If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:2:09

Frequency stability property short film

Video transcript

[TYPING] Consider the following. Imagine two rooms. [DOOR CLOSING] [DOOR CLOSING] Inside each room is a switch. [CLICK] [CLICK] 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. [CLICK] [CLICK] [CLICK] [CLICK] Can you determine which light bulb is being switched by a coin flip? [CLICK] [CLICK] [CLICK] [CLICK] The answer is yes, but how? [CLICK] [CLICK] [CLICK] 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. [CLICK] [CRICKETS CHIRPING]