Probability Math

From Edge of Darkness Wiki

You do not have permission to edit this page, for the following reason:

You can view and copy the source of this page:

{{TOC right}} ==Methods of Calculating== Probabilities for a single die can be calculated directly. (See below for discussion of these probabilities in the new World of Darkness; in the old World of Darkness, they are obvious.) Subsequent probabilities were calculated using a spreadsheet program, using the following formulae: (nWoD) '''P'''(at least '''S''' successes on '''n''' dice)='''P'''(at least '''S''' successes on '''n'''-1 dice)+sum_{'''s'''=0}^{'''S'''-1} '''P'''(at least '''s''' successes on '''n'''-1 dice)'''P'''(exactly '''S-s''' successes on 1 die) (oWoD) '''P'''(at least '''S''' successes on '''n''' dice)=sum_{'''s'''=-1}^{1} '''P'''(at least '''S-s''' successes on '''n'''-1 dice)'''P'''(exactly '''s''' successes on 1 die) (Rolling a 1 is considered to be rolling -1 successes.) ==New World of Darkness== ===Some simple formulas=== A few things are simple enough to calculate on the fly. If all rolls of '''r''' or better are rerolled, then the average number of successes obtained when rolling '''n''' dice is 3'''n'''/('''r'''-1). (In particular, if 10s and only 10s are rerolled, then the average is 3'''n'''/(10-1)='''n'''/3, and if no numbers are rerolled, then the average is 3'''n'''/(11-1)=0.3'''n'''. When using formulas, the easiest way to describe the no-rerolls situation is to call it "11-again" rather than "none-again".) If failures are rerolled once ("rote actions"), then the average number of successes is 5.1'''n'''/('''r'''-1) (usually 0.51'''n''', under 10-again). For non-rote actions, the probability of rolling no successes on '''n''' dice is 0.7^'''n''', and so the probability of rolling at least one success is 1-0.7^'''n'''. For rote actions, failures may be rerolled once, and so the probability of rolling at least one success is 1-0.7^(2'''n'''). With one die, the probability of rolling at least 1 success is 0.51 (rote actions) or 0.3 (anything else). The probability of rolling at least '''S''' successes on one die under '''r'''-again, for '''S'''>1, is (11-'''r''')/3 * 0.3 * P(at least '''S'''-1 successes) = 0.3*(1.1-'''r'''/10)^('''S'''-1) (for non-rote actions) or 0.51*(1.1-'''r'''/10)^('''S'''-1) (for rote actions). ===10 again=== This chart shows the percentage chance of rolling at least '''S''' successes with a pool of '''n''' dice under the normal New World of Darkness rules, as described in [[World of Darkness Sourcebook|nWoD]], page 32. {|border="1" cellpadding="3" cellspacing="1" style="border-collapse: collapse;" | '''Successes''' ! style="background-color:#264d73" | 1 ! style="background-color:#264d73" | 2 ! style="background-color:#264d73" | 3 ! style="background-color:#264d73" | 4 ! style="background-color:#264d73" | 5 ! style="background-color:#264d73" | 6 ! style="background-color:#264d73" | 7 ! style="background-color:#264d73" | 8 ! style="background-color:#264d73" | 9 ! style="background-color:#264d73" | 10 ! style="background-color:#264d73" | 11 ! style="background-color:#264d73" | 12 |- ! style="background-color:#264d73" |1 die |30.00 |3.00 |0.30 |0.03 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |2 dice |51.00 |13.20 |2.13 |0.29 |0.03 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |3 dice |65.70 |26.01 |6.73 |1.30 |0.21 |0.03 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |4 dice |75.99 |38.94 |13.80 |3.64 |0.77 |0.14 |0.02 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |5 dice |83.19 |50.77 |22.53 |7.56 |2.02 |0.45 |0.09 |0.01 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |6 dice |88.23 |61.00 |32.03 |13.00 |4.23 |1.14 |0.27 |0.05 |0.01 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |7 dice |91.76 |69.52 |41.57 |19.66 |7.53 |2.40 |0.65 |0.15 |0.03 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |8 dice |94.23 |76.44 |50.65 |27.14 |11.91 |4.38 |1.38 |0.38 |0.09 |0.02 |0.00 |0.00 |- ! style="background-color:#264d73" |9 dice |95.96 |81.95 |58.94 |35.02 |17.27 |7.17 |2.56 |0.79 |0.22 |0.05 |0.01 |0.00 |- ! style="background-color:#264d73" |10 dice |97.17 |86.27 |66.27 |42.93 |23.39 |10.81 |4.30 |1.50 |0.46 |0.13 |0.03 |0.00 |- ! style="background-color:#264d73" |11 dice |98.02 |89.63 |72.61 |50.57 |30.01 |15.25 |6.70 |2.58 |0.88 |0.27 |0.07 |0.01 |- ! style="background-color:#264d73" |12 dice |98.61 |92.20 |77.97 |57.72 |36.89 |20.37 |9.78 |4.12 |1.54 |0.52 |0.16 |0.04 |- ! style="background-color:#264d73" |13 dice |99.03 |94.17 |82.44 |64.24 |43.79 |26.01 |13.52 |6.19 |2.53 |0.92 |0.31 |0.09 |- ! style="background-color:#264d73" |14 dice |99.32 |95.65 |86.11 |70.07 |50.51 |32.02 |17.87 |8.83 |3.89 |1.54 |0.55 |0.18 |- ! style="background-color:#264d73" |15 dice |99.52 |96.77 |89.08 |75.18 |56.89 |38.20 |22.73 |12.03 |5.69 |2.43 |0.94 |0.33 |} ==9 again== This chart shows the percentage chance of rolling at least '''S''' successes with a pool of '''n''' dice under the 9-again system, as described [[World of Darkness Sourcebook|nWoD]], page 134. {|border="1" cellpadding="3" cellspacing="1" style="border-collapse: collapse;" | '''Successes''' ! style="background-color:#264d73" | 1 ! style="background-color:#264d73" | 2 ! style="background-color:#264d73" | 3 ! style="background-color:#264d73" | 4 ! style="background-color:#264d73" | 5 ! style="background-color:#264d73" | 6 ! style="background-color:#264d73" | 7 ! style="background-color:#264d73" | 8 ! style="background-color:#264d73" | 9 ! style="background-color:#264d73" | 10 ! style="background-color:#264d73" | 11 ! style="background-color:#264d73" | 12 |- ! style="background-color:#264d73" |1 die |30.00 |6.00 |1.20 |0.24 |0.04 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |2 dice |51.00 |17.40 |4.92 |1.27 |0.31 |0.07 |0.01 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |3 dice |65.70 |30.42 |11.26 |3.63 |1.07 |0.29 |0.07 |0.02 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |4 dice |75.99 |43.06 |19.54 |7.58 |2.63 |0.84 |0.25 |0.07 |0.02 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |5 dice |83.19 |54.38 |28.86 |13.03 |5.20 |1.89 |0.64 |0.20 |0.06 |0.01 |0.00 |0.00 |- ! style="background-color:#264d73" |6 dice |88.23 |64.03 |38.44 |19.69 |8.88 |3.62 |1.36 |0.47 |0.15 |0.05 |0.01 |0.00 |- ! style="background-color:#264d73" |7 dice |91.76 |71.99 |47.71 |27.17 |13.62 |6.15 |2.54 |0.98 |0.35 |0.12 |0.04 |0.01 |- ! style="background-color:#264d73" |8 dice |94.23 |78.42 |56.28 |35.05 |19.26 |9.52 |4.30 |1.80 |0.70 |0.26 |0.09 |0.03 |- ! style="background-color:#264d73" |9 dice |95.96 |83.51 |63.94 |42.95 |25.58 |13.70 |6.70 |3.03 |1.28 |0.51 |0.19 |0.07 |- ! style="background-color:#264d73" |10 dice |97.17 |87.49 |70.61 |50.58 |32.32 |18.61 |9.78 |4.75 |2.15 |0.91 |0.37 |0.14 |- ! style="background-color:#264d73" |11 dice |98.02 |90.56 |76.28 |57.72 |39.22 |24.11 |13.53 |7.01 |3.38 |1.53 |0.65 |0.26 |- ! style="background-color:#264d73" |12 dice |98.61 |92.92 |81.04 |64.24 |46.08 |30.01 |17.88 |9.83 |5.03 |2.41 |1.09 |0.47 |- ! style="background-color:#264d73" |13 dice |99.03 |94.71 |84.96 |70.07 |52.69 |36.15 |22.75 |13.22 |7.15 |3.62 |1.73 |0.78 |- ! style="background-color:#264d73" |14 dice |99.32 |96.06 |88.16 |75.17 |58.93 |42.36 |28.01 |17.13 |9.75 |5.20 |2.61 |1.24 |- ! style="background-color:#264d73" |15 dice |99.52 |97.08 |90.73 |79.58 |64.68 |48.48 |33.54 |21.50 |12.84 |7.19 |3.79 |1.89 |} ==8 again== This chart shows the percentage chance of rolling at least '''S''' successes with a pool of '''n''' dice under the 8-again system, as described [[World of Darkness Sourcebook|nWoD]], page 134. {|border="1" cellpadding="3" cellspacing="1" style="border-collapse: collapse;" | '''Successes''' ! style="background-color:#264d73" | 1 ! style="background-color:#264d73" | 2 ! style="background-color:#264d73" | 3 ! style="background-color:#264d73" | 4 ! style="background-color:#264d73" | 5 ! style="background-color:#264d73" | 6 ! style="background-color:#264d73" | 7 ! style="background-color:#264d73" | 8 ! style="background-color:#264d73" | 9 ! style="background-color:#264d73" | 10 ! style="background-color:#264d73" | 11 ! style="background-color:#264d73" | 12 |- ! style="background-color:#264d73" |1 die |30.00 |9.00 |2.70 |0.81 |0.24 |0.07 |0.02 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |2 dice |51.00 |21.60 |8.37 |3.07 |1.09 |0.37 |0.12 |0.04 |0.01 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |3 dice |65.70 |34.83 |16.30 |7.04 |2.87 |1.12 |0.42 |0.15 |0.05 |0.02 |0.00 |0.00 |- ! style="background-color:#264d73" |4 dice |75.99 |47.17 |25.56 |12.60 |5.79 |2.52 |1.05 |0.42 |0.16 |0.06 |0.02 |0.00 |- ! style="background-color:#264d73" |5 dice |83.19 |57.98 |35.29 |19.41 |9.88 |4.73 |2.16 |0.94 |0.40 |0.16 |0.06 |0.02 |- ! style="background-color:#264d73" |6 dice |88.23 |67.05 |44.82 |27.03 |15.02 |7.82 |3.86 |1.82 |0.82 |0.36 |0.15 |0.06 |- ! style="background-color:#264d73" |7 dice |91.76 |74.47 |53.71 |35.03 |21.03 |11.78 |6.23 |3.14 |1.52 |0.71 |0.32 |0.14 |- ! style="background-color:#264d73" |8 dice |94.23 |80.39 |61.72 |43.04 |27.63 |16.53 |9.32 |5.00 |2.56 |1.26 |0.60 |0.28 |- ! style="background-color:#264d73" |9 dice |95.96 |85.06 |68.72 |50.74 |34.56 |21.94 |13.11 |7.43 |4.02 |2.09 |1.05 |0.51 |- ! style="background-color:#264d73" |10 dice |97.17 |88.70 |74.71 |57.93 |41.57 |27.83 |17.53 |10.46 |5.95 |3.25 |1.71 |0.87 |- ! style="background-color:#264d73" |11 dice |98.02 |91.49 |79.75 |64.48 |48.45 |34.02 |22.47 |14.06 |8.39 |4.79 |2.63 |1.40 |- ! style="background-color:#264d73" |12 dice |98.61 |93.63 |83.91 |70.31 |55.00 |40.31 |27.83 |18.19 |11.33 |6.75 |3.87 |2.14 |- ! style="background-color:#264d73" |13 dice |99.03 |95.25 |87.31 |75.41 |61.13 |46.56 |33.44 |22.77 |14.76 |9.15 |5.46 |3.13 |- ! style="background-color:#264d73" |14 dice |99.32 |96.47 |90.06 |79.80 |66.73 |52.61 |39.19 |27.70 |18.64 |12.00 |7.42 |4.42 |- ! style="background-color:#264d73" |15 dice |99.52 |97.38 |92.26 |83.54 |71.77 |58.36 |44.94 |32.87 |22.91 |15.27 |9.78 |6.03 |} ==Rote actions== This chart shows the percentage chance of rolling at least '''S''' successes with a pool of '''n''' dice under the rote-action system, as described [[World of Darkness Sourcebook|nWoD]], page 134. {|border="1" cellpadding="3" cellspacing="1" style="border-collapse: collapse;" | '''Successes''' ! style="background-color:#264d73" | 1 ! style="background-color:#264d73" | 2 ! style="background-color:#264d73" | 3 ! style="background-color:#264d73" | 4 ! style="background-color:#264d73" | 5 ! style="background-color:#264d73" | 6 ! style="background-color:#264d73" | 7 ! style="background-color:#264d73" | 8 ! style="background-color:#264d73" | 9 ! style="background-color:#264d73" | 10 ! style="background-color:#264d73" | 11 ! style="background-color:#264d73" | 12 |- ! style="background-color:#264d73" |1 die |51.00 |5.10 |0.51 |0.05 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |2 dice |75.99 |31.00 |5.44 |0.77 |0.10 |0.01 |0.00 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |3 dice |88.23 |55.17 |20.89 |4.70 |0.83 |0.13 |0.01 |0.00 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |4 dice |94.23 |72.63 |40.12 |14.88 |3.82 |0.79 |0.14 |0.02 |0.00 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |5 dice |97.17 |83.94 |57.83 |29.52 |10.93 |3.04 |0.69 |0.13 |0.02 |0.00 |0.00 |0.00 |- ! style="background-color:#264d73" |6 dice |98.61 |90.83 |71.84 |45.36 |21.99 |8.17 |2.41 |0.59 |0.12 |0.02 |0.00 |0.00 |- ! style="background-color:#264d73" |7 dice |99.32 |94.87 |81.93 |59.87 |35.36 |16.56 |6.18 |1.89 |0.49 |0.11 |0.02 |0.00 |- ! style="background-color:#264d73" |8 dice |99.66 |97.17 |88.76 |71.80 |49.06 |27.52 |12.57 |4.72 |1.49 |0.41 |0.10 |0.02 |- ! style="background-color:#264d73" |9 dice |99.83 |98.46 |93.18 |80.89 |61.57 |39.75 |21.42 |9.61 |3.63 |1.17 |0.33 |0.08 |- ! style="background-color:#264d73" |10 dice |99.92 |99.17 |95.94 |87.43 |72.08 |51.93 |31.99 |16.69 |7.39 |2.80 |0.92 |0.27 |- ! style="background-color:#264d73" |11 dice |99.96 |99.55 |97.63 |91.94 |80.36 |63.03 |43.27 |25.62 |13.02 |5.70 |2.17 |0.73 |- ! style="background-color:#264d73" |12 dice |99.98 |99.76 |98.63 |94.94 |86.57 |72.49 |54.29 |35.72 |20.46 |10.18 |4.42 |1.69 |- ! style="background-color:#264d73" |13 dice |99.99 |99.87 |99.22 |96.88 |91.03 |80.12 |64.34 |46.20 |29.29 |16.30 |7.97 |3.44 |- ! style="background-color:#264d73" |14 dice |99.99 |99.93 |99.56 |98.11 |94.14 |85.99 |72.97 |56.31 |38.92 |23.89 |12.98 |6.25 |- ! style="background-color:#264d73" |15 dice |99.99 |99.96 |99.75 |98.87 |96.24 |90.36 |80.05 |65.52 |48.71 |32.54 |19.41 |10.32 |} ==Other systems== For rolls involving a Gangrel's mental traits, please see the tables under difficulty 8. ===8 dice=== {|border="1" cellpadding="3" cellspacing="1" style="border-collapse: collapse;" |- ! style="background-color:#264d73" | Difficulty ! style="background-color:#264d73" | 2 ! style="background-color:#264d73" | 3 ! style="background-color:#264d73" | 4 ! style="background-color:#264d73" | 5 ! style="background-color:#264d73" | 6 ! style="background-color:#264d73" | 7 ! style="background-color:#264d73" | 8 ! style="background-color:#264d73" | 9 ! style="background-color:#264d73" | 10 |- ! style="background-color:#264d73" | 1 success |99.49 |99.14 |98.08 |95.95 |92.05 |85.35 |74.45 |57.71 |33.39 |- ! style="background-color:#264d73" | 2 successes |99.49 |97.69 |94.92 |90.02 |81.92 |69.61 |52.58 |31.68 |10.82 |- ! style="background-color:#264d73" | 3 successes |96.19 |93.99 |88.33 |79.05 |65.72 |48.66 |29.78 |12.79 |2.30 |- ! style="background-color:#264d73" | 4 successes |96.19 |87.31 |76.69 |62.40 |45.25 |27.64 |12.88 |3.69 |0.32 |- ! style="background-color:#264d73" | 5 successes |81.31 |74.18 |59.41 |41.99 |25.21 |12.03 |4.04 |0.73 |0.03 |- ! style="background-color:#264d73" | 6 successes |81.31 |57.67 |38.70 |22.39 |10.51 |3.71 |0.86 |0.09 |0.00 |- ! style="background-color:#264d73" | 7 successes |43.04 |33.55 |18.94 |8.39 |2.89 |0.72 |0.11 |0.00 |0.00 |- ! style="background-color:#264d73" | 8 successes |43.04 |16.77 |5.76 |1.67 |0.39 |0.06 |0.00 |0.00 |0.00 |} {{Help}}[[Category:Information]]

Return to Probability Math.