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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 ...
(In practice, it would be more appropriate to assume a prior distribution which is much more heavily weighted in the region around 0.5, to reflect our experience with real coins.) The probability of obtaining h heads in N tosses of a coin with a probability of heads equal to r is given by the binomial distribution:
The three-way flip is 75% likely to work each time it is tried (if all coins are heads or all are tails, each of which occur 1/8 of the time due to the chances being 0.5 by 0.5 by 0.5, the flip is repeated until the results differ), and does not require that "heads" or "tails" be called.
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. Subsequently, a fair coin is tossed until either player A's or player B's sequence appears as a consecutive subsequence of the coin toss outcomes. The player ...
Some well-known fountains can collect thousands of dollars in coins each year. According to an NBC report from 2016, the Trevi Fountain accumulated about $1.5 million in coins that year. (The ...
There's no shortage of interesting, old and rare European coins capable of commanding big money at auction -- but are any actually still in circulation and not being handled by private collectors ...
Frobenius coin problem with 2-pence and 5-pence coins visualised as graphs: Sloping lines denote graphs of 2x+5y=n where n is the total in pence, and x and y are the non-negative number of 2p and 5p coins, respectively. A point on a line gives a combination of 2p and 5p for its given total (green).
The probability of 20 heads, then 1 head is 0.5 20 × 0.5 = 0.5 21 The probability of getting 20 heads then 1 tail, and the probability of getting 20 heads then another head are both 1 in 2,097,152. When flipping a fair coin 21 times, the outcome is equally likely to be 21 heads as 20 heads and then 1 tail.