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The basic idea in this thesis is to define, adjust and apply Edgeworth Expansion and Saddle Point approximation for use in the chance game industry. With the help of these examples, the industry will find methods on how to diminish the time needed to release a trustworthy game. With all the simulations carried out using MatLab, this book is directly oriented towards practical application of probability theory, more precisely central limit theorems and series expansion. It is useful for graduate students in mathematics and statistics and for the chance game industry.