> Can you also give an example where "true randomness" would differ from the randomness I describe on the actions a human would take? That is to say, if a my internal model of the world tells me a coin landing on heads is 50/50 how does "true randomness" or not of the resulting coin toss impact how I should gamble on coin tosses?

It's pretty simple. If the world is fundamentally deterministic, then you should only gamble with someone who you believe doesn't possess knowledge you don't. If an advanced alien or an angel offers to call a coin toss, you shouldn't take their bet, since they might know how to determine the result of the coin toss based on the weather and the color of the coin tosser's pants.

On the other hand, if the universe is fundamentally random at every turn, then you can safely take the bet: nothing they know could give them more information than you have about the result of the coin toss.

This is very similar to the difference between pseudo-random number generators (PRNGs) and sources of true randomness in a computer. There is no test you could do on the outputs of an RNG to determine if it is a (good, cryptographic-grade) PRNG or if it is a "true" RNG. However, if you're gambling based on the results of a PRNG, you should try to find out if the one you're gambling against doesn't happen to know the seed (in which case they can predict with 100% certainty what the next number will be).

> Can you clarify what "true randomness" means out side of the context of human agency and perception?

Depending on your Interpretation of QM, randomness is a fundamental aspect of reality. How does a quantum superposition of two states resolve? The canonical view is wavefunction collapse, which is ultimately random, and attempts to find some pattern underneath it all generally fail. Look at the Bell Inequalities, which demonstrate that any theory which attempts to reproduce the successful predictions has to either be non-local, or non-realistic, and must be incompatible with local hidden variables.

Now does that mean nature is random? I don't know, no one does, because we're sure that QM isn't a complete theory. It is a really good theory though, in some domains such as QED it's been tested to more than 11 decimal places and found to hold. The difficulty of making a new theory that matches that precision and represents a paradigm shift can't be overstated. The result is that a lot of time is spent on those aforementioned Interpretations, you've probably heard of some, such as "The Many Worlds Interpretation" aka parallel universes. After all if everything happens, and we just happen to only perceive a part of it, then there is no randomness... no hidden variable. When a quantum state collapses, part of it doesn't just vanish, it's just out of our site.

The problem with that is... there's no evidence to support it, probably no way to even test it. Anyway, the bottom line is that maybe there is real randomness, and maybe there isn't, we just don't know.

You can not predict the future state from the current state, not even in principle.

Measure the spin of an electron along two different axis, to the best of our knowledge - or maybe just my - the result of the second measurement is not predictable by anything. Of course only until it turns out that hidden variables is the correct interpretation and that the hidden variables can be measured, then this also becomes the other kind of randomness.

Do you count wave particle duality as randomness?

Certainly the dual slit experiment makes hidden variables very hard to preserve.

Additionally several tests have shown that hidden variables don't work to explain quantum mechanics, there aren't possible coins the allow the kind of probabilities we see.

In basic interpretations of quantum events, quantum properties are not defined until measured. It's not just that we can't see the other side of the card; the card is blank until we flip it.