Chance

The word "chance" covers two meanings worth keeping apart. In its mathematical sense, a chance is a probability: the measure, between 0 and 1, of seeing a favourable result occur. In everyday language, the same word rather denotes a sense of favourable fortune, the "luck" that may or may not smile on a person.

The most solid intuition is that of frequency. Saying you have "one chance in two" of getting heads means that, over a very large number of tosses, the share of heads tends toward half. Chance is therefore not a quality attached to a player, but a property of the drawing device.

This sense translates directly into numbers. "One chance in two" corresponds to the probability 1/2, that is 0.5; "one chance in six" of drawing a given face of a die corresponds to 1/6, about 0.17. The larger the denominator, the rarer the result. This translation makes it possible to compare situations that, expressed in words, would seem vague.

The trap lies in the slide between the two meanings. Many imagine that chance "builds up" or "catches up": after several failures, success would be "due". This is inaccurate. For independent draws, the probability stays the same on every turn, because the device has no memory of what came before. The chance of one toss never depends on past tosses.

On this site, reasoning in terms of probabilities rather than "luck" helps you use the drawing tools clear-headedly. Understanding chance as a measurable quantity, and not as a force that rewards patience, is at the heart of an educational and responsible approach to chance.