Here's an interesting factoid—my friends and I were part of the alpha playtest (known as the friends and family playtest) of the 5th edition of Dungeons & Dragons. At one point, a heated conversation began to develop over the control of dice—who rolls what and why.  Some people insist that random elements in gaming are vital to its enjoyment factor.  Not only that, but who controls that element of chance is also important. 


Role-playing games at their core involve the interrelationship between static values and dice rolling, with some games promoting more rolling than others.  West End's D6 system had virtually no static values—the attributes were listed as dice rolls, so Strength could be expressed as 3d6+2.  Each time you needed to roll for a Strength check, you would roll those dice and compare the result with the target value.  Amber involved no dice rolling whatsoever.  D&D embraced a common middle-ground of fixed values and dice rolling, who you were was static, but what you did was not. 


Rolling dice is vital to ensuring chance in gaming, of having the possibility of failure, even though players will do everything in their power (even to the extent of embracing superstition) to increase their probability of winning.  I have seen players throw dice across a room in frustration after a string of bad results.  Some have lucky dice they keep in separate containers.  There was even a study that showed that players tend to roll a dice gently when the result is required to be low and vigorously when the result is required to be high.  I had one friend that joked that to acquire high values, it necessitated him "rolling like a waterfall," resulting in ridicule from the group when another player didn't follow these instructions.

How someone rolls is not what concerns me of late; it's about who rolls and how often we do so.  This is somewhat connected to the psychological quirks listed above because despite dice being unemotional, non-magical, inanimate aspects of chance, players still insist in being control of them.  Who rolls shouldn't matter unless you introduce the possibility of cheating, yet show me a player that would prefer someone else to make his attack roll.  Rolling dice makes the player believe he or she is actually contributing to combat beyond presence of character.  In role-playing games, the GM is handling combat; dice rolling is one of the only ways players can control their own fate…even when they aren't. 

Tabletop games are known for their prevalence of dice rolling, more often because of their dependency on the limited variability of the D6.  Warhammer is one such game, where hundreds of dice are rolled in the span of a one-hour game.  Sure, Toughness and Power values are fixed, but attack rolls are still made for each unit and said unit can often be required to make an armor save.  I remember rolling 60 D6s when a squad of hormagaunts assaulted a line of tau warriors.  The gaunts scored a hit on a 5+, wounding on a 4+.  So, of the 60 dice, 25 of them would come up with a hit.  Those were re-rolled, with 13 coming up with a wound.  The dozen warriors then rolled their 5+ save, and five survived. That's a lot of dice rolling for what amounts to two minutes of combat.  Thankfully the system is built so that determining hits and wounds are easy.  Factor hit points and alternate defense values, and suddenly it takes a lot longer.  The time to finish a battle in an RPG or board game is expected to be minutes, not hours, so games have made attempts to shorten this. 

One way is to simplify how damage is inflicted (singular hit points rather than hit location charts).  The other is to reduce the number of dice being rolled.  Many employ the aged and stalwart Armor Class—a fixed value enemies are required to hit to inflict damage.  Although some players still prefer the variable defense system where attacker and defender both roll.  Fixed damage values are less common, especially with games with large hit point values. 

Players may want control over their own defenses, but in truth, all they are doing is gaining a false sense of control by rolling dice.  I, for one, prefer avoiding unnecessary dice rolling, especially in a combat-heavy game.  The last point about reducing die rolls is that it increases the value of character skills as a balance.  In Mekton, your skills had a value between 1 and 10, but your attack dice was D10.  Your enemy mirrored that range, so on a scale between 2 and 40, half of that could be decided by skill.  If you employ larger dice, like D20s, then you would be required to increase the character bonuses to match; otherwise, you reduce the character's contribution.  Then it becomes a crap game more about who rolls the higher value rather than who has the better character, and individual character bonuses become insignificant (or at least devalued).  What good is your character if he is statistically only slightly better than a commoner?  Unless you are running a game about commoners.  In which case, go right ahead.