Taskmaster
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The taskmaster is the system by which the MUD compares skills, and determines whether or not to award a player a free advance (also known as a TM) in a level as a result of using a particular skill.
A TM shows up in different coloured text while playing (by default, yellow), and often contains the words 'You feel more able to...' or 'You learn something new about...'. They are awarded randomly based on the difficulty of the task you are attempting, and are 'free' in that they cost no experience points. You can see any TMs you have acquired during a session by using the hskills command.
Noncompetitive skill checks
There are two different types of basic skill check implemented on the Disc for noncompetitive skill checks  that is, those where you are being tested against a fixed difficulty, not someone else's bonus:
Linear skill check
A linear skill check tests your bonus in the given skill against a minimum and maximum bonus, with the following results:
 If your bonus is less than the minimum, you will always fail the test.
 If your bonus is greater than the maximum, you will always succeed.
 If your bonus is inbetween, then the chance of success is directly proportional to where your bonus is between the minimum and maximum.
An example may help illustrate this. Imagine that you are attempting to light a fire by magical means, and that this involves a linear skillcheck with the following properties:
 It tests against magic.methods.elemental.fire
 The minimum bonus is 150
 The maximum bonus is 200
If your magic.methods.elemental.fire bonus is 100, you will always fail to light the fire, as your bonus is below the minimum. If your bonus is 250, you will always succeed, as it is greater than the maximum. If your bonus is 160, then this is 20% of the way between the minimum (150) and the maximum (200), hence you will succeed 20% of the time. If your bonus is 180, then this is 60% of the way between the two, so you will succeed 60% of the time.
Decay skill check
A decay skill check requires you to have a minimum level in a given skill, and then halves your chance of failure for each multiple of a set number of bonus points (called the halflife) above the minimum. Unlike a linear skill check, there is no maximum bonus for which you will always succeed a decay skill check  increasing your skills makes failure increasingly unlikely, but never impossible.
Again, an example, may help illustrate this. Imagine that we are now attempting to extinguish the fire by magical means, and this involves a decay skillcheck with the following properties:
 It tests against magic.methods.elemental.water
 The minimum bonus is 100.
 The halflife is 50.
If your magic.methods.elemental.water bonus is 50, you will always fail to extinguish the fire, as your bonus is below the minimum. If your bonus is 150, then this is exactly one halflife above the minimum  your chance of failure is halved once, resulting in a 50% chance of success. If your bonus is 200, then this is exactly two halflives above the minimum, so your chance of failure is halved, and then halved again  resulting in a 75% chance of success.
TMing skills
The chance of TMing a skill is related to the shape of the skill checks above. The basic idea is that you are most likely to TM a successful skill check when you are only just able to succeed  that is, your chance of success is low, but nonzero. As your chance of success increases, so your chance of TMing per success decreases. Your chance to TM per attempt is dependent both on your chance to succeed the attempt, and your chance to get a TM, given that you succeed.
Linear skill checks
For a linear skill check, your chance to TM per successful skill check is:
 Zero if your bonus is less than the minimum.
 Zero if your bonus is greater than the maximum.
 Inversely proportional to your chance of success otherwise.
So, your chance to TM if you succeed is greatest just as you pass the minimum bonus, then falls off steadily to zero as you reach the maximum.
Your chance to TM per attempt is greatest halfway between the minimum and maximum bonuses, and falls off to zero as you approach either limit.
Decay skill checks
For a decay skill check, your chance to TM per successful skill check is:
 Zero if your bonus is less than the minimum.
 Inversely proportional to your chance of success otherwise.
So, your chance to TM if you succeed is greatest just as you pass the minimum bonus, then halves with each halflife worth of bonus after that.
Your chance to TM per attempt is greatest one halflife above the minimum bonus, and falls off to zero as you approach the minimum or increase your bonus above one halflife.
TM types
The total chance to TM a skill across all bonuses is scaled according to the type of action being performed, as follows:
Type of skill check  Details  Example  TM chance scaling 

Fixed  Testing against a fixed difficulty.  Climbing a tree.  100% (baseline) 
Free  Tests which cost the player nothing.  Making a snowball.  25% 
Continuous  Actions players do very frequently.  Parrying during combat.  50% 
Command  Skills used in guild commands.  Octograving.  100% 
Ritual  Performing rituals.  Performing Holy Aegis.  50% 
Spell  Used for spell stages.  Casting Hag's Blessing.  60% 
None  Used for tests against skills that the creators don't want you to TM.  Unknown  0% 
Competitive skill checks
Competitive skill checks are checks of one player or NPC's bonus against another's. For example, attempting to hit an enemy with a sword might involve a skill check of your fighting.melee.sword bonus against their fighting.defence.parrying bonus.
The chance of success in a competitive skill check is initially based on the ratio of the offensive to defensive bonuses, as follows:
 If the offensive bonus is greater than the defensive, then the %chance of success is 50 * off_bonus/def_bonus.
 Otherwise, the %chance of success is 100  50 * def_bonus/off_bonus
At this point, the basic consequences of the above are that:
 The attacker has a 0% chance of success if their bonus is half the defender's.
 The attacker has a 50% chance of success if their bonus is equal to the defender's.
 The attacker has a 100% chance of success if their bonus is twice the defender's.
 Note that this chance may be less than 0% or greater than 100% at this point, if the attacker's bonus is more than twice the defender's bonus or viceversa.
The chance may then have a modifier applied to it by various factors associated with the skillcheck. For example, there are tohit modifiers in combat that depend on varying factors ranging from the weight of the weapons to each party's tacticsattitude.
Finally, there is always a chance that either player will succeed, irrespective of their skills. Hence, the chance of success is capped at a maximum of 99% and a minimum of 1% (this also deals with 'impossible' percentages that are still less than 0% or greater than 100% at this point).
The chance of TMing from a competitive skillcheck is only applied to whoever wins the check, and is treated as equivalent to a noncompetitive skillcheck against the opponent's bonus (with appropriate TM type and modifiers as above).
Shared TMs
If you are in a group with someone and in the same room, you can sometimes share a TM with themin other words, they'll TM a skill and you'll learn something by watching them.
The chance of sharing someone else's TM is approximately:
%chance to share = 25000 / (500 + diff^{2} + sqrt(level))
Where:
 Diff is the difference between their level and your level in the appropriate skill, OR the difference between their bonus and your bonus in that skill  whichever is greater.
 Level is your level in the skill that was TMed.
Basically, you're more likely to share someone's TM if you're near the same level/bonus as the person you were watching in the TMed skill, and you're more likely to TM the lower your level in that skill.
Note that language, adventuring.perception and any points skill TMs are not shared.
Related achievments
There are several tmrelated achievements in the Lucky category:
 Scrounger and Good Friend, for shared TMs
 Very Fortunate, for tming skills over level 300
 Lucky Bugger, for tming skills over level 500
 Jammy Bugger, for tming skills over level 800
See also
External links
 Discworld concept help: Taskmaster
 The TM Project: a wiki for listing what skills can by tmed from what actions at what levels