Very interesting! I would like to add a few paragraphs in relation to this:

**Probability**

The problem of probable inference that is, of reaching a decision in the face of incomplete knowledge is a broad one that cuts across many disciplines. However, the formal treatment of probability by the mathematicians has seduced many people into believing they know more than they really do. There are two totally distinct fields of probability, namely class and case probability. The former is applicable to the natural sciences and is governed by causality (i.e. mechanical laws of cause and effect), while the latter is applicable to the social sciences and is governed by teleology (i.e. subjective means/ends frameworks).

**Class Probability**

In class probability we know everything about the entire class of events or phenomena, but we know nothing particular about the individuals making up the class. For example, if we roll a fair die we know the entire class of possible outcomes, but we dont know anything about the particular outcome of the next roll save that it will be an element of the entire class. The formal symbols and operations of the calculus of probability allow the manipulation of this knowledge, but they do not enhance it. The difference between a gambler and an insurer is not that one uses mathematical techniques. Rather, an insurer must pool the risks by incorporating the entire class (or a reasonable approximation to it). If a life insurance company only sells policies to a handful of people, it is gambling, no matter how sophisticated its actuarial methods.

**Case Probability**

Case probability is applicable when we know some of the factors that will affect a particular event, but we are ignorant of other factors that will also influence the outcome. In case probability, the event in question is not an element of a larger class, of which we have very concrete knowledge. For example, when it comes to the outcome of a particular sporting event or political campaign, past outcomes are informative but do not as such make the situation one of class probability these types of events form their own "classes." Other people's actions are examples of case probability. Therefore, even if natural events could be predicted with certainty, it would still be necessary for every actor to be a speculator.

**Numerical Evaluation of Case Probability**

It is purely metaphorical when people use the language of the calculus of probability in reference to events that fall under case probability. For example, someone can say "I believe there is a 70% probability that Hillary Clinton will be the next president." Yet upon reflection, this statement is simply meaningless. The election in question is a unique event, not a member of a larger class where such frequencies could be established.

**Betting, Gambling, and Playing Games**

When a man risks money on an outcome where he knows some of the factors involved, he is betting. When he risks money on an outcome where he knows only the frequencies of the various elements of the class, he is gambling. (The two activities roughly match up with the case/class probability distinction.) To play a game is a special type of action, though the reverse is not true; not all actions can be usefully described as part of a game. In particular, the attempt to model the market economy with "game theory" is very misleading, because in (most) games the participants try to beat their opponents, while in a market all participants benefit.

J. A. Rial, Geology, University of North Carolina at Chapel Hill

While describing interesting aspects of the mathematics of probability, the author takes frequent detours into the history of humanity's understanding (and misunderstanding) of the laws of chance, touching on subjects as diverse as chance in decision-making and the fairness of those decisions, gambling and our intuitive understanding of chance, the likelihood of the extremely rare, the existence of true randomness and how computers have helped shape modern thinking about probabilities. Imagine you are in a dark room and need to get a pair of matching socks out of a drawer. There are two blue socks and one red sock. If you take two socks, one after the other, what are the odds of getting two matching (blue) socks compared with getting a mismatch? The answer is that the chance of getting mismatching socks is double that of getting the matching socks. Isn't this obvious? What are the odds of a meteorite strike being the cause of the crash of TWA Flight 800 in July 1996? Does 1 in 10 sound right? Or is it more like 1 in 1 million? Is it really a 1 in 17 trillion coincidence that the same person wins the New Jersey lottery twice within 4 months?

The coin-toss problem or the roulette red-black dilemma are the mathematician's favorite examples of how deeply ingrained in our psyche is the idea that previous outcomes somehow influence future ones in a game of chance, or in life. Everyone knows that the chances of heads or tails are equally likely in a coin flip. However, not everyone takes this idea seriously enough. Say for instance that, flipping a coin many times, you have overcome great odds and have flipped 100 consecutive heads. What are the chances of the next flip being tails? More than 50-50, or just 50-50? Most people would expect the next flip to be tails more likely than heads and would even bet the farm that black will follow 100 consecutive reds. Yet they are wrong; the odds are still the same as they always are in these yes-or-no situations: 50-50 provided, of course, the coin and the roulette are fair.

Chance or Necessity? The question is very, very old (determinism versus chaos), and the answer is not clear even today. Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Einstein grappled with this conundrum until his death and never ceased to combat the idea that God could conceivably throw dice. How do you generate randomness in a computer? What does it mean to have a program to generate random numbers? Aren't computer programs deterministic things, created by people following rules and thus following patterns? And isn't randomness the negation of pattern? They say, the generation of random numbers is too important to be left to chance... Finally, let's remind ourselves of the impossibility of a gambling system by means of which a gambler can change his long-run frequency of success. The house always wins, or casinos would cease to exist! And yet, although we can understand these things in principle, we keep going to the gambling house in the hope that somehow these rules do not apply to us!

Whether well-educated in mathematics or not, people have always been fascinated by randomness and intrigued by the fundamental question of the real nature of randomness, of how can you tell randomness from something that is not. The theory of deterministic chaos tells us that a simple, deterministic rule can produce a behavior that is, for all practical purposes, indistinguishable from random. For instance, the logistic map Xn+1=4Xn (1-Xn) produces a sequence of random numbers as the equation is iterated and n increases (start for instance with X0=0.3, then calculate X1, X2, X3 and so on). If such a simple rule generates a list of numbers that apparently follow no rule, could it be that what we call random is in fact produced by (hidden) deterministic rules that happen to exhibit stochastic (chaotic) behavior? If so, does this mean that we will eventually find the pattern behind all randomness, as Einstein wanted to believe we would?