Probability theory was developed by Blasé Pascal who was a philosopher and a student of algebra in the 1600's as an offshoot of mathematics. It was a formulation that would deal with a way to chart or predict random events, and was developed by the throw of a dice. The foundation of this theory lies in the fact that, although random events are truly random, if repeated enough times, a pattern will begin to emerge. This probability theory is the genesis of modern statistical analysis.
Probability theory was worked out by casting dice. With each throw of a dice the probability of obtaining a 6 is the same: one in six. The probability of throwing a six is the same for every throw. However, if an individual rolls 5 times and never gets a six the probability increases that his next roll will be a six. That is, if you deplete the probability by repetition, you increase the odds that a desired event will take place. Nevertheless, the probability quotient of one in six remains constant.
This theory of random numbers eventually was worked upon independently in later centuries by Andrey Nikolaevich Kamogorov and Richard von Mises and resulted in the mathematical postulates of the law of Large Numbers and the Central Limit Theorem, which have been elaborated upon to form the basis of modern day statistical theory and statistical packages.
Randomness Has Structure
All of these mathematical equations seek to give order to randomness, an event that is celebrated in the modern Theory of Chaos. It suffices to say that events are independent of each other and independent events are random. However, within the randomness, enough repetition will result in a pattern that will allow the prediction and management of random events, to some extent. This is all well and good for statisticians with huge data bases but not so good for people like gamblers who want to make sense of random events, like the roll of a die or the deal of a card.
For them, the probability remains the same, the roll of each die gives a one in six probability of a particular number appearing and this is doubly unlikely with the addition of another die. That means that two dice give the probability of one in six 2 individual times. That means the odds do not get better. The same is true of cards, if you have been dealt 5 cards and have not gotten, but wish to have, an ace; the probability that your next card is an ace is one in forty seven.
If you do not get an ace on that deal, the odds become one in 46, but does that really help? The probability is the same but the odds do improve, as the desired outcome is not achieved. Gamblers are better to forget probability theory and focus on another scientific phenomenon - luck.
This also applies to statistical analysis. When a probable event does not occur; the odds that it will occur increases. Or as Mark Twain, said, "there are liar, damn liars, and statisticians".
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