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wiki:dice_probabilities

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Probabilities

The tables below show probabilities for outcomes when rolling six sided dice, as it pertains to the two most common forms of rolling dice:

  • Rolling hit dice against an opponent's offensive or defensive formula
  • Rolling your damage dice and summing the result to determine how much damage is dealt



Hit rolls

This section relates to the probability of rolling a four, five, or six when rolling x amount of dice. This is used with all offensive and defensive formulas

At least

This table shows the probabilities for rolling at least that many fours, fives, or sixes

Result1d62d63d64d65d66d67d68d69d610d6
150.0%75.0%87.5%93.8%96.9%98.4%99.2%99.6%99.8%100%
225.0%50.0%68.8%81.3%89.1%93.8%96.5%98.0%99.0%
312.5%31.3%50.0%65.6%77.3%85.5%91.0%94.5%
46.3%18.8%34.8%50.0%63.7%74.6%82.9%
53.1%10.9%22.7%36.3%50.0%62.3%
61.6%6.3%14.5%25.4%37.7%
70.8%3.5%9.0%17.2%
80.4%2.0%5.5%
90.2%1.1%
100.1%

Exact probability

This table shows the probabilities for rolling a specific number successful dice, or dice that roll a “4”,”5”, or “6”. The result column represents the number of successful dice. The remaining columns show the probability of rolling that many successful dice, given the respective amount of dice rolled

Result1d62d63d64d65d66d67d68d69d610d6
050.0%25.0%12.5%6.3%3.1%1.6%0.8%0.4%0.2%0.1%
150.0%50.0%37.5%25.0%15.6%9.4%5.5%3.1%1.8%1.0%
225.0%37.5%37.5%31.25%23.4%16.4%10.9%7.0%4.4%
312.5%25.0%31.3%31.3%27.3%21.9%16.4%11.7%
46.3%15.6%23.4%27.3%27.3%24.6%20.5%
53.1%9.4%16.4%21.9%24.6%24.6%
61.6%5.5%10.9%16.4%20.5%
70.8%3.1%7.0%11.7%
80.4%1.8%4.4%
90.2%1.0%
100.1%



Damage rolls, saves

This section relates to the probability of rolling a specific number when you add up the results of the dice rolled, which applies when rolling damage and when making saving throws

100% probability

The following table shows the probabilities for rolling a specific number, given different amounts of dice, with no filters

Result2d63d64d65d66d67d68d69d610d6
1
2 2.8%
3 5.5% 0.5%
4 8.3% 1.4% 0.08%
5 11.1% 2.8% 0.31% 0.01%
6 13.9% 4.6% 0.77% 0.06% 0.00%
7 16.7% 6.9% 1.54% 0.19% 0.01% 0.00%
8 13.9% 9.7% 2.70% 0.45% 0.05% 0.00% 0.00%
9 11.1% 11.6% 4.32% 0.90% 0.12% 0.01% 0.00% 0.00%
10 8.3% 12.5% 6.17% 1.62% 0.27% 0.03% 0.00% 0.00% 0.00%
11 5.5% 12.5% 8.02% 2.64% 0.54% 0.08% 0.01% 0.00% 0.00%
12 2.7% 11.6% 9.65% 3.92% 0.98% 0.17% 0.02% 0.00% 0.00%
13 - 9.7% 10.80% 5.40% 1.62% 0.32% 0.05% 0.00% 0.00%
14 - 6.9% 11.27% 6.94% 2.49% 0.60% 0.10% 0.01% 0.00%
15 - 4.6% 10.80% 8.37% 3.57% 1.00% 0.20% 0.03% 0.00%
16 - 2.8% 9.65% 9.45% 4.82% 1.58% 0.37% 0.06% 0.01%
17 - 1.4% 8.02% 10.03% 6.12% 2.34% 0.62% 0.12% 0.02%
18 - 0.5% 6.17% 10.03% 7.35% 3.27% 1.00% 0.23% 0.04%
19 - - 4.32% 9.45% 8.37% 4.33% 1.52% 0.39% 0.08%
20 - - 2.70% 8.37% 9.05% 5.45% 2.18% 0.64% 0.14%
21 - - 1.54% 6.94% 9.28% 6.55% 3.00% 0.98% 0.24%
22 - - 0.77% 5.40% 9.05% 7.50% 3.92% 1.45% 0.40%
23 - - 0.31% 3.92% 8.37% 8.20% 4.90% 2.04% 0.63%
24 - - 0.08% 2.64% 7.35% 8.58% 5.88% 2.75% 0.95%
25 - - - 1.62% 6.12% 8.58% 6.77% 3.56% 1.37%
26 - - - 0.90% 4.82% 8.20% 7.48% 4.44% 1.90%
27 - - - 0.45% 3.57% 7.50% 7.93% 5.32% 2.54%
28 - - - 0.19% 2.49% 6.55% 8.09% 6.15% 3.26%
29 - - - 0.06% 1.62% 5.45% 7.93% 6.84% 4.05%
30 - - - 0.01% 0.98% 4.33% 7.48% 7.35% 4.84%
31 - - - - 0.54% 3.27% 6.77% 7.61% 5.61%
32 - - - - 0.27% 2.34% 5.88% 7.61% 6.28%
33 - - - - 0.12% 1.58% 4.90% 7.35% 6.82%
34 - - - - 0.05% 1.00% 3.92% 6.84% 7.15%
35 - - - - 0.01% 0.60% 3.00% 6.15% 7.27%
36 - - - - 0.00% 0.32% 2.18% 5.32% 7.15%
37 - - - - - 0.17% 1.52% 4.44% 6.82%
38 - - - - - 0.08% 1.00% 3.56% 6.28%
39 - - - - - 0.03% 0.62% 2.75% 5.61%
40 - - - - - 0.01% 0.37% 2.04% 4.84%
41 - - - - - 0.00% 0.20% 1.45% 4.05%
42 - - - - - 0.00% 0.10% 0.98% 3.26%
43 - - - - - - 0.05% 0.64% 2.54%
44 - - - - - - 0.02% 0.39% 1.90%
45 - - - - - - 0.01% 0.23% 1.37%
46 - - - - - - 0.00% 0.12% 0.95%
47 - - - - - - 0.00% 0.06% 0.63%
48 - - - - - - 0.00% 0.03% 0.40%
49 - - - - - - - 0.01% 0.24%
50 - - - - - - - 0.00% 0.14%
51 - - - - - - - 0.00% 0.08%
52 - - - - - - - 0.00% 0.04%
53 - - - - - - - 0.00% 0.02%
54 - - - - - - - 0.00% 0.01%
55 - - - - - - - - 0.00%
56 - - - - - - - - 0.00%
57 - - - - - - - - 0.00%
58 - - - - - - - - 0.00%
59 - - - - - - - - 0.00%
60 - - - - - - - - 0.00%
Result2d63d64d65d66d67d68d69d610d6



99% Probability

This is the same table as above, but with anything that is below a 1% chance filtered out for readability

Result2d63d64d65d66d67d68d69d610d6
1
2 2.8%
3 5.5%
4 8.3% 1.4%
5 11.1% 2.8%
6 13.9% 4.6%
7 16.7% 6.9% 1.54%
8 13.9% 9.7% 2.70%
9 11.1% 11.6% 4.32%
10 8.3% 12.5% 6.17% 1.62%
11 5.5% 12.5% 8.02% 2.64%
12 2.7% 11.6% 9.65% 3.92%
13 - 9.7% 10.80% 5.40% 1.62%
14 - 6.9% 11.27% 6.94% 2.49%
15 - 4.6% 10.80% 8.37% 3.57% 1.00%
16 - 2.8% 9.65% 9.45% 4.82% 1.58%
17 - 1.4% 8.02% 10.03% 6.12% 2.34%
18 - - 6.17% 10.03% 7.35% 3.27% 1.00%
19 - - 4.32% 9.45% 8.37% 4.33% 1.52%
20 - - 2.70% 8.37% 9.05% 5.45% 2.18%
21 - - 1.54% 6.94% 9.28% 6.55% 3.00%
22 - - - 5.40% 9.05% 7.50% 3.92% 1.45%
23 - - - 3.92% 8.37% 8.20% 4.90% 2.04%
24 - - - 2.64% 7.35% 8.58% 5.88% 2.75%
25 - - - 1.62% 6.12% 8.58% 6.77% 3.56% 1.37%
26 - - - - 4.82% 8.20% 7.48% 4.44% 1.90%
27 - - - - 3.57% 7.50% 7.93% 5.32% 2.54%
28 - - - - 2.49% 6.55% 8.09% 6.15% 3.26%
29 - - - - 1.62% 5.45% 7.93% 6.84% 4.05%
30 - - - - - 4.33% 7.48% 7.35% 4.84%
31 - - - - - 3.27% 6.77% 7.61% 5.61%
32 - - - - - 2.34% 5.88% 7.61% 6.28%
33 - - - - - 1.58% 4.90% 7.35% 6.82%
34 - - - - - 1.00% 3.92% 6.84% 7.15%
35 - - - - - - 3.00% 6.15% 7.27%
36 - - - - - - 2.18% 5.32% 7.15%
37 - - - - - - 1.52% 4.44% 6.82%
38 - - - - - - 1.00% 3.56% 6.28%
39 - - - - - - - 2.75% 5.61%
40 - - - - - - - 2.04% 4.84%
41 - - - - - - - 1.45% 4.05%
42 - - - - - - - - 3.26%
43 - - - - - - - - 2.54%
44 - - - - - - - - 1.90%
45 - - - - - - - - 1.37%
Result2d63d64d65d66d67d68d69d610d6



At least probability

This table tells you the probability of rolling at least the number in the “At Least” column, when you sum the result of varying numbers of dice

At Least2d63d64d65d66d67d68d69d610d6
2 100.0%
3 97.22% 100.0%
4 91.67% 99.54% 100.0%
5 83.33% 98.15% 99.92% 100.0%
6 72.22% 95.37% 99.61% 99.99% 100.0%
7 58.33% 90.74% 98.84% 99.92% 100.0% 100.0%
8 41.67% 83.80% 97.30% 99.73% 99.98% 100.0% 100.0%
9 27.78% 74.07% 94.60% 99.28% 99.94% 100.0% 100.0% 100.0%
10 16.67% 62.50% 90.28% 98.38% 99.82% 99.99% 100.0% 100.0% 100.0%
11 8.33% 50.00% 84.10% 96.76% 99.55% 99.96% 100.0% 100.0% 100.0%
12 2.78% 37.50% 76.08% 94.12% 99.01% 99.88% 99.99% 100.0% 100.0%
13 - 25.93% 66.44% 90.20% 98.03% 99.72% 99.97% 100.0% 100.0%
14 - 16.2% 55.63% 84.80% 96.41% 99.39% 99.92% 99.99% 100.0%
15 - 9.26% 44.37% 77.85% 93.92% 98.79% 99.82% 99.98% 100.0%
16 - 4.63% 33.56% 69.48% 90.35% 97.79% 99.62% 99.95% 100.0%
17 - 1.85% 23.92% 60.03% 85.54% 96.21% 99.26% 99.89% 99.99%
18 - 0.46% 15.90% 50.00% 79.42% 93.88% 98.63% 99.76% 99.97%
19 - - 9.72% 39.97% 72.06% 90.61% 97.63% 99.54% 99.93%
20 - - 5.4% 30.52% 63.69% 86.28% 96.11% 99.15% 99.85%
21 - - 2.7% 22.15% 54.64% 80.83% 93.93% 98.51% 99.71%
22 - - 1.16% 15.20% 45.36% 74.28% 90.93% 97.53% 99.47%
23 - - 0.39% 9.80% 36.31% 66.78% 87.02% 96.08% 99.06%
24 - - 0.08% 5.88% 27.94% 58.58% 82.11% 94.04% 98.43%
25 - - - 3.24% 20.58% 50.00% 76.23% 91.29% 97.48%
26 - - - 1.62% 14.46% 41.42% 69.46% 87.72% 96.10%
27 - - - 0.72% 9.65% 33.22% 61.98% 83.28% 94.20%
28 - - - 0.27% 6.08% 25.72% 54.05% 77.96% 91.66%
29 - - - 0.08% 3.59% 19.17% 45.95% 71.81% 88.40%
30 - - - 0.01% 1.97% 13.72% 38.02% 64.96% 84.35%
31 - - - - 0.99% 9.39% 30.54% 57.61% 79.50%
32 - - - - 0.45% 6.12% 23.77% 50.00% 73.89%
33 - - - - 0.18% 3.79% 17.89% 42.39% 67.60%
34 - - - - 0.06% 2.21% 12.98% 35.04% 60.79%
35 - - - - 0.02% 1.21% 9.07% 28.19% 53.63%
36 - - - - 0.00% 0.61% 6.07% 22.04% 46.37%
37 - - - - - 0.30% 3.90% 16.70% 39.2%
38 - - - - - 0.10% 2.40% 12.30% 32.4%
39 - - - - - 0% 1.40% 8.70% 26.1%
40 - - - - - 0% 0.7% 6.00% 20.5%
41 - - - - - 0% 0.4% 3.90% 15.7%
42 - - - - - 0% 0.2% 2.50% 11.6%
43 - - - - - - 0.1% 1.5% 8.3%
44 - - - - - - 0% 0.9% 5.8%
45 - - - - - - 0% 0.5% 3.9%
46 - - - - - - 0% 0.2% 2.5%
47 - - - - - - 0% 0.1% 1.6%
48 - - - - - - 0% 0% 0.9%
49 - - - - - - - 0% 0.5%
50 - - - - - - - 0% 0.3%
51 - - - - - - - 0% 0.1%
52 - - - - - - - 0% 0.1%
53 - - - - - - - 0% 0%
54 - - - - - - - 0% 0%
55 - - - - - - - - 0%
56 - - - - - - - - 0%
57 - - - - - - - - 0%
58 - - - - - - - - 0%
59 - - - - - - - - 0%
60 - - - - - - - - 0%
At Least2d63d64d65d66d67d68d69d610d6



Character creation

When creating a character, you assign dice to each ability. You get one point per “5” or “6” you roll, and you roll twice and keep the better result. Below you can find two tables to help you decide how many dice to spend

The table below gives the range of likely range of numbers you will roll given x number of dice rolled. Your chances of rolling a number within the range is above 90%

Dice RolledLikely OutcomesAverage Score
6d6 1-4 2.6
7d6 2-5 3.0
8d6 2-5 3.4
9d6 2-6 3.8
10d6 2-6 4.2
11d6 3-7 4.5
12d6 3-7 4.9
13d6 3-7 5.3
14d6 4-8 5.7
15d6 4-9 6.0
16d6 4-9 6.4
17d6 4-9 6.8
18d6 5-10 7.1
19d6 5-10 7.5
20d6 5-10 7.8
21d6 5-11 8.2
22d6 6-11 8.6
23d6 6-11 8.9
24d6 6-11 9.3


Exact probability

The table below gives the exact probability of rolling each score, with chances above 10% in bold

Dice12345678910+ Average Score
6d611.6%34.0%34.7%15.5%3.3% 0.3% 2.6
7d66.6% 25.6%35.8%22.8%7.5% 1.3% 0.1% 3.0
8d63.7% 18.1%33.0%28.2%12.9%3.4% 0.5% 3.4
9d62.0% 12.2%28.1%30.8%18.6%6.7% 1.5% 0.2% 3.8
10d61.1% 7.9% 22.3%30.6%23.4%10.8%3.2% 0.6% 0.1% 4.2
11d60.6% 4.9% 16.9%28.2%26.5%15.3%5.8% 1.5% 0.2% 4.5
12d60.3% 3.0% 12.2%24.4%27.7%19.5%9.1% 2.9% 0.7% 0.1% 4.9
13d60.1% 1.8% 8.5% 20.1%27.1%22.8%12.8%5.1% 1.4% 0.3% 5.3
14d60.1% 1.0% 5.7% 15.8%25.0%24.8%16.5%7.7% 2.7% 0.8% 5.7
15d6 0.6% 3.7% 11.9%21.9%25.3%19.6%10.8%4.4% 1.7% 6.0
16d6 0.3% 2.4% 8.7% 18.4%24.5%21.9%14.0%6.6% 3.2% 6.4
17d6 0.2% 1.5% 6.2% 14.9%22.6%23.2%16.9%9.1% 5.4% 6.8
18d6 0.1% 0.9% 4.3% 11.7%20.0%23.3%19.3%11.9%8.5% 7.1
19d6 0.1% 0.6% 2.9% 8.8% 17.1%22.4%21.0%14.6%12.5% 7.5
20d6 0.3% 1.9% 6.5% 14.1%20.8%21.8%16.9%17.5% 7.8
21d6 0.2% 1.3% 4.7% 11.3%18.6%21.7%18.8%23.4% 8.2
22d6 0.1% 0.8% 3.3% 8.9% 16.1%20.8%20.0%30.0% 8.6
23d6 0.1% 0.5% 2.3% 6.7% 13.5%19.3%20.5%37.0% 8.9
24d6 0.3% 1.6% 5.0% 11.0%17.4%20.3%44.3% 9.3


At least

This table conveys the probability of getting a score of at least x given the number of dice rolled

Dice Rolled123456789
6d6 99.2% 87.7% 53.7% 19.0% 3.5% 0.3%
7d6 99.7% 93.1% 67.4% 31.7% 8.8% 1.4% 0.1%
8d6 99.8% 96.2% 78.1% 45.0% 16.8% 3.9% 0.5%
9d6 99.9% 98.0% 85.8% 57.7% 26.9% 8.3% 1.6% 0.2%
10d6 98.9% 91.1% 68.7% 38.1% 14.7% 3.9% 0.7% 0.1%
11d6 99.4% 94.5% 77.7% 49.4% 22.9% 7.6% 1.8% 0.3%
12d6 99.7% 96.7% 84.5% 60.1% 32.4% 12.8% 3.7% 0.8%
13d6 99.9% 98.1% 89.6% 69.5% 42.4% 19.6% 6.8% 1.8%
14d6 99.9% 98.9% 93.2% 77.4% 52.4% 27.7% 11.2% 3.5%
15d6 99.4% 95.6% 83.7% 61.8% 36.5% 16.9% 6.1%
16d6 99.6% 97.2% 88.5% 70.1% 45.6% 23.7% 9.7%
17d6 99.8% 98.3% 92.1% 77.2% 54.6% 31.4% 14.5%
18d6 99.9% 99.0% 94.7% 83.0% 63.0% 39.7% 20.4%
19d6 99.4% 96.5% 87.6% 70.5% 48.1% 27.1%
20d6 99.6% 97.7% 91.2% 77.0% 56.2% 34.5%
21d6 99.8% 98.5% 93.8% 82.5% 63.9% 42.2%
22d6 99.9% 99.1% 95.8% 86.9% 70.8% 50.0%
23d6 99.4% 97.1% 90.4% 76.9% 57.6%
24d6 99.6% 98.1% 93.1% 82.0% 64.7%



Psychometry

The following table conveys the percentage of rolling “At least” the value in the column heading given the number of dice rolled, when rolling for Psychometry's “match the GM” rolling mechanic

Dice RolledAt least 5At least 6At least 7Exactly 8
8d6 54.3% 22.8% 4.4% 0.2%
9d6 65.7% 34.1% 9.6% 0.9%
10d6 74.3% 45.1% 16.6% 2.4%
11d6 80.8% 54.5% 23.6% 4.5%
12d6 85.8% 63.0% 32.0% 7.9%
13d6 89.3% 70.0% 39.9% 11.9%
14d6 91.9% 75.6% 47.2% 16.6%
15d6 93.9% 80.2% 53.9% 21.6%
16d6 95.4% 84.2% 60.3% 27.3%
17d6 96.5% 87.1% 65.5% 32.6%
18d6 97.3% 89.5% 70.2% 38.1%
wiki/dice_probabilities.1486198541.txt.gz · Last modified: 2017/02/04 03:55 by caleymccready