Table of Contents

In some early brainstorming of one or more generic RPG systems, I developed my own set of attributes, skills and dice values (not to say that these are in any way innovative). Note that these concepts (attributes/skills, dice values) are à la carte and are not necessarily tied to each other.
Attributes and skills
Attributes in green are skill classes (i.e. skills are associated with the attribute).
Attributes (basic)
These are the innate characteristics that are not dependent on anything else (for our purposes).Name  Abbr.  Description  Component of (derived stats): 

Body  
STRENGTH  STR  Describes the body's ability to exert physical force (lift, push, pull, punch, swing, etc.). I.e. Muscle.  DEFENSE ENDURANCE RECOVERY ATHLETICS 
CONSTITUTION  CONS  Describes the body's internal health and immune system.  RECOVERY 
REFLEXES  REF  Describes the ability to quickly move parts of the body.  REACTION DODGE TAILING TECHNIQUE ATHLETICS AIM 
SPEED  SPD  Describes the max velocity of the whole body moving of its own power.  REACTION 
PHYSIQUE  PHYS  Describes the beauty of the body.  PRESENCE 
Mind  
INTELLIGENCE  INT  Describes the mind's absorption, retention, and application of knowledge. I.e. I.Q.  TRACKING/INVESTIGATION TECHNIQUE 
WILLPOWER  WILL  Describes the mind's ability to withstand influence (either external or internal). I.e. Mind over matter.  ENDURANCE 
CONCENTRATION  CONC  Describes the mind's ability to focus.  TECHNIQUE AIM 
PERCEPTION  PER  Describes the ability to notice and distinguish details of the environment and others.  TRACKING/INVESTIGATION TAILING AIM 
CHARISMA  CHAR  Describes the "beauty" or influential ability of personality.  PRESENCE 
Spirit  
CHI  Prowess of the metaphysical.  
LUCK  Prowess of positive chance. 
Attributes (derived)
These are the results (averages) of combined basic attributes.Name  Abbr.  Description  Average of: 

DEFENSE  DEF  Describes the body's ability to withstand the impacts of physical force.  STR 
ENDURANCE  END  Describes how long the body can sustain continued activity.  STR, WILL 
RECOVERY  REC  How quickly healing (at least physical healing) happens.  STR, CONS, END 
REACTION  REACT  Describes how quickly one responds to the situation.  REF, SPD 
*DODGE  Ability to get out of harm's way.  REF, REACT  
*TRACKING/INVESTIGATION  TRK/INV  The ability to find and analyze clues and artifacts and interpret the events that caused them.  INT, PER 
*TAILING  TAIL  Ability to follow without being noticed.  PER, REF 
TECHNIQUE  TECH  Describes the ability to perform vocational/professional skills.  INT, CONC, REF 
ATHLETICS  ATH  Describes the skills that the body can perform.  STR, END, REF 
AIM  Ability to point a projectile device such that the projectile hits the intended target.  PER, CONC, REF  
PRESENCE  PRE  Describes one's impact on others.  CHAR, PHYS 
* DODGE, TRK/INV, and TAIL are a special category of derived Attributes that are more aptly named "derived Skills". That is because they actually relate to specific actions/abilities (like skills) as opposed to other attributes which are more generic, umbrella descriptions of abilities.
Skills
Suggested list of skills associated with attributes.INT  PER  REF  TECH  ATH  AIM  PRE 

Gaming Species Cultures Organizations Languages Astrology Tactics Scholastic Locality Expert Navigation 
Conceal Hide Lip Reading 
Contortionist Automatic Cars Manual Cars Motorized Bikes Tanks Pickpocket Beast Riding Sleight of Hand Contemporary Piloting Rocket/Jet Pack Operation Powersuit Operation 
Forgery Survival Animal Handling Computer Programming Demolitions Disguise Reload Electronics Lockpicking Mechanics Medic Computer Security Electronics Security Surveillance Communications Systems Weaponsmith 
Brawling Melee Acrobatics Running Jumping Scaling/Climbing Swimming 
1Handed Gun 2Handed Gun Crossbow Bows Throw Shoulder Mounted Weapons Vehicle Weapons 
Bargain Command Convince (con, persuade, act, bribe) Intimidation Teach Wardrobe & Style Interrogation 
Dice values
This is a method of assigning attribute/skill values that equate to dice rolling resolutions. One of my goals was to find a use for the different multisided dice typically owned by an RPG'er.
The concept is that rolling for a particular attribute/skill would result in a value that is
Base (minimum) value + range (dice)
Base value is 0 to 20
Range is 1 to 4, 6, 8, 10, 12, or 20
Therefore an attribute/skill is represented as x + Dy (Example: 15 + D8 allows for values 1623).
Buying initial values or improvements would cost points in a points system (scalable).
Here is the first cost table I came up with ("back in the day"). Recent analysis has proven that these values are way off and unbalanced.
COST TABLE (wrong… do not use) 
D4  D6  D8  D10  D12  D20 

Initial cost (points)  Free  8  20  36  56  80 
Improvement cost (points)  N/A  8  12  16  20  24 
New method
Instead of using the arbitrary, unbalanced costs above, a system based on the average values of the ranges makes more sense. I.e. 6+D4 (which gives values 710) and 2+D12 (which gives values 314) both have the arithmetic mean of 8.5, so they should cost the same. The choice between the two is a player's preference (see http://forum.rpg.net/showthread.php?t=541218).
I've determined that the cost of a particular "offset range" to be calculated in one of two ways (with the same results)…
 arithmetic mean  2.5
 Example: 6+D4 and 2+D12 both have arithmetic mean of 8.5. 8.5  2.5 = 6, so they both cost 6.
 offset + die cost (See table below)
 Example: 6+D4 (6+0) and 2+D12 (2+4) both cost 6.
COST TABLE (NEW) 
D4  D6  D8  D10  D12  D20 

Initial cost (points)  0  1  2  3  4  8 
The next step… merging with attributes
The initial downfall of buying stats as dice described above is that it can't be (easily) utilized in the "derived" attributes described further above. (What's the average of D4 and D6? … D5?). So the next step is to not lock stats down into a single "offset range", but to stick to simple numbers… such as the common factor: cost!
So if we set the stat level equal to its cost (that is initial cost, for character creation), we could have a STR stat of 9. Then, when rolling for STR, the player can choose the offset range based on preference or optimal conditions. I.e. he could roll 9+D4 or 8+D6 or 7+D8 or 6+D10 or 5+D12 or 1+D20.
But how will he know which to roll?
Here's a table for looking up offset ranges based on stat level (cost):
D4  D6  D8  D10  D12  D20 
Level  +  Min  Max  +  Min  Max  +  Min  Max  +  Min  Max  +  Min  Max  +  Min  Max 
0  0  1  4  
1  1  2  5  0  1  6  
2  2  3  6  1  2  7  0  1  8  
3  3  4  7  2  3  8  1  2  9  0  1  10  
4  4  5  8  3  4  9  2  3  10  1  2  11  0  1  12  
5  5  6  9  4  5  10  3  4  11  2  3  12  1  2  13  
6  6  7  10  5  6  11  4  5  12  3  4  13  2  3  14  
7  7  8  11  6  7  12  5  6  13  4  5  14  3  4  15  
8  8  9  12  7  8  13  6  7  14  5  6  15  4  5  16  0  1  20 
9  9  10  13  8  9  14  7  8  15  6  7  16  5  6  17  1  2  21 
10  10  11  14  9  10  15  8  9  16  7  8  17  6  7  18  2  3  22 
11  11  12  15  10  11  16  9  10  17  8  9  18  7  8  19  3  4  23 
12  12  13  16  11  12  17  10  11  18  9  10  19  8  9  20  4  5  24 
13  13  14  17  12  13  18  11  12  19  10  11  20  9  10  21  5  6  25 
14  14  15  18  13  14  19  12  13  20  11  12  21  10  11  22  6  7  26 
15  15  16  19  14  15  20  13  14  21  12  13  22  11  12  23  7  8  27 
16  16  17  20  15  16  21  14  15  22  13  14  23  12  13  24  8  9  28 
17  17  18  21  16  17  22  15  16  23  14  15  24  13  14  25  9  10  29 
18  18  19  22  17  18  23  16  17  24  15  16  25  14  15  26  10  11  30 
19  19  20  23  18  19  24  17  18  25  16  17  26  15  16  27  11  12  31 
20  20  21  24  19  20  25  18  19  26  17  18  27  16  17  28  12  13  32 
21  20  21  26  19  20  27  18  19  28  17  18  29  13  14  33  
22  20  21  28  19  20  29  18  19  30  14  15  34  
23  20  21  30  19  20  31  15  16  35  
24  20  21  32  16  17  36  
25  17  18  37  
26  18  19  38  
27  19  20  39  
28  20  21  40 
Another way of looking at it
Here's another thought on how a player could choose what to roll…
 For a given roll, default to the roll with the largest die. This has the lowest minimum, but the highest maximum.
Level  Largest die/roll 

0  D4 
1  D6 
2  D8 
3  D10 
47  x + D12 (x = Level  4) 
8+  x + D20 (x = Level  8) 
 If a higher minimum is desired, the player can choose to downgrade the die size for an additional bonus of x, where x is the difference in (initial) die cost of the largest die and the downgraded die.
 Example: At Level 6, the default roll is 2+D12. The player can downgrade to a D6 for 3 additional bonus, thus rolling 5+D6.
 Example: At Level 12, the default roll is 4+D20. The player can downgrade to a D10 for 5 additional bonus, thus rolling 9+D10.
Strategic tips
Here are some useful tips for players if the Target Number (TN, a.k.a. difficulty, the number that must be met or exceeded to succeed) that one is rolling against is known:
 With penalty rules (see below)
 If $TN \leq Level+2$, roll smallest die for greatest % chance
 Without penalty rules
 If $TN \leq Level+1$, assume 100% success for Levels 020 only (for Levels 21+, roll smallest die for greatest % chance)
 If $TN = Level+2$, roll smallest die for greatest % chance
 If $TN = Level+3$, all rolls have 50% chance
 If $TN \geq Level+4$, roll largest die for greatest % chance
Bonus/Penalty
To allow some flexibility and the possibility to get numbers outside of a roll's defined range, Bonuses or Penalties may be applied to a roll. These are similar to the concepts of "Critical successes", "Exploding Dice", or "Critical failures". The method described here simply increases or decreases the value of the roll, to potentially make or miss the Target Number (TN, a.k.a. difficulty).
When rolling an Nsided die (with values 1N), rolling a 1 triggers a potential penalty roll, and rolling an N triggers a potential bonus roll. Specifically…
 Bonus: If an N is rolled, the player can roll the Msided bonus die for the stat level (see table below) if the TN has not yet been met.
 If an M is rolled on the bonus die, 1 is added to the original roll, and the bonus die is rerolled (adding 1 to the original roll total each time an M is rolled on the bonus die).
 If any other number is rolled on the bonus die, the bonus is over and the roll total is final.
 Penalty: If a 1 is rolled, the player must roll the penalty die for the stat level (see table below).
 If a 1 is rolled on the penalty die, 1 is subtracted from the original roll total, and the penalty die is rerolled (subtracting 1 from the original roll total each time a 1 is rolled on the penalty die).
 If any other number is rolled on the penalty die, the penalty is over and the roll total is final.
Level  Bonus die  Penalty die 

03  D20  D4 
48  D12  D6 
913  D10  D8 
1418  D8  D10 
1923  D6  D12 
2428  D4  D20 
Examples
 Homer is rolling 3+D20 for his level 11 stat. TN is unknown to him.
 He rolls a 20 on the die, so the original roll total is 23.
 Because he rolled 20 on D20, he gets to roll the bonus die for level 11 (D10).
 His first roll on the bonus die is a 10, so he adds 1 to the total (now it's 24), and rolls the bonus die again.
 He rolls another 10 on the bonus die, so he adds 1 to the total (now it's 25), and rolls the bonus die again.
 This time he rolls a 9 on the bonus die, so the total roll is final at 25.
 Marge is rolling 2+D4 for her level 2 stat. TN is unknown to her.
 She rolls a 1 on the die, so the original roll total is 3.
 Because she rolled a 1, she must roll the penalty die for level 2 (D4).
 Her first roll on the penalty die is a 1, so she subtracts 1 from the total (now it's 2), and rolls the penalty die again.
 She rolls another 1 on the penalty die, so she subtracts 1 from the total (now it's 1), and rolls the penalty die again.
 She rolls another 1 on the penalty die, so she subtracts 1 from the total (now it's 0).
 There is no point in rolling the penalty die any further; the total is 0.
 Bart is rolling 2+D12 for his level 6 stat. He knows the TN to be 16.
 He rolls a 12 on the die, so the original roll total is 14.
 Because he rolled 12 on D12, he gets to roll the bonus die for level 6 (D12).
 His first roll on the bonus die is a 12, so he adds 1 to the total (now it's 15), and rolls the bonus die again.
 He rolls another 12 on the bonus die, so he adds 1 to the total (now it's 16).
 There is no point in rolling the bonus die any further; the total is 16 (the TN).
 Lisa is rolling 11+D20 for her level 19 stat. She knows the TN to be 12.
 She rolls a 1 on the die, so the original roll total is 12.
 Because she rolled a 1, she must roll the penalty die for level 19 (D12).
 Her roll on the penalty die is a 1, so she subtracts 1 from the total (now it's 11).
 There's no point in rolling the penalty die any further; the total is 11 which misses the TN.
 Maggie is rolling 11+D8 for her level 13 stat. TN is unknown to her.
 She rolls a 1 on the die, so the original roll total is 12.
 Because she rolled a 1, she must roll the penalty die for level 13 (D8).
 Her roll on the penalty die is an 8, so the total roll is final at 12.
Luck
Using "Luck" is a playerinitiated attempt at bonus rolls. If a player knows or feels that his roll doesn't meet the TN, he can elect to try and spend points from his Luck Pool* to make bonus rolls that add to the roll total.
*The number of points in a character's Luck Pool is determined by his LUCK attribute. The exact formula for determining the number of Luck Pool points is still TBD.
 When a player chooses to expend Luck, he spends 1 Luck Point (LP) to roll the bonus die for the stat level.
 If he rolls an M on an Msided bonus die, 1 is added to the roll total.
 If any other number is rolled on the bonus die, nothing is added to the roll total
 The player may continue spending LPs to roll the bonus die until one of the following occurs:
 The TN is met, if it is known
 The player gives up, either feeling he has met the unknown TN, or he doesn't want to spend any more LPs
 The player uses up all of the LPs in his character's Luck Pool (for that session, see below).
 Luck can be spent in addition to rolltriggered bonuses described in the previous section, but Luck cannot be used when a penalty roll has been triggered (e.g. to attempt to offset a penalty). In other words, if you originally roll a 1, that's the best you can hope for on that roll.
 LPs are spent for each time the bonus die is rolled, whether or not it adds to the roll total.
 Shortcut: If a player knows that he wants to spend a specific minimum number of LPs, he can roll that number of Msided bonus dice at once (instead of one at a time) and simply count the number of dice that land on M.
 If, after the roll is final, it is determined to be unsuccessful, then all LPs spent on that roll are refunded to the player. Luck Points are only truly spent when they produce successful rolls!
 Characters' Luck Pools are replenished to full at the beginning of each gaming session (or as frequently as deemed fair by the GM and players alike).
Examples
 Lenny is rolling 3+D20 for his level 11 stat. TN is unknown to him.
 He rolls a 15 on the die, so the original roll total is 18.
 He decides to boost his roll by spending Luck, so he rolls the bonus die for level 11 (D10) costing him 1 LP.
 He rolls a 5 on the bonus die, adding nothing to his roll total. He decides to try again, at the cost of another 1 LP.
 This time he rolls a 10 on the bonus die, adding 1 to his roll total (now it's 19). He decides to rest on this roll total final.
 His roll is successful, so the 2 LPs are subtracted from his Luck Pool for this session.
 Carl is rolling 17+D4 on his level 17 stat. TN is unknown to him.
 He rolls a 4 on the die, so the original roll total is 21.
 After rolling his triggered bonus (see previous section), his roll total is now up to 23. He decides that he is on a roll (pun intended) and spends 3 LP to roll 3 bonus dice for level 17 (3D8).
 Only one of the D8 lands on an 8, so only 1 is added to his roll total (now it's 24). He decides to rest on this roll total final.
 Even with the bonus and luck, his roll fails, so the 3 LPs are refunded back to his Luck Pool.
Ability levels and difficulty levels
Ability  Level 

Untrained  0 
Hobbyist/Amateur  17 
Trained/Professional  814 
Experienced/Expert  1521 
Best  2228 
Difficulty  Target Numbers 

Simple/Everyday Task  14 
Unskilled Task  515 
Skilled Task  1626 
Exceptionally Skilled Task  2733 
Heroic Task  3440 
Level reference chart (Master)
Skill range  

Level  Avg roll  Most difficult task (typical)  (Without "penalty" rules) 100% Success TN 
Bonus die  Penalty die  
Untrained  
0  2.5  Simple/Everyday  1  D4 (14)  D20  D4  
Hobbyist/Amateur  
1  3.5  Simple/Everyday  $\leq$ 2  1+D4 (25) Best for TN = 3 (w/o "penalty" rules) Best for TN $\leq$ 3 (w/ "penalty" rules) 
D6 (16) Best for TN $\geq$ 5 
D20  D4  
2  4.5  Unskilled Task  $\leq$ 3  2+D4 (36) Best for TN = 4 (w/o "penalty" rules) Best for TN $\leq$ 4 (w/ "penalty" rules) 
1+D6 (27)  D8 (18) Best for TN $\geq$ 6 
D20  D4  
3  5.5  Unskilled Task  $\leq$ 4  3+D4 (47) Best for TN = 5 (w/o "penalty" rules) Best for TN $\leq$ 5 (w/ "penalty" rules) 
2+D6 (38)  1+D8 (29)  D10 (110) Best for TN $\geq$ 7 
D20  D4  
4  6.5  Unskilled Task  $\leq$ 5  4+D4 (58) Best for TN = 6 (w/o "penalty" rules) Best for TN $\leq$ 6 (w/ "penalty" rules) 
3+D6 (49)  2+D8 (310)  1+D10 (211)  D12 (112) Best for TN $\geq$ 8 
D12  D6  
5  7.5  Unskilled Task  $\leq$ 6  5+D4 (69) Best for TN = 7 (w/o "penalty" rules) Best for TN $\leq$ 7 (w/ "penalty" rules) 
4+D6 (510)  3+D8 (411)  2+D10 (312)  1+D12 (213) Best for TN $\geq$ 9 
D12  D6  
6  8.5  Unskilled Task  $\leq$ 7  6+D4 (710) Best for TN = 8 (w/o "penalty" rules) Best for TN $\leq$ 8 (w/ "penalty" rules) 
5+D6 (611)  4+D8 (512)  3+D10 (413)  2+D12 (314) Best for TN $\geq$ 10 
D12  D6  
7  9.5  Unskilled Task  $\leq$ 8  7+D4 (811) Best for TN = 9 (w/o "penalty" rules) Best for TN $\leq$ 9 (w/ "penalty" rules) 
6+D6 (712)  5+D8 (613)  4+D10 (514)  3+D12 (415) Best for TN $\geq$ 11 
D12  D6  
Trained/Professional  
8  10.5  Skilled Task  $\leq$ 9  8+D4 (912) Best for TN = 10 (w/o "penalty" rules) Best for TN $\leq$ 10 (w/ "penalty" rules) 
7+D6 (813)  6+D8 (714)  5+D10 (615)  4+D12 (516)  D20 (120) Best for TN $\geq$ 12 
D12  D6  
9  11.5  Skilled Task  $\leq$ 10  9+D4 (1013) Best for TN = 11 (w/o "penalty" rules) Best for TN $\leq$ 11 (w/ "penalty" rules) 
8+D6 (914)  7+D8 (815)  6+D10 (716)  5+D12 (617)  1+D20 (221) Best for TN $\geq$ 13 
D10  D8  
10  12.5  Skilled Task  $\leq$ 11  10+D4 (1114) Best for TN = 12 (w/o "penalty" rules) Best for TN $\leq$ 12 (w/ "penalty" rules) 
9+D6 (1015)  8+D8 (916)  7+D10 (817)  6+D12 (718)  2+D20 (322) Best for TN $\geq$ 14 
D10  D8  
11  13.5  Skilled Task  $\leq$ 12  11+D4 (1215) Best for TN = 13 (w/o "penalty" rules) Best for TN $\leq$ 13 (w/ "penalty" rules) 
10+D6 (1116)  9+D8 (1017)  8+D10 (918)  7+D12 (819)  3+D20 (423) Best for TN $\geq$ 15 
D10  D8  
12  14.5  Skilled Task  $\leq$ 13  12+D4 (1316) Best for TN = 14 (w/o "penalty" rules) Best for TN $\leq$ 14 (w/ "penalty" rules) 
11+D6 (1217)  10+D8 (1118)  9+D10 (1019)  8+D12 (920)  4+D20 (524) Best for TN $\geq$ 16 
D10  D8  
13  15.5  Skilled Task  $\leq$ 14  13+D4 (1417) Best for TN = 15 (w/o "penalty" rules) Best for TN $\leq$ 15 (w/ "penalty" rules) 
12+D6 (1318)  11+D8 (1219)  10+D10 (1120)  9+D12 (1021)  5+D20 (625) Best for TN $\geq$ 17 
D10  D8  
14  16.5  Skilled Task  $\leq$ 15  14+D4 (1518) Best for TN = 16 (w/o "penalty" rules) Best for TN $\leq$ 16 (w/ "penalty" rules) 
13+D6 (1419)  12+D8 (1320)  11+D10 (1221)  10+D12 (1122)  6+D20 (726) Best for TN $\geq$ 18 
D8  D10  
Experienced/Expert  
15  17.5  Skilled Task  $\leq$ 16  15+D4 (1619) Best for TN = 17 (w/o "penalty" rules) Best for TN $\leq$ 17 (w/ "penalty" rules) 
14+D6 (1520)  13+D8 (1421)  12+D10 (1322)  11+D12 (1223)  7+D20 (827) Best for TN $\geq$ 19 
D8  D10  
16  18.5  Exceptionally Skilled Task  $\leq$ 17  16+D4 (1720) Best for TN = 18 (w/o "penalty" rules) Best for TN $\leq$ 18 (w/ "penalty" rules) 
15+D6 (1621)  14+D8 (1522)  13+D10 (1423)  12+D12 (1324)  8+D20 (928) Best for TN $\geq$ 20 
D8  D10  
17  19.5  Exceptionally Skilled Task  $\leq$ 18  17+D4 (1821) Best for TN = 19 (w/o "penalty" rules) Best for TN $\leq$ 19 (w/ "penalty" rules) 
16+D6 (1722)  15+D8 (1623)  14+D10 (1524)  13+D12 (1425)  9+D20 (1029) Best for TN $\geq$ 21 
D8  D10  
18  20.5  Exceptionally Skilled Task  $\leq$ 19  18+D4 (1922) Best for TN = 20 (w/o "penalty" rules) Best for TN $\leq$ 20 (w/ "penalty" rules) 
17+D6 (1823)  16+D8 (1724)  15+D10 (1625)  14+D12 (1526)  10+D20 (1130) Best for TN $\geq$ 22 
D8  D10  
19  21.5  Exceptionally Skilled Task  $\leq$ 20  19+D4 (2023) Best for TN = 21 (w/o "penalty" rules) Best for TN $\leq$ 21 (w/ "penalty" rules) 
18+D6 (1924)  17+D8 (1825)  16+D10 (1726)  15+D12 (1627)  11+D20 (1231) Best for TN $\geq$ 23 
D6  D12  
20  22.5  Exceptionally Skilled Task  $\leq$ 21  20+D4 (2124) Best for TN = 22 (w/o "penalty" rules) Best for TN $\leq$ 22 (w/ "penalty" rules) 
19+D6 (2025)  18+D8 (1926)  17+D10 (1827)  16+D12 (1728)  12+D20 (1332) Best for TN $\geq$ 24 
D6  D12  
21  23.5  Exceptionally Skilled Task    20+D6 (2126) Best for TN = 23 (w/o "penalty" rules) Best for TN $\leq$ 23 (w/ "penalty" rules) 
19+D8 (2027)  18+D10 (1928)  17+D12 (1829)  13+D20 (1433) Best for TN $\geq$ 25 
D6  D12  
Best  
22  24.5  Exceptionally Skilled Task    20+D8 (2128) Best for TN = 24 (w/o "penalty" rules) Best for TN $\leq$ 24 (w/ "penalty" rules) 
19+D10 (2029)  18+D12 (1930)  14+D20 (1534) Best for TN $\geq$ 26 
D6  D12  
23  25.5  Heroic Task    20+D10 (2130) Best for TN = 55 (w/o "penalty" rules) Best for TN $\leq$ 25 (w/ "penalty" rules) 
19+D12 (2031)  15+D20 (1635) Best for TN $\geq$ 27 
D6  D12  
24  26.5  Heroic Task    20+D12 (2132) Best for TN = 26 (w/o "penalty" rules) Best for TN $\leq$ 26 (w/ "penalty" rules) 
16+D20 (1736) Best for TN $\geq$ 28 
D4  D20  
25  27.5  Heroic Task    17+D20 (1837)  D4  D20  
26  28.5  Heroic Task    18+D20 (1938)  D4  D20  
27  29.5  Heroic Task    19+D20 (2039)  D4  D20  
28  30.5  Heroic Task    20+D20 (2140)  D4  D20 