Randomness

Randomness is an aspect of die rolls. Number of dice influence this. Compare for example:
*1d6 is a 1/6 chance of maximum damage, 1/6 chance of minimum damage, total 1/3 chance of extremes
*2d6 is a 1/36 chance of maximum damage, 1/36 chance of minimum damage, total 1/18 chance of extremes
*3d6 is a 1/216 chance of one, 1/108 chance of either
The problem created here is that low-dice attacks have a higher probability of doing very little or very much. Higher-dice attacks have a higher probability of averaging out near the middle, and very rarely will do a minimal or maximal amount.
==Modifying==
There are two approaches which could bring this to a higher level.
===More average low dice===
Instate a minimum requirement of dice rolled. For dice lower than this, divide by an appropriate number.
For example: if the minimum requirement is 4 dice and you attack with 2d6, roll 4d6 and divide by 2. Fractions should be rounded normally (0.5 or more up, otherwise down)
===Less average high dice===
Instate a maximum requirement of dice rolled. For dice higher than that, multiply by an appropriate number.
For example, if the maximum requirement is 4 dice and you attack with 8d6, roll 4d6 and multiply by 2.
==Options==
===Character's gamble===
The GM could allow BOTH options, with some player input. Players could choose "more random" or "less random" attacks based on their intentions. How much they want to gamble.
In this case:
*1d6 could be exchanged for 2d6/2, 3d6/3, 4d6/4, etc.
*2d6 could be exchanged for 1d6x2, 3d6 for 1d6x3, 4d6 for 1d6x4, etc
The latter is more balanced because you are simply emulating the ultimate 1/3 chance of absolutes which 1d6 attacks inherently benefit from.
The former is less balanced at extremes because you approach a guarantee of average damage (ie "take 3") which could be perceived as unfair, since you remove the risk of low damage when targeting low-damage opponents.
A less-random attack is "measured" so a mechanic to balance this could be to require some kind of skill roll. For example, to require a cumulative -1 to hit per each multiplier/divisor level. Rounding down fractions instead of rounding normally would also be a balancing factor.
A more-random attack would be an advantage against higher DR opponents who you could only harm via maximal damage.
For example, against someone with DR 11, you need 12 damage to hurt them. Someone with 2d6 would only do this 1/36 of the time, while someone with 1d6x2 would do this 1/6 of the time. So it is an advantage to have more-random damage.
Against DR 5 though, someone using 1d6 attacks already has this benefit. DR 5 less useful against 1d6 than DR 11 is against 2d6.
Someone with an increased chance of minimum damage is losing nothing when it doesn't matter because even their average damage isn't going to do anything.
For that reason it might be good to take a similar approach, a cumulative -1 penalty per 2d6 replaced with 1d6x2. This would represent "wild" attacks being harder to aim, whereas the inverse (similar to deceptive attacks, or targeted attacks) is "measured" attacks require more skill to accomplish.
Another option, rather than penalizing the roll to hit, would be to give defense bonuses. IE a "measured" (less random, more averaged) strike would be more telegraphed, so for every 1d6 = 2d6/2 change a player options for, give +1 to defend against it.
The unfair scaling (+1 to defend is like -2 to hit) is balanced by it not being a negative at all if someone can't make an active defense. Both could be allowed as options.
Measured (less random, approaching fixed) strikes are good both for guaranteeing harm against low DR opponents as well as avoiding inflicting too much damage if you don't want to kill an opponent. These are strategic advantages.
===Character's freebie===
Instead of inherent penalties, another option could be to give these as free benefits to those who succeed on their rolls by more than 0, allowing 1 increment per Margin of Success. This is similar to the built-in MoS-based defense penalties that Trained By A Master get in the 3e GURPS Martial Arts not requireing pre-roll to-hit penalties for Deceptive Attacks
==Fractional Damage==
GURPS is designed around 3D6, so this could be an inconvenient extreme. It works better with automatic die-rollers which can easily total amounts in online gaming.
By replacing 1d6 with 10d6/10 it allows easily-tracked fractional damages kept to a single decimal place. This would also work with 2d6/2 or 4d6/4 or 5d6/5 or 8d6/8 replacements depending on degree of randomness desired inherently by the GM for universal damage, or alteration of randomness a character opts for by being more-measured or more-wild.
This would allow the option of not needing to round results and simply tracking the decimals. This would remove concern with the effects of rounding on the averages, minimums and maximums.
The GM would set a degree of randomness baseline which others should conform to. Those below that dice would be made less random, those above it would be made more random.
The way it works is you define R = randomness factor, then the damage you roll is always rolling dice equal to the randomness factor, multiplied by the normal amount of dice something should do, then divided by the randomness factor.
For example, if base randomness is 3d6 then:
*1d6 = 3d6*1/3
*2d6 = 3d6*2/3
*3d6 = 3d6*3/3
*4d6 = 3d6*4/3
That's not so great because a 3 divisor does not produce easy fractions.
Base randomness 2 works better here:
*1d6=2d6*1/2
*2d6=2d6*2/2
*3d6=2d6*3/2
Then you don't need to round, you can just log "semi-damag" points.
If the Randomness is 1 then:
*1d6 = 1d6*1/1
*2d6 = 1d6*2/1
*3d6 = 1d6*3/1
If random 5
*1d6 = 5d6*1/5
*2d6 = 5d6*2/5
*5d6 = 5d6*5/5
*10d6 = 5d6*10/5
**this will produce odd-numbered damage amounts which are not obtainable like 59 damage, which isn't really any different from how 1d6 cannot produce 3.5 or 5.5 damage, if you think about it
***though it CAN if using randomness factors and not rounding quotients
If random 10...
*1d6=10d6*1/10
*5d6=10d6*5/10 (ie 10d/2)
*10d6=10d6*10/10 (ie 10d)
*20d6=10d6*20/20 (ie 10dx2)
Non-odd damage amounts resulting from this can also result from critical hit multipliers, hit location modifiers, vulnerabilities, etc. so it's nothing unusual
People disliking this could probably instate some sort of randomized chance of adding or subtracting 1 damage from these results. For example roll d6:
*1 or 2 = subtract 1
*3 or 4 = no change
*5 or 6 = add 1
This is basically adding 1d6/2 (rounded up) minus 2 to damage. You do this to create more in-between amounts when the effect is a multiplier from lower dice to a higher dice standard.
Using the example of 20d6 bcoming 10d6*2, while this would create a new lower minimum of 19 damage and a new maximum of 121 damage, because the appropriate alteration only happens 1/3 the time and you only roll max/min on 10d6 very rarely, (1 in 6^10) the influence on the wider range is minimal.
It would be much greater if using less randomness though, such as a base 2 or base 5. You can make these modifiers less random too. For example if you added 2d6/2 (round up) before the -2.
If there is a greater desire for decimal output variety it could also be approached by 
In desiring this outcome, tiers of doubled dice rolled, doubled quotient being tied to progressive penalties work best for player-option. This means the 5/5 would not be used. The benefit here is you could equate the number which is the dice-multiplier and result-quotient as being a skill penalty or halve as a defense bonus to target.
This is probably fairer than applying an amount equal to multiples of 1d6 becoming 2d6/2 because that still gives an advantage to lower-damage attacks being easier to control than higher ones. BUT if you are using a fixed randomness factor which everyone shares, this would not be a concern so you can use replacement-based depending on how hard a GM wants it to be to alter the randomness up or down.
So take for example "measured thrust":
In exchange for -2 to skill, the
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