History of randomness  In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. At the same time, most ancient cultures used various methods of divination to attempt to circumvent randomness and fate. The Chinese were perhaps the earliest people to formalize odds and chance 3,000 years ago. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the sixteenth century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of modern calculus had a positive impact on the formal study of randomness. In the 19th century the concept of entropy was introduced in physics. The early part of the twentieth century saw a rapid growth in the formal analysis of randomness, and mathematical foundations for probability were introduced, leading to its axiomatization in 1933. At the same time, the advent of quantum mechanics changed the scientific perspective on determinacy. In the mid to late 20th-century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness. Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the twentieth century computer scientists began to realize that the "deliberate" introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases, such randomized algorithms are able to outperform the best deterministic methods. Pre-Christian people along the Mediterranean threw dice to determine fate, and this later evolved into games of chance. There is also evidence of games of chance played by ancient Egyptians, Hindus and Chinese, dating back to 2100 BC. The Chinese used dice before the Europeans, and have a long history of playing games of chance. Over 3,000 years ago, the problems concerned with the tossing of several coins were considered in the I Ching, one of the oldest Chinese mathematical texts, that probably dates to 1150 BC. The two principal elements yin and yang were combined in the I Ching in various forms to produce "Heads and Tails" permutations of the type HH, TH, HT, etc. and the Chinese seem to have been aware of Pascal's triangle long before the Europeans formalized it in the 17th century. However, Western philosophy focused on the non-mathematical aspects of chance and randomness until the 16th century. The development of the concept of chance throughout history has been very gradual.