By Jack "The Ghoul" Gulick.

**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 |

**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 |

**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% |

**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% |

**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% |

**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% |

**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% |

**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.