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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.
The coin toss in cricket is more important than in other games because in many situations it can lead a team winning or losing the game. Factors such as pitch conditions, weather and the time of day are considered by the team captain who wins the toss. Now there are websites such as flip a coin online which domestic sports team use to toss the ...
The closing stock price for each day was determined by a coin flip. If the result was heads, the price would close a half point higher, but if the result was tails, it would close a half point lower. Thus, each time, the price had a fifty-fifty chance of closing higher or lower than the previous day. Cycles or trends were determined from the tests.
Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
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 that takes only the ...
The graph on the right shows the probability density function of r given that 7 heads were obtained in 10 tosses. (Note: r is the probability of obtaining heads when tossing the same coin once.) Plot of the probability density f(r | H = 7, T = 3) = 1320 r 7 (1 − r) 3 with r ranging from 0 to 1
Quantum walks are quantum analogs of classical random walks.In contrast to the classical random walk, where the walker occupies definite states and the randomness arises due to stochastic transitions between states, in quantum walks randomness arises through (1) quantum superposition of states, (2) non-random, reversible unitary evolution and (3) collapse of the wave function due to state ...
If a cheat has altered a coin to prefer one side over another (a biased coin), the coin can still be used for fair results by changing the game slightly. John von Neumann gave the following procedure: [4] Toss the coin twice. If the results match, start over, forgetting both results. If the results differ, use the first result, forgetting the ...