It seems that the universe is organized by probability.

For example, the fundamental theories of physics, which could be considered cause and effect theories, I grant you, do not have a time direction. They work just as well with time going backwards as forwards.

Cause and effect implies a time direction, right?

So how do we get a time direction. From what I read, time direction comes primarily from the second law of thermadynamics which states in effect that isolated non-equilibrium systems will always move towards more disorder. When they come to the maximum state of disorder, the state that maximizes entropy, they stabilize in equilibrium and no longer change macroscopically. This all happens on the basis of probability.

So it's fundamentally probability, or a host of random events, that creates the direction of time, and the sense of cause and effect on the macroscopic level. There is no time direction on the microscopic level.

Let's think of an automobile engine, perhaps one of the finest examples of cause and effect. Drive in the wrong direction and you will experience reality big time. Push the accelerator and you go faster. Cause and effect. But if we look at the science of that cause and effect, it is based on the chemistry of getting energy from gasoline plus the thermodynamics of thermal engines plus F=MA, one of Newton's laws. Thermodynamics, which is the science of probabilities, is the essential link between the energy from the gasoline and the force applied to your cars wheels. The thing is that there are such a large host of probabilistic events in exploding gasoline, that we known for almost certain what is going to happen. That is why thermodynamics is a science. But it's still just a matter of probability.