A lower rate of randomness or a higher rate of predictability could hold some weight to your enjoyability of the game, but not always as much as you think. Imagine we expressed randomness according to percentage points, ranging from 0% absence of randomness to 100% randomness. Then let us assume the following cases:
- randomness increased from 0% to 5%
- randomness increased from 50% to 55%
- randomness increased from 95% to 100%
Increases in all three cases are by a margin of 5%, which makes them equal in terms of utility. In other words, they should rationally be considered changes of equal value. However if you're anything like most people, the three cases won't feel the same. The changes from 0% to 5% and from 95% to 100% will feel a lot more significant than does the 50-55% alteration. That's because you intuitively asign weights to each. Changes to the extremes hold more weight than those in the middle.
Coming back to CC, the effect of any change in the randomness of the dice will not hold as much sway as you think it will, unless you're reverting them to (almost) complete predictability or to at least a 'sense' of perfectly random dice.