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  2. St. Petersburg paradox - Wikipedia

    en.wikipedia.org/wiki/St._Petersburg_paradox

    However, the overweighting of small probability events introduced in cumulative prospect theory may restore the St. Petersburg paradox. Cumulative prospect theory avoids the St. Petersburg paradox only when the power coefficient of the utility function is lower than the power coefficient of the probability weighting function. [13]

  3. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...

  4. Pachinko - Wikipedia

    en.wikipedia.org/wiki/Pachinko

    The probability of a kakuhen occurring is determined by a random number generator. Hence, under this system, it is possible for a player to get a string of consecutive jackpots after the first "hard-earned" one, commonly referred to as "fever mode". Another type of kakuhen system is a special time or ST kakuhen.

  5. Random permutation statistics - Wikipedia

    en.wikipedia.org/wiki/Random_permutation_statistics

    This average parameter represents the probability that if we again select a random element of [] of a random permutation, the element lies on a cycle of size m. The function b ( k ) {\displaystyle b(k)} is equal to m {\displaystyle m} for m = k {\displaystyle m=k} and zero otherwise, because only cycles of length m contribute, namely m elements ...

  6. Coin flipping - Wikipedia

    en.wikipedia.org/wiki/Coin_flipping

    A Roman coin with the head of Pompey the Great on the obverse and a ship on the reverse. Coin flipping was known to the Romans as navia aut caput ("ship or head"), as some coins had a ship on one side and the head of the emperor on the other. [1]

  7. Slot machine - Wikipedia

    en.wikipedia.org/wiki/Slot_machine

    The table of probabilities for a specific machine is called the Probability and Accounting Report or PAR sheet, also PARS commonly understood as Paytable and Reel Strips. Mathematician Michael Shackleford revealed the PARS for one commercial slot machine, an original International Gaming Technology Red White and Blue machine. This game, in its ...

  8. Game of chance - Wikipedia

    en.wikipedia.org/wiki/Game_of_chance

    Roulette is a game of pure chance; no strategy can give players advantages, the outcome is determined purely by which numbered pocket a ball randomly falls into.. A game of chance is in contrast with a game of skill.

  9. Ellsberg paradox - Wikipedia

    en.wikipedia.org/wiki/Ellsberg_paradox

    When faced with the choice between a red ball and a black ball, the probability of ⁠ 30 / 90 ⁠ is compared to the lower part of the ⁠ 0 / 90 ⁠ – ⁠ 60 / 90 ⁠ range (the probability of getting a black ball). The average person expects there to be fewer black balls than yellow balls because, in most real-world situations, it would be ...