I describe the relationship between order and chaos as a tension, like a game of tug-of-war. Regarding the dice-rolling analogy, the "pull" that causes the dice to want to produce random results is the pull of chaos, and the "pull" that causes the dice to want to produce an ordered sequence is the pull of order. — mysterio448
The idea that existence is a unity of opposites, the pairing of chaos and order, or flux and logos, goes back to the first metaphysical speculation of Ancient Greece. Check our Anaximander and Heraclitus especially.
But I think where you run into problems is imagining the situation as two kinds of "pulls" as that puts you back into a reductionist metaphysics of causal forces. You have a literal antagonism of one thing against another thing rather than a complementary pair of things, each of which is essential to the other in a way that justifies talk of a resulting unity or synergy.
So the complementary way of talking about this is constraints vs degrees of freedom. Order is the structure that emerges in development to regulate chaos or randomness, giving it concrete shape. You start with complete spontaneity - Anaximander's unbounded Apeiron. Then it begins to divide and get organised in intelligible fashions.
Anaximander's version said first the hot separated from the cold, then the resulting dry separated from the moist. You wind up with the four elements - dry heat being fire, dry cold being air, wet heat being water, wet cold being earth.
Anyway, this dialectical approach to metaphysics is literally how metaphysics got started. And it is now a well modelled concept in physics - especially in condensed matter physics, non-equilibrium thermodynamics, and other "order out of chaos" approaches.
And does your dice story fly when there is no reason to expect a "pull" in terms of order at all. The point of a die is to design out the possibility of a correlation between outcomes. The goal is to make a "machine" that maximises our uncertainty by creating a symmetry among the alternatives.
So nature is being constrained in a special way - one that conforms to a reductionist definiton of randomness as a defined or bounded ensemble of possibilities.
It is actually a cartoon version of spontaneity or actual "pure chaos" when you think about it.
This can be demonstrated by many examples. For example, take snowflakes. Snowflakes are beautiful, ornate, symmetrical designs that materialize out of random activity in clouds. Another example is gemstones, which are orderly-shaped minerals that materialize from random geological processes. The sphericity of stars, planets and moons is a product of the force of order emerging from the chaos of mindless astronomical activity. — mysterio448
Yep, these are all examples of the new physics. But the metaphysics is understood as that of collective and emergent constraints on local degrees of freedom. Spontaneous symmetry breaking.
The theory exists.
There are more sequences like this in the decimal of pi. One might think that such sequences are merely "accidents," statistically inevitable instances of randomness stumbling upon structure. — mysterio448
Or rather this shows that even "chaos" is bounded. The kind of chaos we can model statistically is not "pure chaos" as the very idea of statistics imposes constraints on uncertainty. If nothing else, we have to draw a boundary around a collection of events and say that is the system we are now measuring. So the structure arises from at least some kind of minimal constraints being imposed in a way that results in something to be measured.
If 9 becomes a number that can be rolled, then strings of 9s must occur periodically in a fashion that is itself certain as a "sufficiently random excursion from the mean". You would start to suspect your random number generator if it failed to produce enough such sequences according to a formula you could calculate.
Murphy's law is essentially the opposite of the randomness paradox. — mysterio448
Again, this isn't a surprise but a prediction if you adopt a metaphysics based on constraints of freedoms. If nature is inherently spontaneous, then that spontaneity only ever gets limited, never eliminated.
So that is the power of a complementary approach. One thing already accounts for the other. Order includes these mistakes. Limits only limit them to being on the whole insignificant as perturbations. Disorder is suppressed to the degree that it can cause much actual disruption.