It seems like in everyday probability (not quantum physics), probabilities are really just a substitute for an unknown. Take a coin flip for example. We say it's "random," a 50% change of head and a 50% chance of tails. However, if I knew exactly the density, size, and shape of the coin; the air density; with how much force the coin flipped; where exactly that force was placed; the distance of the coin to the floor; etc., wouldn't I be able to predict, using basic physics, with 100% accuracy whether it would land on heads or tails? If so, isn't probability in this scenario just a way for me handle incomplete information?
Isn't it the same thing if I shuffle a deck of cards (which is what got me thinking about it)? I treat the order of cards as random because I don't know what the order is, but it's not as if there really is a 1/52 chance that the first card I draw is the Ace of Spades–it either 100% is the ace of spades or 100% isn't.
If rolling a die and shuffling a deck isn't really random, wouldn't it follow that computerized random number generators aren't random either, since if I know the algorithm (and probably a few other variables) I'd know what the number is going to be?
Thanks in advance to anyone who takes the time to answer, especially a noob question from a non-math person like myself. I didn't want to go on reddit because a lot of those people pretend to be knowledgeable but aren't. Some additional meta-remarks:
First, I know there is a similar question already been answered Random vs Unknown. So please, don't refer me to that. I think the question I'm about to ask is much more narrow and grounded in much simpler math.
Second, I'm not a math person, so please stick to simple examples and non-technical language (unless absolutely necessary, in which case pretend like you're explaining yourself to a moderately intelligent senior in college majoring in art history).
Third, I have a good understanding of ELEMENTARY probability. This is mostly because I play a lot of poker, but I understand how odds in other gambling games work like roulette, dice, lotteries, etc. Again, this is very BASIC stuff so please no quantum physics if it can be avoided.
Fourth, not to sound callous, but I want people to discuss the answer to my question and not show me how much more they know then me. I say this because I've seen people try "beat" someone in an argument by purposefully using needlessly hyper-technical language and confusing the other person with their vocabulary rather than debating the actual question. For example, instead of saying "it would behoove you to ingest some acetylsalicylic acid" say "you should take some aspirin."
Best Answer
You are perfectly right, probability is the measure of uncertainty. Coin flip is a nice example, as discussed in another thread. Tossing a coin is a physical, deterministic process. In fact there are people who have learned to flip the coin in such way to get the outcome they want and are machines that produce deterministic, predictable coin flips. Let me, once again, quote E. Borel (after Bruno de Finetti, Probabilism: A Critical Essay on the Theory of Probability and on the Value of Science):
To make things even more complicated, there are Bayesians who interpret probability as degree of belief. In fact, there are many different interpretations of probability. When something is impossible, or very, very unlikely we assign zero probability to it (check here, here and here), when it is certain, the probability is equal to unity. When talking only about impossible and unlikely events, probability reduces to logic. When considering uncertain events, it may be seen as an extension of logic.
But probability is not a substitute for "unknown", it is a measure of how much "likely" the unknown is. It may be interpreted in different ways, and so measure slightly different things, but in the end it lets us to quantify the unknown. Probability lets us say much more about the reality, then that something is "unknown", or "uncertain". But it is not only about measuring, probability lets us to make predictions, precisely estimate the expectations and risks, or apply Bayes theorem to combine probabilities, to give only few examples. In fact, as shown by Daniel Kahneman and Amos Tversky, people are poor in reasoning about uncertainties and risks, while using formal, probabilistic reasoning guards us from our biases.