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- Gerolamo Cardano (1501–1576) – known as the first key figure in the development of probability theory around the mid-1500s. His book ‘Games of Chance’ contained the first use of probability along with a few effective cheating techniques.
- Christiaan Huygens (1629–1695) – introduced the concept of expected value, which helped in identifying the probability of likely based on average outcomes from several experiments.
- Abraham de Moivre (1667–1754) – mid-1700s mathematician and analytic probabilist who put forward the central limit theorem, which serves as a cornerstone to statistics. He solved one of the most famous problems – the one where two players start with a fixed number of counters, and the essence of the problem is counting.
- Jacob Bernoulli (1655–1705) – proposing the first version of the law of large numbers.
- Daniel Bernoulli (1700–1782) – known for resolving the St. Petersburg Paradox, a famous paradox in decision theory. It expresses the probability that you can calculate the expected payout at each round.
- Pierre-Simon Laplace (1749–1827) – worked on the blend of gambling and probability theory. He wrote the Analytic Theory of Probability, where he introduced advanced versions of many previous problems.