# Dice Probabilities
[date goes here] | by Old Man Umby
[cover goes here]
## d10+dX Pool
This system utilizes a dice pool consisting of an Action Die (d10) - which increases at each new tier - plus an Ability Die.
The top-end of the Median Range changes with each tier. However, the odds begin to diminish outside the Median Range but by mere decimal places with each difference-in-die.
The Tier Levels represent human and superhuman capabilities. Those tiers could be ignored or removed if you do not need "Superior" abilities in the system. Bear in mind that the abilities of many animals and machines could lie within the Superior or better tiers.
| Rank/Tier | Dice Pool | Median Range | Total Range |
| --------: | --------- | :----------: | :---------: |
| Feeble | 1d4 | 01-04 | 01-04 |
| | 1D6 | 01-06 | 01-06 |
| | 1d8 | 01-08 | 01-08 |
| | 1d10 | 01-10 | 01-10 |
| | 1d12 | 01-12 | 01-12 |
| | - | - | - |
| Ordinary | 1d10+1d4 | 05-11 | 02-14 |
| Capable | 1d10+1d6 | 07-11 | 02-16 |
| Talented | 1d10+1d8 | 09-11 | 02-18 |
| Gifted | 1d10+1d10 | 10-12 | 02-20 |
| Elite | 1d10+1d12 | 11-13 | 02-22 |
| | - | - | - |
| Superior | 2d10+1d4 | 13-14 | 03-24 |
| | 2d10+1d6 | 14-15 | 03-26 |
| | 2d10+1d8 | 15-16 | 03-28 |
| | 2d10+1d10 | 16-17 | 03-30 |
| | 2d10+1d12 | 17-18 | 03-32 |
| | - | - | - |
| Legendary | 3d10+1d4 | 19 | 04-34 |
| | 3d10+1d6 | 20 | 04-36 |
| | 3d10+1d8 | 21 | 04-38 |
| | 3d10+1d10 | 22 | 04-40 |
| | 3d10+1d12 | 23 | 04-42 |
| | - | - | - |
| Unearthly | 4d10+1d4 | 24-25 | 05-44 |
| | 4d10+1d6 | 25-26 | 05-46 |
| | 4d10+1d8 | 26-27 | 05-48 |
| | 4d10+1d10 | 27-28 | 05-50 |
| | 4d10+1d12 | 28-29 | 05-52 |
| | - | - | - |
| Mythical | 5d10+1d4 | 30 | 06-54 |
| | 5d10+1d6 | 31 | 06-56 |
| | 5d10+1d8 | 32 | 06-58 |
| | 5d10+1d10 | 33 | 06-60 |
| | 5d10+1d12 | 34 | 06-62 |
## d20+dX Pool
This system utilizes a dice pool consisting of an Action Die (d20), plus a Tier Die (d20 or d10), plus an Ability Die.
Utilizing a d20 Action Die - over a d10, for example - allows for a greater range of possible numbers for each roll of the pool, thus allowing "Ordinary" characters to better mingle with "Superior" (or above) characters.
The top-end of the Median Range changes with each tier. However, the odds begin to diminish outside the Median Range but by mere decimal places with each difference-in-die.
The Tier Levels represent human and superhuman capabilities. Those tiers could be ignored or removed if you do not need "Superior" abilities in the system. Bear in mind that the abilities of many animals and machines could lie within the Superior or better tiers.
| Rank/Tier | Dice Pool | Median Range | Total Range |
| --------: | -------------- | :----------: | :---------: |
| Feeble | 1d20 | 01-20 | 01-20 |
| | - | - | - |
| Ordinary | 1d20+1d4 | 05-21 | 02-24 |
| Capable | 1d20+1d6 | 07-21 | 02-26 |
| Talented | 1d20+1d8 | 09-21 | 02-28 |
| Gifted | 1d20+1d10 | 11-21 | 02-30 |
| Elite | 1d20+1d12 | 13-21 | 02-32 |
| | - | - | - |
| Superior | 1d20+1d10+1d4 | 15-22 | 03-34 |
| | 1d20+1d10+1d6 | 17-22 | 03-36 |
| | 1d20+1d10+1d8 | 19-22 | 03-38 |
| | 1d20+1d10+1d10 | 21-22 | 03-40 |
| | 1d20+1d10+1d12 | 22-23 | 03-42 |
| | - | - | - |
| Legendary | 1d20+1d20+1d4 | 23-24 | 03-44 |
| | 1d20+1d20+1d6 | 24-25 | 03-46 |
| | 1d20+1d20+1d8 | 25-26 | 03-48 |
| | 1d20+1d20+1d10 | 26-27 | 03-50 |
| | 1d20+1d20+1d12 | 27-28 | 03-52 |
| | - | - | - |
| Unearthly | 2d20+1d10+1d4 | 29 | 04-54 |
| | 2d20+1d10+1d6 | 30 | 04-56 |
| | 2d20+1d10+1d8 | 31 | 04-58 |
| | 2d20+1d10+1d10 | 32 | 04-60 |
| | 2d20+1d10+1d12 | 33 | 04-62 |
| | - | - | - |
| Mythical | 3d20+1d4 | 34 | 04-64 |
| | 3d20+1d6 | 35 | 04-66 |
| | 3d20+1d8 | 36 | 04-68 |
| | 3d20+1d10 | 37 | 04-70 |
| | 3d20+1d12 | 38 | 04-72 |
## d6 Pool
In this system you roll 1d6 plus the character's Ability Rank (the table below takes this into account); this is the character's unadjusted dice pool.
### Sample Skill Ranks
| Proficiency | d6 TN |
| ----------- | ----- |
| Layman | 6 |
| Adept | 5+ |
| Expert | 4+ |
| Master | 3+ |
***Successes.*** From the dice pool, the average number of dice to roll 5+ (Adept), top three, in order ("=" means equal chances). Interestingly, the number of d6 successfully reaching the target numbers equals 30% (+/- 10%) compared to the number of dice rolled.
The Tier Levels represent human and superhuman capabilities. Those tiers could be ignored or removed if you do not need "Superior" abilities in the system. Bear in mind that the abilities of many animals and machines could lie within the Superior or better tiers.
| Rank/Tier | Dice Pool | Adept 5+ | Successes | Expert 4+ | Master 3+ |
| --------: | :-------: | :------: | :-------: | :-------: | :-------: |
| Feeble | 1d6 Only | 33% | 1 | 50% | 67% |
| Ordinary | 2d6 | 56% | 1,2 | 75% | 89% |
| Capable | 3d6 | 70% | 1,2,3 | 88% | 96% |
| Talented | 4d6 | 80% | 1,2,3 | 93% | 99% |
| Gifted | 5d6 | 87% | 1=2,3 | 97% | 99+% |
| Elite | 6d6 | 91% | 2,1,3 | 98% | 99+% |
| | - | - | - | - | - |
| Superior | 7d6 | 94% | 2,3,1 | 99% | 99+% |
| | 8d6 | 96% | 2=3,4 | 99+% | 99+% |
| | 9d6 | 97% | 3,2,4 | 99+% | 99+% |
| | 10d6 | 98% | 3,4,2 | 99+% | 99+% |
| | 11d6 | 99% | 3=4,5 | 99+% | 99+% |
| | - | - | - | - | - |
| Legendary | 12d6 | 99+% | 4,3,5 | 99+% | 99+% |
| | 13d6 | 99+% | 4,5,3 | 99+% | 99+% |
| | 14d6 | 99+% | 4=5,6 | 99+% | 99+% |
| | 15d6 | 99+% | 5,4,6 | 99+% | 99+% |
| | 16d6 | 99+% | 5,6,4 | 99+% | 99+% |
| | - | - | - | - | - |
| Unearthly | 17d6 | 99+% | 5=6,7 | 99+% | 99+% |
| | 18d6 | 99+% | 6,5,7 | 99+% | 99+% |
| | 19d6 | 99+% | 6,7,5 | 99+% | 99+% |
| | 20d6 | 99+% | 6=7,8 | 99+% | 99+% |
| | 21d6 | 99+% | 7,6,8 | 99+% | 99+% |
| | - | - | - | - | - |
| Mythical | 22d6 | 99+% | 7,8,6 | 99+% | 99+% |
| | 23d6 | 99+% | 7=8,9 | 99+% | 99+% |
| | 24d6 | 99+% | 8,7,9 | 99+% | 99+% |
| | 25d6 | 99+% | 8,9,7 | 99+% | 99+% |
| | 26d6 | 99+% | 8=9,10 | 99+% | 99+% |
## d10 Pool
In this system you roll 1d6 plus the character's Ability Rank (the table below takes this into account); this is the character's unadjusted dice pool. However, for our purposes, the die range is read from 0-9 rather than 1-10 as typical, but the odds and the percentages are the same (1 in 10 for each side of the die).
Reading a d10 in this manner allows for correct "die-flips" and improved "exploding-die" results should those mechanics be utilized. Together, the d10 is the most versatile solo-die to use for dice pool mechanics.
### Sample Skill Ranks
| Proficiency | D9 TN |
| :---------: | :---: |
| Layman | 9 |
| Novice | 8+ |
| Adept | 7+ |
| Specialist | 6+ |
| Expert | 5+ |
| Veteran | 4+ |
| Master | 3+ |
| Legend | 2+ |
| Paragon | 1+ |
***Successes.*** From the dice pool, the average number of dice to roll 7+ (Adept), top three, in order ("=" means equal chances). Interestingly, the number of d10 successfully reaching the target numbers equals 40% (+/- 10%) compared to the number of dice rolled.
***UNK***. The server could not compute.
The Tier Levels represent human and superhuman capabilities. Those tiers could be ignored or removed if you do not need "Superior" abilities in the system. Bear in mind that the abilities of many animals and machines could lie within the Superior or better tiers.
| Rank/Tier | Dice Pool | Novice 8+ | Adept 7+ | Successes | Expert 5+ | Master 3+ |
| --------: | :-------: | :-------: | :------: | :-------: | :-------: | :-------: |
| Feeble | 1d10 Only | 30% | 40% | 1 | 60% | 90% |
| Ordinary | 2d10 | 51% | 64% | 1,2 | 84% | 96% |
| Capable | 3d10 | 66% | 78% | 1,2,3 | 94% | 99% |
| Talented | 4d10 | 76% | 87% | 1=2,3 | 97% | 99+% |
| Gifted | 5d10 | 83% | 92% | 2,1,3 | 99% | 99+% |
| Elite | 6d10 | 88% | 95% | 2,3,1 | 99+% | 99+% |
| | - | - | - | - | - | - |
| Superior | 7d10 | 92% | 97% | 3,2,4 | 99+% | 99+% |
| | 8d10 | 94% | 98% | 3,4,2 | 99+% | 99+% |
| | 9d10 | 96% | 99% | 3=4,5 | 99+% | 99+% |
| | 10d10 | 97% | 99+% | 4,3,5 | 99+% | 99+% |
| | 11d10 | 98% | 99+% | 4,5,3 | 99+% | 99+% |
| | - | - | - | - | - | - |
| Legendary | 12d10 | 99% | 99+% | 5,4,6 | 99+% | 99+% |
| | 13d10 | 99+% | 99+% | 5,6,4 | 99+% | 99+% |
| | 14d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 15d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 16d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | - | - | - | - | - | - |
| Unearthly | 17d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 18d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 19d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 20d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 21d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | - | - | - | - | - | - |
| Mythical | 22d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 23d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 24d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 25d10 | 99+% | 99+% | UNK | 99+% | 99+% |
| | 26d10 | 99+% | 99+% | UNK | 99+% | 99+% |