What is the probability of getting identical decks of cards after shuffling? Detailed answer

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What is the probability of getting identical decks of cards after shuffling? Detailed answer

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What is the probability of getting identical decks of cards after shuffling?

Every time you shuffle a deck, you create a sequence of cards that, with a very high degree of probability, never existed in the universe. The number of combinations in a standard playing deck is 52!, or 8x10⁶⁷. To achieve at least a 50% chance of getting a combination a second time, you need to make 9x10³³ mixing. And if you hypothetically force the entire population of the planet over the past 500 years to continuously interfere with cards and receive a new deck every second, you will end up with no more than 10²⁰ different sequences.

Authors: Jimmy Wales, Larry Sanger

Random interesting fact from the Great Encyclopedia:

How accurate is an atomic clock?

An atomic (quantum) clock is a time measuring device containing a crystal oscillator controlled by a quantum frequency standard.

The role of the "pendulum" in the atomic clock is played by atoms. The frequency of radiation of atoms during their transition from one energy level to another regulates the course of atomic clocks. This frequency is so stable that atomic clocks can measure time more accurately than astronomical methods.

In 2005, an atomic clock was made in Japan, which, if it had been switched on at the moment of the birth of the Universe, by now would not have “gone” even for one second.

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Random news from the Archive

Packaging affects the properties of water 28.09.2013

Scientists at the Georgia Institute of Technology have found that the properties of the pipeline material affect the viscosity of water. True, this is noticeable only at the nanolevel.

The phenomenon does not affect the speed at which water pours out of the bottle, but at the nanoscale, under specific conditions, differences in the behavior of water are clearly visible. A new study shows that in nanoscopic glass channels, the viscosity of water can be twice as high as in plastic channels. Simply put, in nanoscale glass channels, water behaves like a ketchup-thick liquid.

At first glance, this discovery is of little use, but in fact it is very important, especially in light of the spread of nanotechnologies, such as microfluidic chips, designed to instantly diagnose infectious diseases. In addition, this information is important for developers of micromechanical systems, ultra-precise 3D printers and other devices where liquids have to be forced through tiny holes.

Changing the viscosity of water is another example of amazing phenomena at the nanoscale. It has long been known that the so-called hydrophilic materials attract water molecules and impede their movement, while hydrophobic materials, on the contrary, make it easier. But at the macro level, this is not so noticeable, but at the nano level, when water moves in a layer of only a few molecules, the viscosity increases sharply due to the fact that water molecules “stick” to the hydrophilic surface and move in a closer group.

The researchers studied the behavior of water at the nanoscale on various types of surfaces: mica, graphene oxide, silicon, diamond-like carbon and graphite. Mica, used in the drilling industry, and at the nanoscale, turned out to be the most hydrophilic material, while graphite was the most hydrophobic.

Scientists believe that a sharp increase in viscosity on hydrophilic surfaces will be observed for other liquids, not just water. Thus, developers of miniature machines, metamaterials, nanostructured materials, etc. this factor should be taken into account.

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