I would suggest that if you toss a coin the possibility that it would be either heads or tails would be ever so slightly less than 0.5, because it could land on its edge or be snatched up by an egret or vaporized by a rogue streak of lightning, etc. (though the probablity of those other events is very low, or one might say, improbable, or even interpret as random).

Quite so. However, what is improbable does occur and is not necessarily random at all. That would be a black swan.

Skewed distributions. Many real life phenomena are not 50:50 bets like tossing a coin, but have various unusual and counter-intuitive distributions. An example of this is a 99:1 bet in which you almost always win, but when you lose, you lose all your savings. People can easily be fooled by statements like “I won this bet 50 times”.

This is when our belief in induction as infallible, fail us and the ludic fallacy.

It’s the same with the roll of a die. The possibilities we are interested in are the ones that have a probability of 1 in 6. These probabilities are our “guide to life”. What’s interesting is how it works, why are they a guide to life?

But if in a given set of circumstances the die could land on any other number than it does is of no interest to us at all, for practical purposes.

That may be so only in gaming when the probabilities are known and defined. However, they cannot be a guide to life per se because there is no universality in the roll of a die wrt life.

It’s the same with the roll of a die. The possibilities we are interested in are the ones that have a probability of 1 in 6. These probabilities are our “guide to life”. What’s interesting is how it works, why are they a guide to life?

But if in a given set of circumstances the die could land on any other number than it does is of no interest to us at all, for practical purposes.

That may be so only in gaming when the probabilities are known and defined. However, they cannot be a guide to life per se because there is no universality in the roll of a die wrt life.

No. The real probability is the one that we can say would converge if we did this enough times, that’s what we are interested in and that is 1 in 6 as long as the die is not loaded.

The question is what is it about the universe that makes it the case that it will behave like this?

The expected value may be intuitively understood by the law of large numbers: The expected value, when it exists, is almost surely the limit of the sample mean as sample size grows to infinity. More informally, it can be interpreted as the long-run average of the results of many independent repetitions of an experiment (e.g. a dice roll).

However:

The expected value does not exist for some distributions with large “tails”, such as the Cauchy distribution.

The real probability cannot be known unless you throw the dice an infinite number of times and the distribution is found to be exactly normal or Gaussian.

Robustness of a normal distribution due to outliers:

As a result, statistical inference using a normal distribution is not robust to the presence of outliers (data that is unexpectedly far from the mean, due to exceptional circumstances, observational error, etc.). When outliers are expected, data may be better described using a heavy-tailed distribution such as the Student’s t-distribution.

IC the question now but I believe that the dials are not so fine tuned as you posit. They are only fine tuned by the potentials present for individual throws., i.e force, trajectory, bounce, rotation. Thus determinism will produce a certain number dialed up by those converging potentials, true.

Ok

But in a truly random environment these potentials shift with each throw, dialing up a number which corresponds to all the factors involved for that particular throw.

The shift with each throw is just as deterministic as the throws themselves.

It is a perfect example of potential as “that which may become reality”. Six potential outcomes, from which one is choosen by the mathematical forces at that specific instant.

Only due to our lack of knowledge.

If you say the universe just is and that’s the end of it and reasons why are something peculiar to creatures like us with knowledge and who want to predict and so on, that’s fine.

But if reasons why are more fundemental as you believe, then knowledge should have nothing to do with it. Reasons why should be there even with no observers with partial knowledge.

The real probability cannot be known unless you throw the dice an infinite number of times and the distribution is found to be exactly normal or Gaussian.

How would that tell us what the real probability was? What if what happened deviated from the real probability?

Yes, but not purely from probabilities as defined in gaming. Real world situations have many unknowns which makes it impossible to compute real probabilities at all.

In reality, we all muddle through with whatever information is available.

Yes, but not purely from probabilities as defined in gaming. Real world situations have many unknowns which makes it impossible to compute real probabilities at all.

In reality, we all muddle through with whatever information is available.

I think in gaming all the unknowns are there too.

The probability we are interested in is the probability given what we know, which can in principle be calculated just like in the casino, I think?

It is a perfect example of potential as “that which may become reality”. Six potential outcomes, from which one is choosen by the mathematical forces at that specific instant.

Only due to our lack of knowledge.

I don’t understand that conclusion. Our lack of knowledge has nothing to do with it. A number will be choosen deterministically regardless of knowledge, we just can’t predict what that number will be, but we can predict with certainty that it will be one of the six available numbers. This would be true even if a bird were to swoop and catch the die in flight. Eventually the die would drop to the ground and 1 of the 6 possible numbers would result (perhaps after some cleaning).
If we could control (know) all the potentials present for a specific roll, we could predict the outcome, but then there is no longer randomness, just pre-determinism.

IMO the terms random and certainty are mutually exclusive. But the terms probability and averages are compatible, perhaps even deterministically related.

I don’t understand that conclusion. Our lack of knowledge has nothing to do with it.

Doesn’t it?

A number will be choosen deterministically regardless of knowledge, we just can’t predict what that number will be, but we can predict with certainty that it will be one of the six available numbers.

Due to lack of knowledge.

If we could control (know) all the potentials present for a specific roll, we could predict the outcome, but then there is no longer randomness, just pre-determinism.

So the difference between determinism and randomness is lack of knowledge.