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Coin flipping, coin tossing, or heads or tails is the practice of throwing a coin in the air and checking which side is showing when it lands, in order to randomly choose between two alternatives. It is a form of sortition which inherently has two possible outcomes. The party who calls the side that is facing up when the coin lands wins.
Penney's game. Penney's game, named after its inventor Walter Penney, is a binary (head/tail) sequence generating game between two players. Player A selects a sequence of heads and tails (of length 3 or larger), and shows this sequence to player B. Player B then selects another sequence of heads and tails of the same length.
Two-up is a traditional Australian gambling game, involving a designated "spinner" throwing two coins, usually Australian pennies, into the air. Players bet on whether the coins will both fall with heads (obverse) up, both with tails (reverse) up, or with a head and one a tail (known as "Ewan").
Sleeping Beauty problem. The Sleeping Beauty problem, also known as the Sleeping Beauty paradox, [1] is a puzzle in decision theory in which an ideally rational epistemic agent is told she will be awoken from sleep either once or twice according to the toss of a coin. Each time she will have no memory of whether she has been awoken before, and ...
St. Petersburg paradox. The St. Petersburg paradox or St. Petersburg lottery[1] is a paradox involving the game of flipping a coin where the expected payoff of the lottery game is infinite but nevertheless seems to be worth only a very small amount to the participants. The St. Petersburg paradox is a situation where a naïve decision criterion ...
Until the advent of computer simulations, Kerrich's study, published in 1946, was widely cited as evidence of the asymptotic nature of probability. It is still regarded as a classic study in empirical mathematics. 2,000 of their fair coin flip results are given by the following table, with 1 representing heads and 0 representing tails.
Tails. −1, +1. +1, −1. Matching pennies. Matching pennies is a non-cooperative game studied in game theory. It is played between two players, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), then ...
After each flip of the coin the loser transfers one penny to the winner. The game ends when one player has all the pennies. If there are no other limitations on the number of flips, the probability that the game will eventually end this way is 1. (One way to see this is as follows. Any given finite string of heads and tails will eventually be ...