64.15200000 92.72880000 4.87890000 2.392300007 30.55968000 72.60840000 94.59666000 3.58263000 1.820710008 41.99040000 79.05859200 95.95584000 2.65558500 1.388575009 52.27804800 83.97380160 96.95627100 1.98251550 1.0612135010 61.17161472 87.72004512 97.69888872 1.48853781 0.81257347

4.2.5 Difficulty 6


1 0.00000000 0.00000000 50.00000000 40.00000000 10.000000002 0.00000000 0.00000000 65.00000000 26.00000000 9.000000003 0.00000000 12.50000000 74.00000000 18.40000000 7.600000004 0.00000000 26.25000000 80.05000000 13.66000000 6.290000005 3.12500000 38.75000000 84.40000000 10.42400000 5.176000006 9.06250000 49.43750000 87.64700000 8.09960000 4.253400007 16.75000000 58.35625000 90.12960000 6.37424000 3.496160008 25.21562500 65.72112500 92.05948500 5.06416600 2.876349009 33.76437500 71.77542500 93.57795200 4.05289840 2.3691496010 41.95775000 76.74410000 94.78372450 3.26251276 1.95376274

11

4.2.6 Difficulty 7


1 0.00000000 0.00000000 40.00000000 50.00000000 10.000000002 0.00000000 0.00000000 56.00000000 33.00000000 11.000000003 0.00000000 6.40000000 65.20000000 24.50000000 10.300000004 0.00000000 15.36000000 71.52000000 19.21000000 9.270000005 1.02400000 24.70400000 76.24400000 15.52500000 8.231000006 3.48160000 33.53600000 79.94000000 12.79050000 7.269500007 7.26016000 41.54560000 82.91420000 10.67925000 6.406550008 12.03404800 48.66969600 85.35344000 9.00454500 5.642015009 17.44875520 54.94581760 87.38141800 7.64995250 4.9686295010 23.19732736 60.44886016 89.08484376 6.53808673 4.37706951

4.2.7 Difficulty 8


1 0.00000000 0.00000000 30.00000000 60.00000000 10.000000002 0.00000000 0.00000000 45.00000000 42.00000000 13.000000003 0.00000000 2.70000000 54.00000000 32.40000000 13.600000004 0.00000000 7.29000000 60.21000000 26.46000000 13.330000005 0.24300000 12.79800000 64.90800000 22.35600000 12.736000006 0.94770000 18.58950000 68.67180000 19.29960000 12.028600007 2.21616000 24.31215000 71.79840000 16.90632000 11.295280008 4.04813700 29.78766900 74.45884500 14.96669400 10.574461009 6.38122860 34.93557540 76.76107560 13.35557160 9.8833528010 9.12503880 39.72816720 78.77814570 11.99254572 9.22930858

4.2.8 Difficulty 9


1 0.00000000 0.00000000 20.00000000 70.00000000 10.000000002 0.00000000 0.00000000 32.00000000 53.00000000 15.000000003 0.00000000 0.80000000 39.80000000 42.70000000 17.500000004 0.00000000 2.40000000 45.28000000 36.01000000 18.710000005 0.03200000 4.59200000 49.40200000 31.36700000 19.231000006 0.14080000 7.16000000 52.67840000 27.95090000 19.370700007 0.36640000 9.93400000 55.39494000 25.31291000 19.292150008 0.73600000 12.79414400 57.71913600 23.19580900 19.085055009 1.26289280 15.66096320 59.75439860 21.44486470 18.8007367010 1.94868992 18.48410912 61.56786592 19.96241653 18.46971755

12

4.2.9 Difficulty 10


1 0.00000000 0.00000000 10.00000000 80.00000000 10.000000002 0.00000000 0.00000000 17.00000000 66.00000000 17.000000003 0.00000000 0.10000000 22.00000000 56.00000000 22.000000004 0.00000000 0.33000000 25.65000000 48.70000000 25.650000005 0.00100000 0.68600000 28.37600000 43.24800000 28.376000006 0.00490000 1.14950000 30.45980000 39.08040000 30.459800007 0.01408000 1.69765000 32.08976000 35.82048000 32.089760008 0.03098500 2.30819700 33.39324500 33.21351000 33.393245009 0.05782300 2.96161060 34.45747600 31.08504800 34.4574760010 0.09638872 3.64173712 35.34301122 29.31397756 35.34301122

4.3 Successes by Difficulty by Dice Pool

4.3.1 Dice Pool •10 9 8 7 6 5

Diff 4 3 2 1 0 Botch

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 90.00000000 0.00000000 10.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 80.00000000 10.00000000 10.00000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 70.00000000 20.00000000 10.00000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 60.00000000 30.00000000 10.00000000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 50.00000000 40.00000000 10.00000000

7 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 40.00000000 50.00000000 10.00000000

8 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 30.00000000 60.00000000 10.00000000

9 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 20.00000000 70.00000000 10.00000000

10 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 10.00000000 80.00000000 10.00000000

13

4.3.2 Dice Pool • •10 9 8 7 6 5


2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 81.00000000 0.00000000 18.00000000 1.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 64.00000000 16.00000000 17.00000000 3.00000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 49.00000000 28.00000000 18.00000000 5.00000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 36.00000000 36.00000000 21.00000000 7.00000000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 25.00000000 40.00000000 26.00000000 9.00000000

7 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 16.00000000 40.00000000 33.00000000 11.00000000

8 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 9.00000000 36.00000000 42.00000000 13.00000000

9 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 4.00000000 28.00000000 53.00000000 15.00000000

10 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 1.00000000 16.00000000 66.00000000 17.00000000

4.3.3 Dice Pool • • •10 9 8 7 6 5


2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 72.90000000 0.00000000 24.30000000 0.00000000 2.80000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 51.20000000 19.20000000 21.60000000 4.90000000 3.10000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 34.30000000 29.40000000 23.10000000 9.20000000 4.00000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 21.60000000 32.40000000 27.00000000 13.50000000 5.50000000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 12.50000000 30.00000000 31.50000000 18.40000000 7.60000000

7 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 6.40000000 24.00000000 34.80000000 24.50000000 10.30000000

8 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 2.70000000 16.20000000 35.10000000 32.40000000 13.60000000

9 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.80000000 8.40000000 30.60000000 42.70000000 17.50000000

10 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.10000000 2.40000000 19.50000000 56.00000000 22.00000000

14

4.3.4 Dice Pool • • • •10 9 8 7 6 5


2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000065.61000000 0.00000000 29.16000000 0.00000000 4.86000000 0.37000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000040.96000000 20.48000000 24.32000000 8.00000000 4.81000000 1.43000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000024.01000000 27.44000000 25.48000000 14.00000000 6.46000000 2.61000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000012.96000000 25.92000000 28.08000000 19.44000000 9.45000000 4.15000000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000006.25000000 20.00000000 29.00000000 24.80000000 13.66000000 6.29000000

7 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000002.56000000 12.80000000 26.56000000 29.60000000 19.21000000 9.27000000

8 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.81000000 6.48000000 20.52000000 32.40000000 26.46000000 13.33000000

9 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.16000000 2.24000000 12.08000000 30.80000000 36.01000000 18.71000000

10 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.01000000 0.32000000 3.88000000 21.44000000 48.70000000 25.65000000

4.3.5 Dice Pool • • • • •10 9 8 7 6 5


2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 59.049000000.00000000 32.80500000 0.00000000 7.29000000 0.00000000 0.85600000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 32.7680000020.48000000 25.60000000 10.88000000 7.08000000 2.08100000 1.11100000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 16.8070000024.01000000 25.72500000 17.64000000 9.87000000 4.09200000 1.85600000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 7.7760000019.44000000 25.92000000 22.68000000 14.31000000 6.72300000 3.15100000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 3.1250000012.50000000 23.12500000 26.00000000 19.65000000 10.42400000 5.17600000

7 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 1.024000006.40000000 17.28000000 26.40000000 25.14000000 15.52500000 8.23100000

8 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.243000002.43000000 10.12500000 22.68000000 29.43000000 22.35600000 12.73600000

9 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.032000000.56000000 4.00000000 14.84000000 29.97000000 31.36700000 19.23100000

10 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.001000000.04000000 0.64500000 5.28000000 22.41000000 43.24800000 28.37600000

15

4.3.6 Dice Pool • • • • • •10 9 8 7 6 5


2 0.00000000 0.00000000 0.00000000 0.00000000 53.14410000 0.0000000035.42940000 0.00000000 9.84150000 0.00000000 1.45800000 0.12700000

3 0.00000000 0.00000000 0.00000000 0.00000000 26.21440000 19.6608000025.80480000 13.31200000 9.31200000 3.46080000 1.62410000 0.61110000

4 0.00000000 0.00000000 0.00000000 0.00000000 11.76490000 20.1684000024.49020000 19.89400000 13.00950000 6.60240000 2.79240000 1.27820000

5 0.00000000 0.00000000 0.00000000 0.00000000 4.66560000 13.9968000022.16160000 23.32800000 17.98200000 10.59480000 4.87890000 2.39230000

6 0.00000000 0.00000000 0.00000000 0.00000000 1.56250000 7.5000000016.87500000 23.50000000 22.53750000 15.67200000 8.09960000 4.25340000

7 0.00000000 0.00000000 0.00000000 0.00000000 0.40960000 3.0720000010.21440000 19.84000000 24.98400000 21.42000000 12.79050000 7.26950000

8 0.00000000 0.00000000 0.00000000 0.00000000 0.07290000 0.874800004.51980000 13.12200000 23.44950000 26.63280000 19.29960000 12.02860000

9 0.00000000 0.00000000 0.00000000 0.00000000 0.00640000 0.134400001.19520000 5.82400000 16.78200000 28.73640000 27.95090000 19.37070000

10 0.00000000 0.00000000 0.00000000 0.00000000 0.00010000 0.004800000.09660000 1.04800000 6.52950000 22.78080000 39.08040000 30.45980000

4.3.7 Dice Pool • • • • • • •10 9 8 7 6 5


2 0.00000000 0.00000000 0.00000000 47.82969000 0.00000000 37.200870000.00000000 12.40029000 0.00000000 2.29635000 0.00000000 0.27280000

3 0.00000000 0.00000000 0.00000000 20.97152000 18.35008000 25.2313600015.19616000 11.36128000 5.03104000 2.57656000 0.85457000 0.42743000

4 0.00000000 0.00000000 0.00000000 8.23543000 16.47086000 22.3533100020.84068000 15.53447000 9.21298000 4.57611000 1.87896000 0.89720000

5 0.00000000 0.00000000 0.00000000 2.79936000 9.79776000 17.9625600022.04496000 20.00376000 14.08428000 7.90398000 3.58263000 1.82071000

6 0.00000000 0.00000000 0.00000000 0.78125000 4.37500000 11.5937500019.25000000 22.35625000 19.20100000 12.57235000 6.37424000 3.49616000

7 0.00000000 0.00000000 0.00000000 0.16384000 1.43360000 5.6627200013.35040000 20.93504000 23.04400000 18.32460000 10.67925000 6.40655000

8 0.00000000 0.00000000 0.00000000 0.02187000 0.30618000 1.888110006.73596000 15.36003000 23.37174000 24.11451000 16.90632000 11.29528000

9 0.00000000 0.00000000 0.00000000 0.00128000 0.03136000 0.333760002.01488000 7.55272000 18.07708000 27.38386000 25.31291000 19.29215000

10 0.00000000 0.00000000 0.00000000 0.00001000 0.00056000 0.013510000.18256000 1.50101000 7.60648000 22.78563000 35.82048000 32.08976000

16

4.3.8 Dice Pool • • • • • • • •10 9 8 7 6 5


2 0.00000000 0.00000000 43.04672100 0.00000000 38.26375200 0.0000000014.88034800 0.00000000 3.30674400 0.00000000 0.45927000 0.04316500

3 0.00000000 0.00000000 16.77721600 16.77721600 24.11724800 16.5150720013.13177600 6.68057600 3.70048000 1.44441600 0.60076900 0.25523100

4 0.00000000 0.00000000 5.76480100 13.17668800 19.76503200 20.7062240017.27759600 11.64004800 6.59932000 3.15179200 1.29101400 0.62748500

5 0.00000000 0.00000000 1.67961600 6.71846400 13.99680000 19.5955200020.41200000 16.65619200 10.96804800 5.92920000 2.65558500 1.38857500

6 0.00000000 0.00000000 0.39062500 2.50000000 7.62500000 14.7000000020.03750000 20.46800000 16.20220000 10.13616000 5.06416600 2.87634900

7 0.00000000 0.00000000 0.06553600 0.65536000 2.99827200 8.3148800015.61548800 21.02016000 20.94534400 15.73840000 9.00454500 5.64201500

8 0.00000000 0.00000000 0.00656100 0.10497600 0.75232800 3.184272008.83839600 16.90113600 22.79340000 21.87777600 14.96669400 10.57446100

9 0.00000000 0.00000000 0.00025600 0.00716800 0.08883200 0.639744002.95433600 9.10380800 18.88600000 26.03899200 23.19580900 19.08505500

10 0.00000000 0.00000000 0.00000100 0.00006400 0.00180000 0.029120000.29750000 1.97971200 8.51384800 22.57120000 33.21351000 33.39324500

4.3.9 Dice Pool • • • • • • • • •10 9 8 7 6 5


2 0.00000000 38.74204890 0.00000000 38.74204890 0.00000000 17.218688400.00000000 4.46410440 0.00000000 0.74401740 0.00000000 0.08909200

3 0.00000000 13.42177280 15.09949440 22.64924160 17.30150400 14.568652808.30914560 4.94161920 2.19363840 0.99510480 0.34896010 0.17086630

4 0.00000000 4.03536070 10.37664180 17.04734010 19.76503200 18.2120652013.67417520 8.67529320 4.69012320 2.19400020 0.88856120 0.44140720

5 0.00000000 1.00776960 4.53496320 10.58158080 16.62819840 19.5255360018.07686720 13.61888640 8.51355360 4.46891580 1.98251550 1.06121350

6 0.00000000 0.19531250 1.40625000 4.85156250 10.65000000 16.6612500019.71900000 18.29205000 13.59576000 8.20676700 4.05289840 2.36914960

7 0.00000000 0.02621440 0.29491200 1.53354240 4.89062400 10.7034624017.04729600 20.44976640 18.87004800 13.56555240 7.64995250 4.96862950

8 0.00000000 0.00196830 0.03542940 0.28934010 1.41717600 4.6373148010.69180560 17.86254120 21.92948640 19.89601380 13.35557160 9.88335280

9 0.00000000 0.00005120 0.00161280 0.02280960 0.19084800 1.047571203.95277120 10.44529920 19.33837920 24.75505620 21.44486470 18.80073670

10 0.00000000 0.00000010 0.00000720 0.00023130 0.00435840 0.053226000.43888320 2.46490440 9.26616960 22.22969580 31.08504800 34.45747600

17

4.3.10 Dice Pool • • • • • • • • • •10 9 8 7 6 5


2 34.86784401 0.00000000 38.74204890 0.00000000 19.37102445 0.000000005.73956280 0.00000000 1.11602610 0.00000000 0.14880348 0.01469026

3 10.73741824 13.42177280 20.97152000 17.61607680 15.64999680 9.834332166.24107520 3.07998720 1.50960960 0.59804240 0.23391697 0.10625183

4 2.82475249 8.07072140 14.41200250 18.28265460 18.40618605 15.1908388810.62874680 6.38556240 3.34135410 1.52980520 0.61651228 0.31086330

5 0.60466176 3.02330880 7.81021440 13.60488960 17.76193920 18.3666009615.54694560 11.00148480 6.59730420 3.38153940 1.48853781 0.81257347

6 0.09765625 0.78125000 3.00781250 7.40625000 13.07578125 17.5890000018.69975000 16.08660000 11.37089250 6.66873200 3.26251276 1.95376274

7 0.01048576 0.13107200 0.76349440 2.75251200 6.88005120 12.6597120017.77390080 19.47763200 16.90622160 11.72976200 6.53808673 4.37706951

8 0.00059049 0.01180980 0.10825650 0.60229980 2.27043405 6.1316481612.23757720 18.36555120 20.91275010 18.13722840 11.99254572 9.22930858

9 0.00001024 0.00035840 0.00569600 0.05429760 0.34538880 1.542938884.96075680 11.57466240 19.53240660 23.55135020 19.96241653 18.46971755

10 0.00000001 0.00000080 0.00002890 0.00062160 0.00883245 0.086904960.60291960 2.94242880 9.88239570 21.81887840 29.31397756 35.34301122

4.4 Successes by Dice Pool by Difficulty

4.4.1 Difficulty 2

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 90.00000000 0.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 81.00000000 0.00000000 18.00000000 1.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 72.90000000 0.00000000 24.30000000 0.00000000 2.80000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000065.61000000 0.00000000 29.16000000 0.00000000 4.86000000 0.37000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 59.049000000.00000000 32.80500000 0.00000000 7.29000000 0.00000000 0.85600000

6 0.00000000 0.00000000 0.00000000 0.00000000 53.14410000 0.0000000035.42940000 0.00000000 9.84150000 0.00000000 1.45800000 0.12700000

7 0.00000000 0.00000000 0.00000000 47.82969000 0.00000000 37.200870000.00000000 12.40029000 0.00000000 2.29635000 0.00000000 0.27280000

8 0.00000000 0.00000000 43.04672100 0.00000000 38.26375200 0.0000000014.88034800 0.00000000 3.30674400 0.00000000 0.45927000 0.04316500

9 0.00000000 38.74204890 0.00000000 38.74204890 0.00000000 17.218688400.00000000 4.46410440 0.00000000 0.74401740 0.00000000 0.08909200

10 34.86784401 0.00000000 38.74204890 0.00000000 19.37102445 0.000000005.73956280 0.00000000 1.11602610 0.00000000 0.14880348 0.01469026

18

4.4.2 Difficulty 3

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 80.00000000 10.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 64.00000000 16.00000000 17.00000000 3.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 51.20000000 19.20000000 21.60000000 4.90000000 3.10000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000040.96000000 20.48000000 24.32000000 8.00000000 4.81000000 1.43000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 32.7680000020.48000000 25.60000000 10.88000000 7.08000000 2.08100000 1.11100000

6 0.00000000 0.00000000 0.00000000 0.00000000 26.21440000 19.6608000025.80480000 13.31200000 9.31200000 3.46080000 1.62410000 0.61110000

7 0.00000000 0.00000000 0.00000000 20.97152000 18.35008000 25.2313600015.19616000 11.36128000 5.03104000 2.57656000 0.85457000 0.42743000

8 0.00000000 0.00000000 16.77721600 16.77721600 24.11724800 16.5150720013.13177600 6.68057600 3.70048000 1.44441600 0.60076900 0.25523100

9 0.00000000 13.42177280 15.09949440 22.64924160 17.30150400 14.568652808.30914560 4.94161920 2.19363840 0.99510480 0.34896010 0.17086630

10 10.73741824 13.42177280 20.97152000 17.61607680 15.64999680 9.834332166.24107520 3.07998720 1.50960960 0.59804240 0.23391697 0.10625183

4.4.3 Difficulty 4

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 70.00000000 20.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 49.00000000 28.00000000 18.00000000 5.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 34.30000000 29.40000000 23.10000000 9.20000000 4.00000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000024.01000000 27.44000000 25.48000000 14.00000000 6.46000000 2.61000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 16.8070000024.01000000 25.72500000 17.64000000 9.87000000 4.09200000 1.85600000

6 0.00000000 0.00000000 0.00000000 0.00000000 11.76490000 20.1684000024.49020000 19.89400000 13.00950000 6.60240000 2.79240000 1.27820000

7 0.00000000 0.00000000 0.00000000 8.23543000 16.47086000 22.3533100020.84068000 15.53447000 9.21298000 4.57611000 1.87896000 0.89720000

8 0.00000000 0.00000000 5.76480100 13.17668800 19.76503200 20.7062240017.27759600 11.64004800 6.59932000 3.15179200 1.29101400 0.62748500

9 0.00000000 4.03536070 10.37664180 17.04734010 19.76503200 18.2120652013.67417520 8.67529320 4.69012320 2.19400020 0.88856120 0.44140720

10 2.82475249 8.07072140 14.41200250 18.28265460 18.40618605 15.1908388810.62874680 6.38556240 3.34135410 1.52980520 0.61651228 0.31086330

19

4.4.4 Difficulty 5

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 60.00000000 30.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 36.00000000 36.00000000 21.00000000 7.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 21.60000000 32.40000000 27.00000000 13.50000000 5.50000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.0000000012.96000000 25.92000000 28.08000000 19.44000000 9.45000000 4.15000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 7.7760000019.44000000 25.92000000 22.68000000 14.31000000 6.72300000 3.15100000

6 0.00000000 0.00000000 0.00000000 0.00000000 4.66560000 13.9968000022.16160000 23.32800000 17.98200000 10.59480000 4.87890000 2.39230000

7 0.00000000 0.00000000 0.00000000 2.79936000 9.79776000 17.9625600022.04496000 20.00376000 14.08428000 7.90398000 3.58263000 1.82071000

8 0.00000000 0.00000000 1.67961600 6.71846400 13.99680000 19.5955200020.41200000 16.65619200 10.96804800 5.92920000 2.65558500 1.38857500

9 0.00000000 1.00776960 4.53496320 10.58158080 16.62819840 19.5255360018.07686720 13.61888640 8.51355360 4.46891580 1.98251550 1.06121350

10 0.60466176 3.02330880 7.81021440 13.60488960 17.76193920 18.3666009615.54694560 11.00148480 6.59730420 3.38153940 1.48853781 0.81257347

4.4.5 Difficulty 6

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 50.00000000 40.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 25.00000000 40.00000000 26.00000000 9.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 12.50000000 30.00000000 31.50000000 18.40000000 7.60000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000006.25000000 20.00000000 29.00000000 24.80000000 13.66000000 6.29000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 3.1250000012.50000000 23.12500000 26.00000000 19.65000000 10.42400000 5.17600000

6 0.00000000 0.00000000 0.00000000 0.00000000 1.56250000 7.5000000016.87500000 23.50000000 22.53750000 15.67200000 8.09960000 4.25340000

7 0.00000000 0.00000000 0.00000000 0.78125000 4.37500000 11.5937500019.25000000 22.35625000 19.20100000 12.57235000 6.37424000 3.49616000

8 0.00000000 0.00000000 0.39062500 2.50000000 7.62500000 14.7000000020.03750000 20.46800000 16.20220000 10.13616000 5.06416600 2.87634900

9 0.00000000 0.19531250 1.40625000 4.85156250 10.65000000 16.6612500019.71900000 18.29205000 13.59576000 8.20676700 4.05289840 2.36914960

10 0.09765625 0.78125000 3.00781250 7.40625000 13.07578125 17.5890000018.69975000 16.08660000 11.37089250 6.66873200 3.26251276 1.95376274

20

4.4.6 Difficulty 7

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 40.00000000 50.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 16.00000000 40.00000000 33.00000000 11.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 6.40000000 24.00000000 34.80000000 24.50000000 10.30000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000002.56000000 12.80000000 26.56000000 29.60000000 19.21000000 9.27000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 1.024000006.40000000 17.28000000 26.40000000 25.14000000 15.52500000 8.23100000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.40960000 3.0720000010.21440000 19.84000000 24.98400000 21.42000000 12.79050000 7.26950000

7 0.00000000 0.00000000 0.00000000 0.16384000 1.43360000 5.6627200013.35040000 20.93504000 23.04400000 18.32460000 10.67925000 6.40655000

8 0.00000000 0.00000000 0.06553600 0.65536000 2.99827200 8.3148800015.61548800 21.02016000 20.94534400 15.73840000 9.00454500 5.64201500

9 0.00000000 0.02621440 0.29491200 1.53354240 4.89062400 10.7034624017.04729600 20.44976640 18.87004800 13.56555240 7.64995250 4.96862950

10 0.01048576 0.13107200 0.76349440 2.75251200 6.88005120 12.6597120017.77390080 19.47763200 16.90622160 11.72976200 6.53808673 4.37706951

4.4.7 Difficulty 8

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 30.00000000 60.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 9.00000000 36.00000000 42.00000000 13.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 2.70000000 16.20000000 35.10000000 32.40000000 13.60000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.81000000 6.48000000 20.52000000 32.40000000 26.46000000 13.33000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.243000002.43000000 10.12500000 22.68000000 29.43000000 22.35600000 12.73600000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.07290000 0.874800004.51980000 13.12200000 23.44950000 26.63280000 19.29960000 12.02860000

7 0.00000000 0.00000000 0.00000000 0.02187000 0.30618000 1.888110006.73596000 15.36003000 23.37174000 24.11451000 16.90632000 11.29528000

8 0.00000000 0.00000000 0.00656100 0.10497600 0.75232800 3.184272008.83839600 16.90113600 22.79340000 21.87777600 14.96669400 10.57446100

9 0.00000000 0.00196830 0.03542940 0.28934010 1.41717600 4.6373148010.69180560 17.86254120 21.92948640 19.89601380 13.35557160 9.88335280

10 0.00059049 0.01180980 0.10825650 0.60229980 2.27043405 6.1316481612.23757720 18.36555120 20.91275010 18.13722840 11.99254572 9.22930858

21

4.4.8 Difficulty 9

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 20.00000000 70.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 4.00000000 28.00000000 53.00000000 15.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.80000000 8.40000000 30.60000000 42.70000000 17.50000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.16000000 2.24000000 12.08000000 30.80000000 36.01000000 18.71000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.032000000.56000000 4.00000000 14.84000000 29.97000000 31.36700000 19.23100000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.00640000 0.134400001.19520000 5.82400000 16.78200000 28.73640000 27.95090000 19.37070000

7 0.00000000 0.00000000 0.00000000 0.00128000 0.03136000 0.333760002.01488000 7.55272000 18.07708000 27.38386000 25.31291000 19.29215000

8 0.00000000 0.00000000 0.00025600 0.00716800 0.08883200 0.639744002.95433600 9.10380800 18.88600000 26.03899200 23.19580900 19.08505500

9 0.00000000 0.00005120 0.00161280 0.02280960 0.19084800 1.047571203.95277120 10.44529920 19.33837920 24.75505620 21.44486470 18.80073670

10 0.00001024 0.00035840 0.00569600 0.05429760 0.34538880 1.542938884.96075680 11.57466240 19.53240660 23.55135020 19.96241653 18.46971755

4.4.9 Difficulty 10

Dice 10 9 8 7 6 5Pool 4 3 2 1 0 Botch

1 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 0.00000000 10.00000000 80.00000000 10.00000000

2 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.00000000 1.00000000 16.00000000 66.00000000 17.00000000

3 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.00000000 0.10000000 2.40000000 19.50000000 56.00000000 22.00000000

4 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.000000000.01000000 0.32000000 3.88000000 21.44000000 48.70000000 25.65000000

5 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.001000000.04000000 0.64500000 5.28000000 22.41000000 43.24800000 28.37600000

6 0.00000000 0.00000000 0.00000000 0.00000000 0.00010000 0.004800000.09660000 1.04800000 6.52950000 22.78080000 39.08040000 30.45980000

7 0.00000000 0.00000000 0.00000000 0.00001000 0.00056000 0.013510000.18256000 1.50101000 7.60648000 22.78563000 35.82048000 32.08976000

8 0.00000000 0.00000000 0.00000100 0.00006400 0.00180000 0.029120000.29750000 1.97971200 8.51384800 22.57120000 33.21351000 33.39324500

9 0.00000000 0.00000010 0.00000720 0.00023130 0.00435840 0.053226000.43888320 2.46490440 9.26616960 22.22969580 31.08504800 34.45747600

10 0.00000001 0.00000080 0.00002890 0.00062160 0.00883245 0.086904960.60291960 2.94242880 9.88239570 21.81887840 29.31397756 35.34301122

22

Contents

1 Introduction 1

2 The probability function 2

3 C code for the calculation of probabilities 5

4 Probability tables 74.1 Success classes by Difficulty by Dice Pool . . . . . . . . . . . . . . . . . . . . . . . 7

4.1.1 Dice Pool • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.1.2 Dice Pool • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.1.3 Dice Pool • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.1.4 Dice Pool • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.1.5 Dice Pool • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84.1.6 Dice Pool • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.1.7 Dice Pool • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.1.8 Dice Pool • • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.1.9 Dice Pool • • • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . 94.1.10 Dice Pool • • • • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.2 Success classes by Dice Pool by Difficulty . . . . . . . . . . . . . . . . . . . . . . . 104.2.1 Difficulty 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2.2 Difficulty 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2.3 Difficulty 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2.4 Difficulty 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2.5 Difficulty 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.2.6 Difficulty 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.7 Difficulty 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.8 Difficulty 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.9 Difficulty 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Successes by Difficulty by Dice Pool . . . . . . . . . . . . . . . . . . . . . . . . . . 134.3.1 Dice Pool • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.3.2 Dice Pool • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.3.3 Dice Pool • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144.3.4 Dice Pool • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3.5 Dice Pool • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.3.6 Dice Pool • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3.7 Dice Pool • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.3.8 Dice Pool • • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.3.9 Dice Pool • • • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.3.10 Dice Pool • • • • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.4 Successes by Dice Pool by Difficulty . . . . . . . . . . . . . . . . . . . . . . . . . . 184.4.1 Difficulty 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.4.2 Difficulty 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.4.3 Difficulty 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.4.4 Difficulty 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.4.5 Difficulty 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.4.6 Difficulty 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.4.7 Difficulty 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.4.8 Difficulty 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.4.9 Difficulty 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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d10 Probability