I was thinking along similar lines to a comment by Morten Bek in a recent thread about the simulation argument, after I read Nick Bostrom's simulation argument from 2003. I continued developing my counterargument and made it a little more general. I don't just conclude we're not living in a simulation, I conclude the universe we live in isn't essentially digital.
1. If something can be simulated on a digital computer, then it is represented by a series of bits, which could be in the form of an array in multiple dimensions. Mathematicians call a particular kind of array a matrix. (That explains only part of the connotations of the name of the movie The Matrix.)
2. All arrays of various sizes already exist in the mathematical sense of existence. They exist in the same way as all counting numbers exist, the same way an infinite number of primes exist, and the same way an answer exists for every addition problem of counting numbers. Also, all various possibilities of digital contents of arrays already exist mathematically. For example:       ... [0000,0110,0110,0000] ...
3. If some array contains a description of part of our universe that is adequate to describe someone's conscious experience, then at least a certain number of the bits in that array are determined by that description. If a computer is producing a series of three-dimensional arrays that represents a fourth dimension, time, then if those arrays describe someone's world, what happens in someone's future is described by the rest of the series.
4. It isn't necessary for a computer actually to run for the arrays to exist. You don't have to ask a computer to calculate pi to exact precision and wait for the computer to output an infinite string of digits to know that pi is irrational and has an infinite number of digits in its digital form. You can know that pi is like that with certainty by mathematics. If you accept the same mathematical assumptions, one of the consequences is that all arrays exist.
5. So, somewhere in mathematical space is someone described digitally, whose future is every possible digital array that could follow, no matter how improbable. Some sort of laws of physics might appear to be followed in part of the arrays, but not in other parts.
6. We do not observe the world around us to contain such improbabilities. It appears to contain consistent laws of physics, not things popping into and out of existence on a massive scale and not edges of chaos that swallow up orderly existence.
7. Therefore, our conscious experience implies order that encompasses the material cosmos. That's not to say that we're conscious of how it implies order, just that it does. While all versions of us described digitally, which go through every imaginable digital future possibility and then some, exist mathematically, our conscious selves experience a reasonably orderly universe. The real universe is not digital. Q.E.D.
8. Some physicists believe in interpretations of quantum mechanics that seem to have something to do with this subject. The order we experience may be implied by our conscious existence only to a certain extent of orderliness, while leaving many variations to be determined by the irreducible randomness of standard quantum mechanics. If so, that's still more order than any sort of digital array simulation allows for. The physical things that are supposed to be random under that theory are so small that on the human scale the chance of anything highly unusual happening because of them averages out to about none.
9. The many-worlds interpretation of quantum mechanics is not compatible with this ontology. If all existent things exist on an equal footing, whether mathematical possibilities or some other sort of reality, then all branches of a many-worlds universe exist equally as much. However, in quantum physics most of the types of random events aren't binary choices and even when they are binary, don't have equal probability of going either way in real world situations, only in thought experiments of theoretically perfectly symmetrical measuring devices. How can we keep experiencing probabilities that are unequal, for example the blurring that happens at the magnification limit of a telescope in a smooth probability curve, if we live in a many-worlds universe where all possibilities are equally real?
I meant to get around to proving that nothing is random and something about our existential responsibilities, but I guess those are subjects for another night.
Looking at Morten's argument and mine side by side, I'd put the counterargument to the counterargument like this: To determine if the universe is orderly, if you're a rational skeptic and think by the anthropic principle that you may have arrived here despite the universe not being orderly, you can apply Bayes' theorem. Assign the odds of the universe actually being orderly 1 to 1 as your prior assumption. Then for every moment you continue to exist and don't change into a frog or whatever, double the first number in the odds. If you're not such a skeptic that you disbelieve there was similar existence in the past, then counting historical moments too gives you a way to instantly increase the odds to an absolutely astronomical number to 1, favoring the universe being and remaining orderly.