Vorobyev, Oleg Yu. (2016): The bet on a bald. Published in: Proceedings of the XV FAMEMS2016 Conference and the Workshop on Hilbert's sixth problem, Krasnoyarsk, Russia (30 September 2016): pp. 98101.

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Abstract
A fixed company of players observes a person selected from a fixed queue. After each observation, players are asked to bet the dollar secret from others, either on the fact that person is bald or on what is not. A definite formula for the gain is suggested, such that every time after bets the gain of each player from a given company is completely determined by this formula. However, before bets player’s gain is an uncertain value. Is it possible for a given company of players and a given queue of people before bets to build a correct mathematical model of an uncertain gain of each player within the framework of Kolmogorov’s probability theory? If not, what else do you need to add to the foundations of probability theory so that before bets to be able to use this model for decision making? The paper answers these questions within the framework of the new theory of experience and of chance (the certainty theory) [1] that consists of two dual halves: the believability theory and the probability theory, and that is intended for the mathematical description of experiencedrandom experiments, the uncertainty in outcomes of which is generated by the observer.