My personal recommendation is to use a dice roller. If you have an iPhone, I recommend Dicenomicon ($5), dynamicDICE ($1) or Dice Bag (free). I have heard that Pip ($1) is also pretty good. I have found that the luck associated with physically rolling dice is dissociated from digitally rolling them.
If you find that you still think that a dice roller is giving you below average rolls, try one of these solutions:
Pre-Generated Dice Roll List
This is very similar to using the dice card decks suggested in another answer, but relies on a computer rather than a deck of cards.
- Generate a list of 1,000 random integers between 1 and 20. Do not look at the individual numbers.
- Average the numbers.
- If the average is between 10.0 and 11.0, your set is not necessarily smooth, but is going to have a fairly even distribution.
- Whenever you need to roll a die, instead use the next number on the list.
- Continue to use this list until you have used all 1,000 numbers before generating a new list.
Point Buy System
- Choose an average dice roll - 9, for example. This is the roll that you get if you do not apply any points to the roll. Important rolls are not every roll - instead, they are rolls that your DM feels are important enough for it to matter if you subtracted points from them. For everything else, you roll manually.
- Whenever you need to make an important roll, you instead get to use the "average dice roll." You can accept a lower dice roll. Based off of how low you reduce your roll, you get that many points to add to future rolls. For example, 8=>1, 7=>2, 6=>3, 5=>5, 4=>7, 3=>9, 2=>12, 1=>16
- You could instead choose to use points you have accumulated to increase your roll. For example, 10=>1, 11=>2, 12=>3, 13=>5, 14=>7, 15=>9, 16=>11, 17=>14, 18=>17, 19=>20, 20=>24
Alternatively, have this system apply to every roll, but let the DM rate the importance of given rolls, with a multiplier of anywhere from 0.5 to 3. Adding or subtracting points to such rolls costs or rewards the multiplier times the cost/reward.
Point Buy Modifier System
This system is identical to the one above, but you instead modify your actual roll. This modification may be required to be before your roll or may be after it. Alternatively: It costs half as much and rewards twice as much if the change is determined before the roll rather than after.
You are encouraged to narrate your actions in exquisite detail. Doing so (before rolling) in a way appreciated by the DM and other players grants the acting player either a +4 bonus to his/her roll (if the roll is between 8 and 13) or the ability to re-roll if the roll is below 8. Alternatively, base the bonus off of how effective your narration was.
Pure Narration System
As above, but the DM determines your success based on the quality of your narration.