"The great superstition of modern times is focused on the role given to chance in human affairs. Chance is the new reigning deity of the modern mind. Chance inhabits the castle of the gods. Chance is given credit for the creation of the universe and the emergence of the human race from the slime.
"Chance is a shibboleth. It is a magic word we use to explain the unknown. It is the favorite power of causality for those who will attribute power to anything or anyone but God. This superstitious attitude toward chance is not new. We read of its attraction very early in biblical history:
Take the ark of the Lord and put it on the cart, and in a chest beside it put the gold objects you are sending back to him as a guilt offering. Send it on its way, but keep watching it. If it goes up to its own territory, toward Beth Shemesh, then the LORD has brought this great disaster on us. But if it does not, then we will know that it was not his hand that struck us and that it happened to us by chance. (1 Samuel 6:8-9)
"Chance can do nothing because it is nothing...We use the word 'chance' to describe mathematical possibilities. For example, when we flip a coin we say that it has a fifty/fifty chance to come up heads. If we call heads on the toss and it turns up tails, we might say that our luck was bad and that we missed our chance.
"How much influence does chance have on the toss of a coin? What makes the coin turn up heads or tails? Would the odds change if we knew which side the coin started on, how much pressure was exerted by the thumb, how dense the atmosphere was, and how many revolutions the coin made in the air? With this knowledge, our ability to predict the outcome would far exceed fifty/fifty.
"But the hand is faster than the eye. We can't measure all these factors in the normal tossing of the coin. Since we can reduce the possible outcome to two, we simplify matters by talking about chance. The point to remember, however, is that chance exercises absolutely no influence on the coin toss. Why not? As we keep saying, chance can do nothing because it IS nothing. It is NO THING. Before something can exert power or influence it must first be something. It must be some kind of entity, either physical or nonphysical. Chance is neither. It is merely a mental construct. It has no power because it has no being. It is nothing.
"To say that something has happened by chance is to say that it is a coincidence. This is simply a confession that we cannot perceive all the forces and causal powers that are at work in an event. Just as we cannot see all that is happening in a coin toss with the naked eye, so the complex affairs of life are also beyond our exact ability to penetrate. So we invent the term 'chance' to explain them. Chance really explains nothing. It is merely a word we use as a shorthand for our ignorance."
- Chosen By God, R.C. Sproul, pp. 191-194
As such, Chance is no better a mental construct / superstition than the idea of God is. At the end of the day, both religious and non-religious folk are just admitting, "We don't know", although one group is attributing causal power to a sentient Being (an extension of our self-image and perceived ability to cause things), and the other group is attributing causal power to something that doesn't have causal power in and of itself, but tends to be what it is because of the Law of Large Numbers, which can be observed by causing the same thing to happen lots of times and seeing that it most often tends towards producing a particular outcome. Like the idea of God, Chance is a self-supporting mental construct, no more rational than the "God delusion".