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Frequency Stability with English subtitles  


Consider the following.

Imagine two rooms.



Inside each room is a switch.



In one room, there is a man who flips his switch according

to a coin flip.

If he lands heads, the switch is on.

If he lands tails, the switch is off.

In the other room, a woman switches her light

based on a blind guess.

She tries to simulate randomness without a coin.

Then we start a clock, and they make their switches in unison.





Can you determine which light bulb

is being switched by a coin flip?





The answer is yes, but how?




And the trick is to think about properties of each sequence

rather than looking for any specific patterns.

For example, first, we may try to count

the number of 1's and 0's which occur in each sequence.

This is close, but not enough since they

will both seem fairly even.

The answer is to count sequences of numbers, such as runs

of three consecutive switches.

A true random sequence will be equally

likely to contain every sequence of any length.

This is called the frequency stability property

and is demonstrated by this uniform graph.

The forgery is now obvious.

Humans favor certain sequences when they make guesses,

resulting in uneven patterns such as we see here.

One reason this happens is because we

make the mistake of thinking certain outcomes

are less random than others.

But realize, there is no such thing as a lucky number.

There is no such thing as a lucky sequence.

If we flip a coin 10 times, it is

equally likely to come up all heads, all tails,

or any other sequence you can think of.



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