Feng Shui Die Roll Probabilities

By Jack "The Ghoul" Gulick.

Feng Shui Closed Roll

Scheme:
Roll 1d6 then subtract the result of a second d6 from that roll. Exactly equivalent in every way to 2d6-7.
Mean:
0
Variance:
5.83333
roll percent chance in 36
-5 2.778% 1
-4 5.556% 2
-3 8.333% 3
-2 11.111% 4
-1 13.889% 5
0 16.667% 6
1 13.889% 5
2 11.111% 4
3 8.333% 3
4 5.556% 2
5 2.778% 1

Feng Shui Closed Roll with Fortune Die

Scheme:
As Feng Shui Closed Roll plus an extra positive d6 and so 3d6-7.
Mean:
3.5
Variance:
8.75
roll percent chance in 216
-4 0.463% 1
-3 1.389% 3
-2 2.778% 6
-1 4.630% 10
0 6.944% 15
1 9.722% 21
2 11.574% 25
3 12.500% 27
4 12.500% 27
5 11.574% 25
6 9.722% 21
7 6.944% 15
8 4.630% 10
9 2.778% 6
10 1.389% 3
11 0.463% 1

Feng Shui Open Roll

Scheme:
As Feng Shui Closed Roll, only use open-ended d6 where a 6 on either die means roll again and add 6 to the result. Most certainly not equivalent to two open d6 minus 7.
Mean:
0
Variance:
21.28

(Note: This distribution is symmetric about 0. Therefore, negative p[roll] values have the same probability as like positive values. Thus, the probability of a roll of -7 is the same as for a roll of 7 or 1.9048%.)

(p[success] is the chance of rolling the given number or higher and is the chance of succeeding given you need to roll at least the number shown. For negative rolls, p[success] is equal to 100% minus the listed p[success] for -roll+1. Thus, p[success] for -3 is 100%- p[success] for 4 or 100% - 15.7143% = 84.2857%.)

roll p[+/-roll] p[success] roll p[+/-roll] p[success]
0 14.2857% 57.1429% 21 0.0309% 0.1036%
1 11.4286% 42.8571% 22 0.0198% 0.0728%
2 9.0476% 31.4286% 23 0.0088% 0.0529%
3 6.6667% 22.3810% 24 0.0110% 0.0441%
4 4.2857% 15.7143% 25 0.0088% 0.0331%
5 1.9048% 11.4286% 26 0.0070% 0.0243%
6 2.3810% 9.5238% 27 0.0051% 0.0173%
7 1.9048% 7.1429% 28 0.0033% 0.0121%
8 1.5079% 5.2381% 29 0.0015% 0.0088%
9 1.1111% 3.7302% 30 0.0018% 0.0073%
10 0.7143% 2.6190% 31 0.0015% 0.0055%
11 0.3175% 1.9048% 32 0.0012% 0.0040%
12 0.3968% 1.5873% 33 0.0009% 0.0029%
13 0.3175% 1.1905% 34 0.0006% 0.0020%
14 0.2513% 0.8730% 35 0.0002% 0.0015%
15 0.1852% 0.6217% 36 0.0003% 0.0012%
16 0.1190% 0.4365% 37 0.0002% 0.0009%
17 0.0529% 0.3175% 38 0.0002% 0.0007%
18 0.0661% 0.2646% 39 0.0001% 0.0005%
19 0.0529% 0.1984% 40 0.0001% 0.0003%
20 0.0419% 0.1455% 41+ 0.0002%

Feng Shui Open Roll with Fortune Die

Scheme:
As Feng Shui Open Roll, only add an additional positive d6. Note that the extra d6 (the Fortune Die) is not open-ended.
Mean:
3.5
Variance:
24.19667

(Note: This distribution is symmetric about 3.5. Therefore, rolls of 3 or less have the same p[roll] values as rolls of 4 or more. The p[roll] values for a roll of 3 or less are equal to the listed p[roll] values for 7 minus roll. Thus, the probability of a roll of -4 is the same as for a roll of 7 - (-4) = 11 or 1.5873%.) (p[success] is the chance of rolling the given number or higher and is the chance of succeeding given you need to roll at least the number shown. For rolls under 3, p[success] is equal to 100% minus the listed p[success] for 8 minus roll. Thus, p[success] for 2 is 100%- p[success] for 6 or 100% - 30.1587% = 69.8413%.)

roll p[roll] p[success] roll p[roll] p[success]
3 10.3175% 60.3175% 25 0.0276% 0.1029%
4 10.3175% 50.0000% 26 0.0202% 0.0753%
5 9.5238% 39.6825% 27 0.0144% 0.0551%
6 7.9365% 30.1587% 28 0.0101% 0.0407%
7 5.9524% 22.2222% 29 0.0073% 0.0306%
8 4.3651% 16.2698% 30 0.0061% 0.0233%
9 3.1085% 11.9048% 31 0.0046% 0.0171%
10 2.1825% 8.7963% 32 0.0034% 0.0126%
11 1.5873% 6.6138% 33 0.0024% 0.0092%
12 1.3228% 5.0265% 34 0.0017% 0.0068%
13 0.9921% 3.7037% 35 0.0012% 0.0051%
14 0.7275% 2.7116% 36 0.0010% 0.0039%
15 0.5181% 1.9841% 37 0.0008% 0.0029%
16 0.3638% 1.4660% 38 0.0006% 0.0021%
17 0.2646% 1.1023% 39 0.0004% 0.0015%
18 0.2205% 0.8377% 40 0.0003% 0.0011%
19 0.1653% 0.6173% 41 0.0002% 0.0009%
20 0.1213% 0.4519% 42 0.0002% 0.0006%
21 0.0863% 0.3307% 43 0.0001% 0.0005%
22 0.0606% 0.2443% 44 0.0001% 0.0003%
23 0.0441% 0.1837% 45 0.0001% 0.0003%
24 0.0367% 0.1396% 46+ 0.0002%

Feng Shui Alternate Gambler Schtick ("It's Not Luck, It's Skill")

Scheme:
As Feng Shui Open Roll, except the positive and negative dice are selected after being rolled, so the positive is always the larger result rolled. Note that using this schtick costs a Fortune point, so this table should be compared to the w/ Fortune Die table.
Mean:
3.2
Variance:
11.04

Note that this table is not symmetric at all; results less than 0 are not possible.

roll p[roll] p[success] roll p[roll] p[success]
0 14.2857% 100.0000% 23 0.0176% 0.1058%
1 22.8571% 85.7143% 24 0.0220% 0.0882%
2 18.0952% 62.8571% 25 0.0176% 0.0661%
3 13.3333% 44.7619% 26 0.0140% 0.0485%
4 8.5714% 31.4286% 27 0.0103% 0.0345%
5 3.8095% 22.8571% 28 0.0066% 0.0243%
6 4.7619% 19.0476% 29 0.0029% 0.0176%
7 3.8095% 14.2857% 30 0.0037% 0.0147%
8 3.0159% 10.4762% 31 0.0029% 0.0110%
9 2.2222% 7.4603% 32 0.0023% 0.0081%
10 1.4286% 5.2381% 33 0.0017% 0.0058%
11 0.6349% 3.8095% 34 0.0011% 0.0040%
12 0.7937% 3.1746% 35 0.0005% 0.0029%
13 0.6349% 2.3810% 36 0.0006% 0.0024%
14 0.5026% 1.7460% 37 0.0005% 0.0018%
15 0.3704% 1.2434% 38 0.0004% 0.0013%
16 0.2381% 0.8730% 39 0.0003% 0.0010%
17 0.1058% 0.6349% 40 0.0002% 0.0007%
18 0.1323% 0.5291% 41 0.0001% 0.0005%
19 0.1058% 0.3968% 42 0.0001% 0.0004%
20 0.0838% 0.2910% 43 0.0001% 0.0003%
21 0.0617% 0.2072% 44 0.0001% 0.0002%
22 0.0397% 0.1455% 45+ 0.0002%

Feng Shui Fortune Schtick (Double or Nothing)

Scheme:
As Feng Shui Open Roll, except roll 2 positive and 2 negative dice.
Mean:
0
Variance:
42.56

(Note: This distribution is symmetric about 0. Therefore, negative p[roll] values have the same probability as like positive values. Thus, the probability of a roll of -7 is the same as for a roll of 7 or 2.7229%.) (p[success] is the chance of rolling the given number or higher and is the chance of succeeding given you need to roll at least the number shown. For negative rolls, p[success] is equal to 100% minus the listed p[success] for -roll+1. Thus, p[success] for -3 is 100%- p[success] for 4 or 100% - 25.6583% = 74.3417%.)

roll p[+/-roll] p[success] roll p[+/-roll] p[success]
0 7.8950% 53.9475% 23 0.0564% 0.2414%
1 7.5755% 46.0525% 24 0.0430% 0.1850%
2 6.8758% 38.4770% 25 0.0329% 0.1420%
3 5.9429% 31.6012% 26 0.0254% 0.1091%
4 4.9305% 25.6583% 27 0.0199% 0.0837%
5 3.9927% 20.7278% 28 0.0155% 0.0638%
6 3.3113% 16.7350% 29 0.0115% 0.0483%
7 2.7229% 13.4237% 30 0.0087% 0.0368%
8 2.2321% 10.7008% 31 0.0066% 0.0281%
9 1.8159% 8.4687% 32 0.0051% 0.0215%
10 1.4525% 6.6528% 33 0.0039% 0.0164%
11 1.1205% 5.2003% 34 0.0031% 0.0125%
12 0.8845% 4.0798% 35 0.0023% 0.0094%
13 0.6972% 3.1953% 36 0.0017% 0.0071%
14 0.5531% 2.4981% 37 0.0013% 0.0054%
15 0.4402% 1.9451% 38 0.0010% 0.0041%
16 0.3472% 1.5049% 39 0.0008% 0.0031%
17 0.2626% 1.1577% 40 0.0006% 0.0024%
18 0.2028% 0.8951% 41 0.0004% 0.0018%
19 0.1568% 0.6922% 42 0.0003% 0.0014%
20 0.1223% 0.5355% 43 0.0002% 0.0010%
21 0.0963% 0.4131% 44 0.0002% 0.0008%
22 0.0754% 0.3168% 45+ 0.0006%

Feng Shui Fortune Schtick (Double or Nothing) With a Fortune Die

Scheme:
As Feng Shui Double or Nothing, but add one additional (closed) positive d6.
Mean:
3.5
Variance:
45.47667

(Note: This distribution is symmetric about 3.5. Therefore, rolls of 3 or less have the same p[roll] values as rolls of 4 or more. The p[roll] values for a roll of 3 or less are equal to the listed p[roll] values for 7 minus roll. Thus, the probability of a roll of -4 is the same as for a roll of 7 - (-4) = 11 or 2.5879%.) (p[success] is the chance of rolling the given number or higher and is the chance of succeeding given you need to roll at least the number shown. For rolls under 3, p[success] is equal to 100% minus the listed p[success] for 8 minus roll. Thus, p[success] for 2 is 100%- p[success] for 6 or 100% - 36.0774% = 63.9226%.)

roll p[roll] p[success] roll p[roll] p[success]
3 7.1234% 57.1234% 28 0.0422% 0.1797%
4 7.1234% 50.0000% 29 0.0322% 0.1375%
5 6.7992% 42.8766% 30 0.0247% 0.1053%
6 6.2021% 36.0774% 31 0.0190% 0.0806%
7 5.4381% 29.8753% 32 0.0146% 0.0616%
8 4.6294% 24.4372% 33 0.0112% 0.0470%
9 3.8554% 19.8078% 34 0.0086% 0.0358%
10 3.1676% 15.9524% 35 0.0065% 0.0273%
11 2.5879% 12.7848% 36 0.0049% 0.0208%
12 2.1092% 10.1969% 37 0.0038% 0.0158%
13 1.7047% 8.0877% 38 0.0029% 0.0121%
14 1.3671% 6.3830% 39 0.0022% 0.0092%
15 1.0873% 5.0158% 40 0.0017% 0.0070%
16 0.8580% 3.9286% 41 0.0013% 0.0053%
17 0.6738% 3.0706% 42 0.0010% 0.0040%
18 0.5308% 2.3968% 43 0.0007% 0.0030%
19 0.4172% 1.8660% 44 0.0006% 0.0023%
20 0.3271% 1.4488% 45 0.0004% 0.0017%
21 0.2553% 1.1217% 46 0.0003% 0.0013%
22 0.1980% 0.8664% 47 0.0002% 0.0010%
23 0.1527% 0.6684% 48 0.0002% 0.0008%
24 0.1183% 0.5157% 49 0.0001% 0.0006%
25 0.0917% 0.3974% 50 0.0001% 0.0004%
26 0.0711% 0.3056% 51 0.0001% 0.0003%
27 0.0549% 0.2346% 52+ 0.0002%

Feng Shui Open Roll with Two Fortune Dice

Scheme:
As Feng Shui Open Roll, only add two additional positive d6. Note that the extra 2d6 (the Fortune Dice) are not open-ended. Note also that the rules usually forbid multiple Fortune Dice on any one roll, but some unusual effects or house rules allow them.
Mean:
7.0
Variance:
27.11333

(Note: This distribution is symmetric about 7. Therefore, rolls of 6 or less have the same p[roll] values as rolls of 8 or more. The p[roll] values for a roll of 6 or less are equal to the listed p[roll] values for 14 minus roll. Thus, the probability of a roll of -2 is the same as for a roll of 14 - (-2) = 16 or 1.2217%.) (p[success] is the chance of rolling the given number or higher and is the chance of succeeding given you need to roll at least the number shown. For rolls under 7, p[success] is equal to 100% minus the listed p[success] for 15 minus roll. Thus, p[success] for 2 is 100%- p[success] for 13 or 100% - 3.0864% = 88.1944%.)

roll p[roll] p[success] roll p[roll] p[success]
7 9.2593% 54.6296% 29 0.0255% 0.0996%
8 8.9286% 45.3704% 30 0.0194% 0.0740%
9 8.0688% 36.4418% 31 0.0143% 0.0547%
10 6.8673% 28.3730% 32 0.0105% 0.0404%
11 5.5115% 21.5057% 33 0.0077% 0.0299%
12 4.1887% 15.9943% 34 0.0057% 0.0222%
13 3.0864% 11.8056% 35 0.0043% 0.0166%
14 2.2597% 8.7191% 36 0.0032% 0.0123%
15 1.6534% 6.4594% 37 0.0024% 0.0091%
16 1.2217% 4.8060% 38 0.0017% 0.0067%
17 0.9186% 3.5843% 39 0.0013% 0.0050%
18 0.6981% 2.6657% 40 0.0009% 0.0037%
19 0.5144% 1.9676% 41 0.0007% 0.0028%
20 0.3766% 1.4532% 42 0.0005% 0.0021%
21 0.2756% 1.0766% 43 0.0004% 0.0015%
22 0.2036% 0.8010% 44 0.0003% 0.0011%
23 0.1531% 0.5974% 45 0.0002% 0.0008%
24 0.1164% 0.4443% 46 0.0002% 0.0006%
25 0.0857% 0.3279% 47 0.0001% 0.0005%
26 0.0628% 0.2422% 48 0.0001% 0.0003%
27 0.0459% 0.1794% 49 0.0001% 0.0003%
28 0.0339% 0.1335% 46+ 0.0002%

Last modified: March 25th, 2000; please send comments to durrell@innocence.com.